DESIGN OF HEAT SINK FOR THE COOLING OF A CENTRAL PROCESSING UNIT SUBMITTED BY SERRANO

DESIGN OF HEAT SINK FOR THE COOLING OF A CENTRAL PROCESSING UNIT

SUBMITTED BY
SERRANO, JOSHUA CORNELLUS M.

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SUBMITTED ON:
JULY 19, 2018
Executive Summary
During this modern age where technology reigns supreme where day by day we gain advancements on our technology, among those technology there we have the central processing unit or what you could call what gives the computer its commands and interpret its data. This central processing unit has a tendency to overheat when the processes of a central processing unit stops the movement of an electronic signal thus that converting that electric signal into heat energy. The central processing unit has two units within it and those are the arithmetic and logical units of the central processing unit where both help each other to interpret the data given.

A cheap man encountered a problem when buying new parts for his desktop computer he already bought so many and much and looking to get a better price for an item he went ahead and designed a heat sink and set out to look for the variant he designed. A heat sink is an electronic attached to the central processing unit with the goal of absorbing the heat from the central processing unit by conduction and by releasing it through the air by convection. Heat sinks are classified by how they are made and what their fin arrangements are. There are many variants of heat sinks among them are the active heat sink that usually comes with a fan as they tend to retain heat a lot causing overheating this type of heat sink is usually made up of copper.

The man after going through the design considerations he needed from the materials he needed wherein which he had two options from and needs to choose one among them. These are aluminium and copper in which both have their weaknesses and strengths that differ them from each other. Aluminium is the mostly commonly used material for a heat sink for the reasons that it is cheap and light which in today’s era of electronics where the technologies get smaller and smaller resulting in the need of more compact heat sink’s thus the light and ease of manufacturability of the aluminium heat sink will provide the needed properties looked for in a heat sink in this day and age.

Copper and Aluminium have each their own weaknesses and strengths. Copper has its strength of great thermal and electric conductivity allowing the flow of both and electricity through it very easily compared to other metals which already in paper makes it a better heat sink material than aluminium who has lower thermal conductivity but compared to other metals has also a very high thermal conductivity but the biggest weakness of using copper as a material is that copper cannot have fins extruded from it, making the manufacturing of the heat sink a very hard task making copper heat sinks to be more expensive and usually comes in the form of an active heat sink making it much more costly. The need of a fan for a copper heat sink stems from the ability of a copper to retain heat thus the absorbed heat is now staying in the fins much longer thus decreasing its efficiency. The solution to both of their of weaknesses is that they manufactured a hybrid of both the aluminium and copper heat sinks that hide their weaknesses and show their strengths this heat sink variant has its base plate made of copper allowing its strong ability to absorb heat faster than the aluminium heat sink with a base plate of aluminium, The new variant then have its material for the fins as aluminium due to its ability to release heat much faster than the copper thus being allowed to be a passive heat sink.

Here we use the ANSYS software to evaluate and analyse the differences between copper and aluminium as material in the designed heat sink to find out if the worth of the heat sink as copper as the material is truly worth it and more efficient than of the aluminium heat sink. Here we have both be affected by the same boundary conditions and the same design to find out how it affects both and what the results are.

Upon simulation the discover is that even with the high property differences between them they still somewhat work almost identical with the only biggest difference upon steady-state thermal analysis is that the minimum total heat flux experienced by the aluminium increases only 4% when the material is changed to copper thus proving that the more expensive price of a copper heat sink does not truly compensate it as the much cheaper aluminium alloy heat sink is much more cheaper and much more practical . The simulation showed how much better aluminium is to copper and is recommended for the man to buy the aluminium variant of his designed heat sink.

TABLE OF CONTENTS
Page No.

Title Page i
Executive Summary ii
Table of Contentsiii
Problem Definition1
Problem Scope1
Technical Review1
Central Processing Unit1
Heat Sink2
Fin Arrangements 4
Convection6
Fourier’s Law of Conduction8
Benefits of Heat Sinks and Its Weaknesses10
Applications of Heat Sinks11
Design Requirements12
Design Description14
Overview14
Detailed Description17
Use19
Evaluation20
Overview20
Analysis and Results 22
Assessment24
Reference26
Appendix A-1
PROBLEM DEFINITION
Problem Scope
Today where we could call it the age of electronics where most jobs and activities done by the human race today involves electronics from sports where the electronics would be used for analytics and stats to working as an accountant or engineering which would be during the time when it would have been impossible for computers to be used in this line of work. Inside the computer there we would see the random access memory, motherboard and the central processing unit. The central processing unit found in a central processing unit is one of the best inventions invented in the line of electronics as this would be so soon called as the brain of the computer as this is not only found on the computer but also found on other electronics like cellphones , laptops and other electronics this central processing units could be found in it but this central processing unit would have its glaring weakness and this glaring weakness would be its ability to overheat when it is being used this is where the invention of a heat sink comes in where another great invention in the line of electronics was invented as this would help regulate the temperature of the central processing unit and comes in different types and forms to help the costs of the already expensive central processing units but as the higher the performance a central processing unit is the higher the expense of the heat sink is. A cheap man who looks to buy a new desktop computer for himself but he noticed that his central processing unit was still in working shape and order even if it was a discontinued version of central processing unit that only dissipated 18 watts of power. He decided to keep the central processing unit a to find a way to have better other components , once he finished shopping for the other components of his desktop computer he had one component left to buy and that was the heat sink for his central processing unit. In a way to have him save some money he bought an aluminium plate heat sink which was what he needed so that his still old school central processing unit would benefit from it and the heat sink would be cheap and still affordable allowing him to save some more money in his purchasing of a new desktop computer to use.

Technical Review
1. Central Processing Unit
A Central Processing Unit is circuitry found in computers, mobile phones, game consoles or in the military and is considered to be the brain of the CPU as it translates software and carries out its instructions of basic logical, arithmetic, control and input/output operations. A central processing unit is usually created from silicon as its semiconductor sometimes germanium is used, copper as its conductor so it can conduct electricity and lastly plastics as its insulator.

The Central Processing Unit operates by the action of interpreting data inputted to the gadget or electronics into information for example the act of pressing a letter or number on your keyboard would be interpreted by your central processing unit to show up in your screen .
The Central Processing Unit has two units wherein the processes of each of the central processing unit is divided the first one of the would be the Arithmetic Logic Unit which would have the process of computing simple arithmetic equations and logic equations for the CPU that’s why it was give the name of the Arithmetic Logic Unit. The simple arithmetic operations it can do are addition, subtraction, multiplication and division. The logical operations it can do and achieve are mostly comparisons of data from each other which includes the six logical relationships which are greater than, less than , equal to, greater than or equal to, less than or equal to. And lastly not equal.

The other unit of the Central Processing Unit would be the control unit which is where the instructions of the arithmetic unit’s input comes from the control unit interprets the data given and gives the arithmetic unit these data for it compute and solve.

There are three types of central processing units as well which are the single core type of central processing unit and the dual core type of central processing unit and last but not the least in fact the highest performing one which is the quad core central processing unit. The single core central processing unit would be the one of the oldest if not the oldest central processing unit today available in the market these type of central processing unit as this is one of oldest central processing units today as expected its performance compared to other types of central processing units are poor this single core central processing unit can only operate one operation at a time and tend to not multi-task very well.
The performance on these central processing units tend to be dependent on their clock speeds thus resulting in its common slow or inconvenient performance issues compared to the next one which would be the dual core central processing unit.

The Dual Core Central Processing Unit would be like two single core central processing units have been combined together and their performance would be added to each other and that would be what a dual core processing unit is. The improvements of the dual core central processing unit would be very apparent if you noticed the changes need or the performance issues experienced in a single core central processing unit.
The problems involving multi-tasking for the single core central processing unit would be solved or would be done more efficiently compared to the single core. The Dual Core processing unit tends to be written in a special code called as the simultaneous multi-threading technology.

The Quad Core Central processing unit would be the next which would like the improvements of dual core central processing unit is to the single core central processing unit quad core central processing unit would be to the dual core processing unit. The multi-tasking of this type of central processing unit would improve as well but its performance would not increase four times the amount with the reason being that it has four cores in its central processing unit.
The processing speed does increase but not at a high rate like the change between the single core and dual core plus the speed increase won’t take in effect unless the quad core central processing unit uses the simultaneous multi-tasking threading technology as well as used on the quad core central processing unit.

As stated before what is the multi-tasking threading technology used both in quad core central processing unit and the single core central processing unit which means that the reason it’s called multi-threading for it can have multiple threads on single central processing unit core thus allowing multi-tasking on a single core causing higher performance speeds in central processing units.

2. Heat Sink
A heat sink is a passive heat exchanger that absorbs and moves the heat generated by a central processing unit or any other electronic and mechanical medium. The heat sink is normally attached so that it can absorb and transfer the heat towards the surrounding fluid around it usually the air.

The Heat sink has a variant which would be called the active heat sink which involves the usage of a Fan and is also called heat sink and fan which most modern computers have and are used when the singular heat sink is not enough for a central processing unit to take before damage.

The heat sink has its primary medium of heat transfer to be convection where there is the natural convection where it is the movement of fluid is caused by the transferring of the heat from a solid to a fluid causing changes in its density which results in the said movement of the particles. Next we have the forced convection which uses an outside force for the particles of fluids to move those outside forces could be a fan thus a forced convection would be used by the heat sink and fan or also known as the active heat sink.

The material used in the making of a heat sink is mostly aluminum and sometimes copper is used as the material for a heat sink these materials were chosen because of their ability to conduct heat and absorb it from the central processing unit so the heat sink can do its purpose of transferring the heat generated by the central processing unit to the air.

There are many types of heat sinks and these are:
Active Heat Sinks as stated above these types of Heat sinks usually comes with a fan and are used for central processing units that tend to overheat above the usual capacity of a single heat sink for a central processing unit.

Passive Heat Sinks which are the standard and most commonly used heat sink these types of heat sinks are usually made of aluminum and they use aluminum finned radiators for the process of heat transfer by scattering the heat it absorbs from the central processing unit by using the convection heat transfer process. These are much more reliable than the active heat sink.

Stamped Heat Sinks these are heat sinks made of various metals. The stamped heat sinks are a cheap alternative or variant from the other heat sinks and are used for low power applications but the cheapness of the stamped heat sink results in below average performance of the stamped heat sink. The stamped heat sink is made usually by the process of the stamping to the shape desired by the manufacturer.

The machining heat sink are expensive unlike the stamped heat sinks mentioned before the reason of these increase price is that the manufacturing process tends to be expensive compared to the others as the machining heat sink is made by machining which removes blocks of metals to make the fins and these results into wasting metal resulting into its expensiveness.

Bonded-Fin Heat Sinks are another type of heat sink which is created by bonding as the name suggests fins made of metal on the base of a heat sink there are two ways of bonding these heat sinks and these are by the use of epoxy which is relatively simple and affordable way and there is brazing which is much more expensive. This type of heat sink is mostly used in welding like electric welding.

Bent Fin Heat Sinks as noticeable in the other types of heat sink these are manufactured by folding the heat sink material and with a large surface area results to very high performance and very high flux density. With it performing at a very great standard this would always have its downside of being an expensive form of heat sink.

Skived Heat sinks are made by the skiving process which is slicing of metal but in the case of heat sinks is generally copper which is a great a conductor of heat these skived heat sinks normally is a medium to high performance heat sink compared to other forms or variants of heat sink.

Forged Heat Sink this as the name also suggest is created by the process of forming this type of heat sink has its fin arrays formed by the usage of a molding die wherein raw material is forced through it. The benefits of these forged heat sink is that results into high uniformity of the metal and structural rigidity and superior surface finish and these typically have low rejection rate resulting it to be economical as well.

Single Fin Assembly Heat sinks are very expensive variant of a heat sink these are worth the price though as it has very small and lightweight and can be installed into tight places these also have the capability of a low to high end performance
Swaged Heat Sinks are formed by the swaging process wherein it is a cold working forging process which results to denser and stronger fins for the heat sink this form of heat sink is low-cost variant of a heat sink that is a medium performing heat sink compared to the others.
The heat sink are not only used for the purpose of scattering the heat of that the central processing unit produces but it is also used as a thermal energy management of the central processing unit or any other electronic device it is attached to the definition or why it is used as a thermal energy management that it does not only lowers the heat of the central processing unit but it also increases it when the central processing unit is at lower temperatures.

There are many ways of attaching heat sinks to central processing unit or other electrical devices or mechanical mediums.

The first one of many examples would be the thermal tape which is a low cost way of attaching it but it has its negatives of low thermal conductivity, cannot be used to attached large heat sinks and to equipment that vibrate most of the time.

Another example would be the epoxy which is a strong mechanical adhesion also relatively cheap its negatives is that for epoxy to attach it properly is that area needs to be cleaned so you can attach it the best way possible.
Next would be the wires from z-clips which gives improved thermal performance very useful in the use of heat sinks and has easy removal for changes but is much more costly than the epoxy and thermal tape and it needs to bore holes to be attached.

Clip-on is also a way to attach the heat sink but it requires no holes or anchors unlike the z-clips but like the z-clips this clip-on also improves thermal performance but its downsides is that the area where the clip is attached is not allowed to be used and it has its extra assembly steps.
Push pins with compression springs another way to attach the heat sink and its benefits are great like that among the ways this has the highest thermal interface among them and it is also easy to remove and install but just like the problems of the z-clips this requires bore holes and thus increases its complexity.

Stand-offs with compression rings are Ideal for large heat sinks which the thermal tape can’t be used for but has strong mechanical attachment and like the push pins with compression rings who had the highest thermal interface preload the stand-offs with compression rings have the highest preload for thermal interface but its weaknesses are much more severe than the other’s weaknesses and it’s the expensiveness of it plus the complexity of its tracing of the board because of once again boring holes for it to be attached.

As discussed there are many types and many ways for a heat sink to be attached to the central processing unit but the design factors of the heat sink would be of use in determining how efficient a heat sink would be and these design factors would help differentiate a heat sink from each other and these design factors are thermal resistance, material, fin efficiency , spreading resistance , fin arrangements , cavities , conductive thick plate between the heat source and the heat sink and surface color this design factors of the heat sink would help.

3. Fin Arrangements
Heat sinks has two components one of these is the base plate where it absorbs the heat of the central processing unit and another component of the heat sink would be the fin which is a component that extends from the base of the heat sink where its material would also be made from what the heat sink is made of from copper to aluminum.

This fin that extends from the base plate of the heat sink would be an item that increases the heat transfer of the heat sink because of its ability to increase the convection of a heat sink which the heat sink uses to get the heat it absorbed from the central processing unit out into the air surrounding the heat sink which is also a factor to the efficiency of a fin as its temperature would help the fin of the heat sink’s heat transferring capabilities of convection which needs both the temperature of the heat surface and the heat sink.
The increase of the surface area of the heat sink at the fins will help increase how fast heat would be transferred to the air surrounding it by the idea of the heat spreading towards the larger area then being transferred by large amounts as heat is not concentrated towards one area to leave from the heat sink’s fins thus a larger fin surface area is always welcome in a heat sink because of its better heat transferring ability.

Fins are not only found on a heat sink, fins can also be found in the motorcycle bikes, radiators and heat exchangers that can be found in power plants as fins are very useful in the industries that need the transferring of heat from the industrial and power industries all use the ability of a heat sink to raise the ability of the heat transfer process of convection.

The fin has a form called cavities which in itself is an inverted fin meaning that the fin instead of extruding from a surface it is an area created between fins next together this cavity promotes the processes of boiling and condensation these type of fin is being studied upon in researching for the best possible iteration of this fin for use.

Fins are also called cooling fins because of its ability to cool the device it intends to cool because of its as stated ability to convection with the increase of its surface area thus stating that the power of heat sink to cool is proportional to its surface area. Convection is given by the equation
q=hA (Ts-Tsur) for convectiom
(where h= heat transfer coefficient ; A = area of the heat sink ; Ts= Surface Temperature ; Tsur= Surrounding temperature ; q= Heat Transfer rate) with the temperature of the device and surroundings dependent on where the heat sink would be attached and the heat transfer coefficient would be dependent on the material used on the heat sink which would depend on the preference of the buyer if he wants an expensive heat sink which would be made of copper and has a fan adding more variables to the heat rate of a heat sink or a simple but still efficient aluminum passive heat sink leaving the area of the heat sink to be another variable that would help the efficiency of the heat sink we would need to increase the area of the heat sink in which thus we need the better surface area of a fin as this itself increases the heat sink’s area thus increasing the proportional to it heat rate.

Fins are a great invention to the heat transfer processes industry as stated before for these great innovations helps the process of convection tremendously from out large refrigerators to the small central processing units most of the devices that need its heat to be regulated would experience the need of a fin in some way or another as the ability to increase the surface area for heat rate of a material.
But fins can not only be found mechanically or electronically as fins can also be found in animals as some animals have fins which they use to transfer heat from not the fins of fishes but like rabbits which fins can be found in their ears so that they can lose body temperature even humans have fins are hands and legs can also be considered as fins as they areas that help the transfer of heat from the body to the surrounding air
As stated before the fins increase the heat transferring capability of a heat sink through its convection but it also increase its overall heat transferring ability for it also increases the heat transfer processes of conduction and radiation as both heat transfer rate is proportional to the the area of the heat sink thus addition of a fin which increases the heat sink’s surface area increases the heat sinks with the formulas for each with
q=kA (T1-T2) for conduction
q=??A(Ts4-T?4) for radiation
Where q= heat transfer rate; k= thermal conductivity; T1 = temperature of the left side; T2= temperature of the right side; A= area of the heat sink; Ts = Surface temperature; T?= Surrounding Room Temperature; ?=emmisivity ; ?=stefann boltzman constant.To help these fins have a better or more efficient way of increasing the surface area of the heat sink and there we would differentiate its many fin arrangements where it would differentiate the types of arrangements the fins will have how it affects the heat sink and what it does to the surface area it must increase so the heat sink can have a much more efficient heat transfer rate.

The first and probably most common heat sink fin arrangement would be the plate type heat sink or straight type fin where in the fin is in rectangular shape allowing the air between the heat sink to flow easily but the most noticeable difference in the fin arrangement of a plate type heat sink is the six parameters that involve it are thickness of the base plate of the heat sink as well as its length , its height and the spacing of between each fins as well as its thickness all of these are parameters for the design of a heat sink with a straight type fin arrangement or also known as a base plate fin arrangement.

Another type of fin would be the radial fin heat sinks which as the name suggest would have circular fins where the transferring of heat between a heat sink is by the evenly spaced cylinders meaning that unlike the first one which is a straight type fin arrangement or base plate fin arrangement this type of would have lesser parameters in its design and providing a better surface area distribution resulting into a better heat transfer rate plus reducing the volume of the heat sink making it more compact and more in line this new form of technology today this heat sinks fin arrangement may be much more noticeably different in geometry with the plate type as that one was obviously rectangular while the radial one is more circular they still have somewhat the same way of computing the overall heat transfer area even if they’re shape is vastly different.

The Pin type heat sink is one of most common types of heat sinks because of its ability to have a better surface area than that of the plate type while practically maintaining the same size this type of heat sink has the pins for fins where these fins would be either square or cylindrical in shape but what it makes up for its surface area the pin type heat sink loses to the plate type heat sink in terms of height as it is smaller than the plate type heat sink which is more common than the pin type heat sink.
The round shape of the pin type heat sink also gives it an advantage of having a more aerodynamic space for air to flow around between the spaces of the fins in a pin where it reduces resistance from other air sources allowing free flow for the air surrounding pins.

4. Convection
A central processing unit because of how it works tends to generate heat which could damage the central processing unit resulting in performance issues or worse the central processing unit would overheat so much that it won’t work anymore. That is where the heat sink comes in to the rescue as it would regulate the heat generated by the central processing unit so that the heat sink won’t overheat and cause the central processing unit to be lost forever.
Whether it’s a single core central processing unit or quad core central processing unit they all use a heat sink but how does a heat sink help the central processing unit cool off or lose hit thus fully keeping it safe from overheating it works by the higher temperature central processing unit would transfer it heat to a cooler fluid medium or in this case air. But what is this process called and that process would be called convection and conduction.

First to be discussed would be convection is the movement of heat from higher temperature area to lower temperature by using the motion of fluids. There are two types of convection and these are the free or natural convection and the forced convection. These types of convection have their own disadvantages and advantages.
The differences of each of this types of convection would determine what type of heat sink it is be it the active heat sinks for they are the ones that comes with a fan or you could say comes with an outside force thus it would fall to the category of a forced convection then there would be the natural convection which would coordinate with the natural convection.

Natural Convection Heat Transfer would be a type of convection that would consider the density differences for it to move not with outside forces this type of heat transport or heat transfer is experienced in a heat sink when a heat sink is when the air surrounding the heat sink’s fins increase when the central processing unit starts operating thus generating heat in which the heat sink must cool off by using the heated air surrounding the heat sink to be less dense than the air surrounding the heat sink itself not its fins.

Thus the heat of the air to flow out of the heat sink thus cooling the central processing unit keeping it safe from damage it may experience when it gets overheated from the operation of the central processing unit.

There are many factors to consider when the natural convection process of heat transfer like the orientation of the fins if the heat sink’s fins are too constrictive of the air flow the, the flowing of the hot air to spread through the surrounding air outside the heat sink would result into reduced efficiency of the heat sink or even worse if it is blockfd resulting into the heat sink being utterly useless and not doing its purpose.
Next would be the impact of power dissipation of a heat sink on the performance of a heat sink where the thermal resistance value will change depending on the power dissipation of the heat source in this case would be the central processing unit in this case the higher or better the power dissipated in the problem given which would be 130 W would result into a greater natural convection air flow thus improving the performance of the heat sink overall. In the case of effect of power dissipation on the performance of a heat sink we would receive a formula W=?*?t1.25 where it is the relationship between the power consumption of the heat source and temperature rise from it.

Another type of convection would be the forced convection which uses outside forces like pumps, fans and suction devices which would unlike natural heat convection would rely on these outside forces for it cool off the heat source or central processing unit but these type of convection can’t or most of time will not be experienced by a heat source or the central processing unit solely or it being the only heat transfer method experienced as the natural convection form of convection heat transfer also is experienced as it is in the case of an active heat sink which is like any other passive heat sink for the addition of a fan for its heat to be regulated better increasing its efficiency as this type of phenomenon is called mixed convection where the experience of two of types or all the types of convection would operate at the same time resulting into better efficiency as the heat or air won’t transfer naturally in itself but would receive help from external sources.
The level of heat transfer would increase dramatically with this happenings as not only the density of airs caused by the difference of temperature will result into the hot air between the fins and the hope of it not having an obstructed pathway to be released and mix with air surrounding the heat sink.

The part following this paragraph will have equations, tables and figures taken from the book Fundamentals of Heat Transfer Sixth Edition by Incorpera, Dewitt, Bergman and Lavine.

Figure 1: CONVECTION HEAT TRANSFER PROCESSES
Figure above illustrates the types of convection that was discussed before here we can see the different types of convection from forced convection which illustrates a fan working on hot components on a circuit board which means that by using the fan as an outside force the cooling process that the hot components would undergo on would be a forced convection type on the second illustration or (b) would demonstrate a natural convection process for as the hot components on printed circuit boards would be cooled without any outside forces thus being in the form of natural convection. Then there is the boiling and condensation illustration shown where it shows phase changes of water from water to steam in the boiling illustration in (c) and the air to moist water droplets in illustration.

The formula used for the convection heat transfer process is always whatever the type of the convection heat transfer process it is be it natural or forced convection would always be the q”=h(Ts-T?) where q” would be the convective heat flux that would have the units of W/m2 which would be equal to the convective heat transfer coefficient also known as h multiplied to the difference in surface temperature and fluid temperature would equal the convective heat flux. The convective heat transfer coefficient is normally gotten from a table as the table shown below.

Process Heat Transfer Coefficient
Free Convection Gases 2-25
Liquids 50-1000
Forced Convection Gases 25-250
Liquids 100-20000
Convection with Phase Change Boiling or Condensation 2500-100000
TABLE 1: HEAT TRANSFER COEFFICIENTS
The units used by the heat transfer coefficient are W/m2?K and the expression of the surface temperature subtracted by the fluid temperature is called the newton’s law of cooling where it shows the temperature difference of the fluid and the surface as at a heat sink the heat from the central processing unit which would be absorbed by the heat sink then the heat sink would dissipate this into the air surrounding the heat sink.

5. Fourier’s Law of Conduction
Conduction can be simply stated as the transfer of heat by direct contact where the heat transfer is always as the concept says is from hot to cold as heat spreads towards a cold area not the other way around as believed by many. The Fourier’s Law of Conduction can be also called as the rate equations of conduction as this equation is used to know how much heat is transferred between each surface that made contact with each other from the higher temperature region to the lower temperature region.

Conduction in a heat sink happens when the central processing unit generates heat that would or is near its breaking point where the temperature of the central processing unit would start to slow down its progress or worse make it permanently damaged to the point it is unusable then there’s where the central processing unit steps in as heat regulator of the central processing unit making sure it is not too cold or too hot , with direct contact with the central processing unit the heat sink would experience the heat transfer process of conduction where the tiny particles would transfer from each other with like temperature the higher one would transfer or spread through the lower one , in this case that would be the energy not temperature to transfer from lower to higher.

The following equations and figures following this paragraph would have been taken from the book Fundamentals of Heat Transfer by Incorpera , Dewitt , Bergman and Lavine.

FIGURE 2: CONDUCTION
In the figure shown from the book Fundamentals of Heat Transfer by Incorpera, Dewitt, Bergman and Lavine there would be an observation a heat transfer from the left to the right where from the hotter left side would reach its lower temperature counterpart through the L it went through.

In the figure the formulas or the rate equations are now more easily understandable and these rate equations would be qx”=-kdtdx which would be derived into a new formula when subjected to steady state conditions and these formulas are qx”=-kT1-T2L=k?TL where we solve for the heat flux when heat goes through a wall in heat process of heat transfer.

FIGURE 3: HEAT TRANSFER THROUGH PLAIN WALL
In conduction there would be heat transfer through a composite wall where the figure would illustrate the heat transfer between a composite wall where it shows a thermal resistance circuit representative of the heat transfer of the left side to the right side this figure shows both convection and conduction experienced by the wall here we would first see the heat transfer between the hot fluid and the wall where it would be represented at the thermal circuit with a resistance of formula of 1/h1A then the thermal circuit would show the formula for the thermal resistance experienced in the conduction which is L/kA with the nodes surrounding it would Ts1 and Ts2 which is the surface temperature on each side of the plane wall.

6. Benefits of Heat Sinks and Its Weaknesses
Heat Sinks would have their own benefits as you could say as there are many types of heat sinks out there and these heat sinks would have each of their own weaknesses and strengths from the passive heat sink to the active heat sinks all of these would each of their own design resulting in very different advantages and disadvantages.

First would be a specific type of heat sink which would be the aluminum passive heat sink which would already have the benefit of being made from a cheap but still somewhat efficient material thus reducing the cost needed but this type of heat sink has its weakness of having no fan on it as that would be a great way to help reduce the temperature of the central processing unit it is attached on as this would produce the process of forced convection.

This type of heat sink also has other glaring weaknesses like it being more easily corroded because of the material being used which is aluminum and there is the possibility of integrating the printed circuit board into it but it’s not possible thus requiring a separate printed circuit board to be used on it . It also needs electric insulation when attached because of the electricity involved in the central processing unit.

Another Heat Sink that would have apparent advantages would be the meticulousness forged heat sink wherein the industry of heat sinks would be monopolized by the extruded and die cast forms of heat sinks but in the age of growing advancements of technology we have the need to improve the heat sink as well as the times show better processing speed and the fact that the central processing unit’s size is growing smaller and smaller by the creation of a new heat sink then comes the meticulously forged heat sink thanks to its:
Thermal Conductivity where unlike the die casted heat sinks which have its disadvantage of being porous in itself as it was made by casting it into a mold thus affecting its thermal conductivity and extruding involves being formed by die also reducing its thermal conductivity unlike forging which as stated before would be formed where high pressure controls it thus improving the thermal performance of the heat sink.

Increased surface area is also another area where the meticulous forged heat sink would have an advantage over the industry leaders and this would be the will have its fins to be formed into a shape that would help it have better thermal conductivity compared to the others.

The forged heat sinks gives the industry leaders a run for their money as they have key benefits over the die cast and extruded ones. Once again the thermal conductivity is one of them as the way these heat sinks are manufactured is a critical factor in the heat sink thermal conductivity plus the way how it is flexible in the adding fins in the heat sink.

The creation of a heat sink that has is forged precisely causes the increase of thermal conductivity wherein the power to absorb heat is strengthened and at the same time by using the forging method we would have the ability to increase the area in which heat would flow through plus with the area being proportional to the heat rate we would have better overall heat flow. Plus the idea of increasing the heat rate by its surface area without the need of making the base plate or the whole heat sink to be larger gives benefit to the producer of this kind of heat sink as this heat sink is what is needed in this modern age . Meticulous forging can also produce complex shapes of fins which would be proven useful within the tool. The features stated before would have not been possible with other forms of manufacturing heat sinks. This form of heat sink is well known to be more economical as it is cheap to produce and helps in the production of copper heat sinks which are well known to be hard to produce as they have this inability to be extruded making forging the ideal way of making copper heat sinks or copper base plates for hybrid heat sinks.

7. Applications of Heat Sinks
As discussed heat sinks are used on central processing units to reduce the temperature it produces and thus regulating the temperature of the central processing unit this application of a heat sink is one of its well-known uses for it, if not it’s most known use of the heat sink as most people even if they are not what you call tech savvy would have seen or heard about the heat sink as it is very common form of heat exchanger as this type of heat sink. The central processing unit is where most people would think the heat sink would be attached to but the central processing unit is not the only one.

Another application of a heat sink is the use of vapes which is an electronic cigarette this vape as the name suggests vaporizes a liquid mixture which does not contain harmful carcinogens found in a normal cigarette but this vape uses a radial heat sink as the vaporizing process uses heat to prevent the device to overheat a heat sink is used so that it’s heat could be regulated easily.

Radiators are another device that uses heat sinks where in it is the heating system in a house wherein could you could normally find it in a comfort room its application is for a boiler that’s why it is normally found in the rest room as a boiler is where hot water is found and heated this hot water heaters need this radiators as a heat sink’s job is to regulate the heat of a device and in this case the heat sink regulates the heat of the boiler in the bathroom.

Motors also have heat sinks in them as they are technically radiators to that produces heat the most obvious feature signifying that a motor has a heat sink is when it has noticeably cooling fins surrounding it for motors needs to have their heat regulated to prevent overheating which may damage the motor and render it unusable this motors in return needs the use of a heat sink.

Amplifiers tend to increase or amplify as the name suggests power as these amplifiers amplify a signal they tend to generate a lot of heat which in itself could damage the amplifier rendering it useless and unusable in foreseeable future. To prevent this occurrence we have a way of doing it and this is the aforementioned heat sink which regulates the heat of the amplifier preventing it to overheat making it perform better in amplifying signals and making it much more consistent in its use.

As you may have noticed that heat sinks are normally applied to electronics especially ones with transistors which is a semiconductor who acts as an amplifier but tends to overheat as well like the amplifier resulting in the need of the heat sink as these transistors not only amplify signals there are also the power signal as these heat is the effect of the resistance to power going through the resistor would need a heat sink.

Cell phones today as a person may notice when using one when used in longer periods may tend to heat up a lot and this is where the heat sink comes in and thus proving the need of small and compact heat sinks as these type of heat sink is needed so that a cell phone may be smaller and more portable for the consumer but still be useful as a cell phone without a heat sink may tend to slow down thus turning off the consumer who wants to buy one heat sink and that heat sink that are used are usually small heat sinks.

Design Requirements
The Central Processing Unit that the custom built desktop needs to have a heat sink so that it won’t malfunction because of overheating as it slows down the processing power of the central processing unit. The procurement of the aluminum passive heat sink would provide the necessary heat regulating properties it provides while reducing price the cheap man needs to purchase one because of the need of this cheaper and but still somewhat efficient heat sink that can handle his central processing unit he needs to buy the passive aluminum heat sink or a passive copper heat sink if the efficiency beats the cost which both can reduce the heat of the central processing unit he bought thus actually helping his case of needing the central processing unit to be cooled while still being in budget or at a great advantage compared to the cheaper aluminum heat sink.

Prices of Heat a heat sink tend to range from 100 pesos to 2000 pesos as they vary from passive aluminum heat sinks to active copper heat sinks which are superior to passive aluminum heat sinks by the concept of better thermal conductivity compared to the aluminum heat sink but the aluminum heat sink has alloys in which it can compete with the thermal conductivity of the copper heat sink.

The heat sink is used for electronics and other smaller forms of devices that generates heat is the reason of its small design and availability and the cost which would very important in the production of small devices for these small electronics tend to get very expensive.

To select the best possible heat sink needed there are many parameters involved for the selection of these heat sink and the problem suggested earlier in the problem scope would focus on the heat sinks cost but not only the cost is important there are also these factors so that the young man could have himself buy a heat sink that both is efficient on the central processing unit he bought and the be very economical to his already expensive investment of a custom built computer.
The first heat sink parameter needed for the best selection possible is the heating power of the central processing unit. The heat generated of the central processing unit would determine how strong, how powerful a heat sink needs to be as this the very basis of what a heat sink needs to do as the higher the power produced by a central processing unit the higher its heat that would generate making the heat sink move in action to immediately reduce its temperature making it a very important parameter in selecting the best heat sink in the budget.

The air surrounding the heat sink is as key as the power generated by the central processing unit is as this heat sink parameter would generally help determine how much convection would be experienced by the heat sink. This parameter would change by the way the room wherein the custom built computer will be placed if the room is an air conditioned room the heat sink will have an aid for the cooling process of a central processing unit as just like an active heat sink with a fan that uses forced convection as better means to transfer heat as the surrounding heat will be more easily transferred because of the lower temperature the surrounding air has unlike the room which would be not air conditioned as this room’s air temperature would be about room temperature thus reducing the rate of heat a heat sink would perform at thus making the room temperature to be another key of choosing a heat sink among its other peers.

Stated before were factors in choosing a heat sink but these factors were not involved in the heat sink in it for these factors would all be about the heat sink but the next and final factor would be the heat sink’s fins which would help determine the heat transfer rate of the heat sink by increasing its surface area which is proportional to the heat transfer processes conduction, convection and radiation. These fin arrangements are vital in the creation of a heat sink from the benefits of a plate type fin heat sink to the radial heat sinks this heat sinks would allow the central processing unit to be more advanced but still provide a cheap cost with the way the heat sinks fins would act form the pin type heat sink which help the airflow between the crevices of a fin reducing the resistances in it plus maintaining turbulent flow helpful in heat regulation.
In Solving for a heat sink’s design we have the following formulas so that the heat sink design will be useful among the assumed values. First in solving for the design of a heat sink we get the Rayleigh number which is the instability of the fluid or in this case the surrounding air of the heat sink this Rayleigh number is dimensionless meaning there is no units. (Reddy, 2015, pp. 145-153)
Ra =gx?xTs-TaxL3xPrv2Where we would have these variables
g = gravity ; ?=2Ts+Ta; Ts = surface temperature; Ta = ambient temperature; L= Length of The Heat Sink; Pr = Prandtl Number; v = kinematic viscosity at ambient temperature.

Next we solve for the optimum fin spacing so that the convection could flow much better and freely with the equation
Sopt= 2.714 x (LRa0.25)When we get the optimum fin spacing we could solve for the heat sink’s number of fins to maximize the design of the heat sink
N = base width fin thickness + Sopt
When the number of fins is solved by assuming the fin thickness to be used relative to the size of base width of the desired base size for the heat sink we could now solve for the area of heat sink using assumed values of power dissipated.

A =QhTs-TaAfter solving for the area we could now solve for the fin height thus completing the design of straight type heat sink to be used on a central processing unit that correlates with the assumed power dissipated
H = A – L X W2 x N x L DESIGN DESCRIPTION
OVERVIEW

FIGURE 4: PASSIVE HEAT SINK
A Heat sink is a heat exchanger that uses conduction to remove heat from electronics and mechanical devices that generates heat this heat sink needs to have a material that has great thermal conductivity to be efficient in its heat transfer process of conduction and that material that has a great thermal conductivity is aluminum.

Aluminum is well known for its capability to conduct heat greatly that’s why its uses a conductor had been well documented throughout the years these uses are for cans, foils and other ways of storing food and beverages because of its excellent thermal conductivity it being non-toxic making it safe for food to be stored in it and its ability to be easily formed making the necessary shape of the container to be formed easily.

Aluminum is also not used for food storage but it is also used in other fields like the construction of airplanes because of it being lightweight compared to other metals but this aluminum that is used in the construction of the airplanes.
Aluminum’s purpose of food storage has long been done and practiced by humanity this form of preservation of food from using of aluminum foil to the use of aluminum cans for our soft drinks and or other beverages we drink from then the aluminum foil for covering our food.

Aluminum has always been used as a conductor of heat like from the aforementioned heat sink and various other equipment or electronics that use aluminum as a conductor of heat like cooling it down when it overheats or regulating it’s heat when it gets to cold but how does it compare to other metals in the essence of it as a material that conducts heat.
Stainless Steels is one if these which are compared to Aluminum and this stainless steels are compared from its strength and its weight as stainless steel is indeed more stronger or sturdier than the aluminum but stainless steel loses to aluminum in the weight department as aluminum is lighter compared to stainless steel thus it having the advantage of being easier to be attached to an electronic especially on portable ones.

Another variable of comparison of stainless steel and aluminum is its workability or known as how easy it is to bend, form and cut this property is very useful in the making of a heat sink as you may have discovered in the previous discussion of the heat sink most of its kinds are from how it is made and the variations of these forms from the stamped heat sink, machined heat sink and the folded fin heat sinks none of these types of heat sinks would be possible without it being easily workable and not difficult to bend, form or cut and among them stainless steel is known to be difficult to work due to its high strength compared to aluminum which is known to be weaker than stainless steel but lighter and thus the workability of aluminum.

A very important factor in the using of materials for a heat sink is the cost of this material as heat sinks tend to be small compared to other forms of heat exchangers but heat sinks need to be or at least affordable for they are attached to electronics which tend to be expensive already thus adding to the expense of those electronics which result into a reason for consumers to not buy the product but aluminum is well known for being cheap thus being better to be used for making heat sinks compared to stainless steel.

But the most important property between stainless steel and aluminum in the quest of being the material to be used for making a heat sink is the thermal conductivity as this is the rate at which heat passes through a specified material as this would help the ability of the heat sink to absorb the heat from the central processing unit or other forms of electronics or mechanical medium that uses the heat sink and between aluminum and stainless steel clearly and decisively wins in this category thus being the better material to be used for making heat sinks.

As Aluminum was proven to be superior to Stainless steel in the making of a heat sink there would be another contender to be compared to stainless steel which would be copper and the properties to compare between copper and stainless steel are the thermal conductivity which copper is superior to aluminum and thus already a better material to be used for making heat sinks than aluminum.

But what is the advantage of aluminum to copper that would provide a reason to make an aluminum heat sink instead of a copper heat sink and that is its price and its weight which already factors in to the making of heat sinks which need to be cheap and lightweight for central processing units that are small and to be used mostly and making it cheaper to purchase for the average consumer.

Heat sinks tend to use aluminum as its material but the most common form of aluminum that is used to make heat sinks is the aluminum alloy 1050 which is an alloy based on aluminum as the name suggests this type of aluminum alloy is used for heat sinks because of its high thermal conductivity which can rival copper as this aluminum alloy is still somewhat inexpensive or affordable compared to copper but its benefits not only extends to its price but it also extends towards its high electrical conductivity, ability to be formed, bended or cut and its high corrosion resistance but this form of aluminum alloy has also its weaknesses as such is its low mechanical strength thus making it very weak but this alloy can be strengthened using cold working procedure and not heat treatment as it may soften the alloy more.

Alloys are more commonly used in the making of heat sinks than aluminum only as aluminum tends to be not be mechanically strong and thus the making of aluminum alloys to fill in the weaknesses of aluminum but still making it relatively cheap then in comes the aluminum alloy 6061 which contains silicon and magnesium as its major alloying elements.

This type of alloy is one of the most common if not the common form of alloy as this is usually used for general use because of its properties that are its amazing tensile strength with its great tensile strength and its ability or suitability of aluminum alloy 6061 to forging this type of alloy turns into the mention before forged heat sink which results into high uniformity of the metal and structural rigidity and superior surface finish thus increasing its strength but still have the great thermal conductivity of aluminum this is tend to be used on larger heat sinks.

There is also the aluminum alloy 6063 like 6061 with the same alloying elements of magnesium and silicon but what are the benefits of these compared to the other aluminum alloys like 6061 and the mostly used 1050 or what improvements does this give from pure aluminum thus making it a better material for the use in heat sinks and the benefits of these its great mechanical properties, its ability to be heat treated and being weld able but how does this help in the production of heat sinks. The production of heat sinks of many shapes and size be it complex or simple can be done using an aluminum alloy 6063 plus maintaining the key important property which is the property of thermal conductive relatively lower to copper but its ability to be easily shaped, formed or bended makes it a better choice and once again another key factor would be in play for production of a heat sink and it would be it being economical.

As stated on before aluminum is considerably better than other forms of heat conductors except for copper which is the most commonly used in heat conduction but the benefits of aluminum would always put them side by side as equals or aluminum would be slightly above the copper because of the forms of aluminum alloys of aluminum which improves upon the weaknesses of aluminum or improves already on its strengths for it to be further improved like the aluminum alloy 1050 would always be the most commonly used alloy in making aluminum as it has high conduction rate for the payment of a low mechanical strength but that can be solved by the process of cold working.

Copper as stated before was the expensive more efficient cousin of aluminum as copper has higher thermal conductivity than the aluminum and much better overall than aluminum. But an aluminum alloy could compare to the copper heat sink and still maintain its cheap appeal.

Copper when used as material of a heat sink as stated before would be much better than aluminum except for one aluminum alloy which can compute with it but copper is known as a soft metal which is one of the reasons it is used as wires and its great electric conductibility its ability to be a great thermal and electric conductor is one of the reasons of its higher value than aluminum.

Copper heat sinks tends to need to be used for forced convection processes to be truly effective as copper heat sinks have been shown to heat up fast but retain its temperature probably causing it to overheat as the copper heat sink usually but its great thermal conductivity still trumps its opponent the aluminum heat sink but it truly loses in its cost as the copper heat sink is known to be three times more expensive than aluminum or more expensive depending on the market.

Another weakness of using copper as heat sink would be its manufacturability as copper can’t be extruded to make its fins which as stated before help convection of the heat sink by increasing its surface area but with difficulty in extruding fins which is the most common procedure in making heat sinks with aluminum as a material. Copper heat sinks are then manufactured in a variety of different ways from just welding or in this case soldering the fins to the base plate of the heat sink to skiving which is letting it go through a skiving machine where it slices the copper to turn into fins for the heat sink.

The disadvantages of using copper as a heat sink can be covered up by a technique where the heat sink would have the base plate of heat sink would have copper as the material of the base plate. While the fins and others would use aluminum alloy as material so that the disabilities of both can be solved in one go as the aluminum’s problem of having a longer time heating up which the copper material for a heat sink excels in when copper is used as a material as stated before, would heat up faster than the aluminum alloy but will retain its temperature much more slowly compared to aluminum, it can be compared to a double edged sword where it will indeed absorb the temperature much faster but will take a longer time for it to cool down and this type of copper heat sinks tend to be noisy and produce a lot of noise. But with aluminum being the material of the fins the need to cool down or lose its heat absorbed much faster is observed thus with the design of copper base plate and aluminum heat sink would cover each other’s weaknesses but still maintain and take advantage of the strengths of the other.

When compared to each other aluminum and copper the first one to be pointed out would be the thermal conductivity of copper and aluminum’s ability to be extruded which copper heat sink’s lack which in return gives another reason why copper heat sink’s expensive compared to aluminum heat sinks.

The reason why almost all heat sinks are made of copper is because that copper’s weaknesses are too great to ignore but there are still some copper heat sink’s made in which the whole heat sink is made of copper not only the base plate which is one of the most common practices in making a heat sink in today’s era. Thus full copper heat sinks tend to have fans with them as its strength of great absorbing of heat also damages it at the same time as those absorb fast but let go slow causing in a high temperature risk of damaging the central processor unit that will make the central processing unit slow down or worse overheat be permanently broken.
Characteristics needed of a Heat Sink
Heat sinks needs to have a large surface area so that the fin arrangements would have a large area so that the heat can be much more dissipated easily compared to a smaller surface area for the heat sink.

Heat sink ability to transfer heat of the device to the surrounding air from the central processing unit is dependent on the temperature of both as heat transfer is normally is.

The direct contact between the heat sink and the central processing unit is important as the heat sink uses the process of conduction so that it can be the medium between the central processing unit and the surrounding air.

The use of a fan may result into a much more expensive heat sink but may increase the performance of a heat sink compared to a passive heat sink which uses the concept of natural convection as a means to transfer the heat of the central processing unit that goes in the heat sink through convection to the air.

The way to attach the heat sink is one of the most important factors for a heat sink to be effective and one of these ways would be the use of screws as the heat sink would be much more effective with this method of attaching it to the central processing unit.

DETAILED DESCRIPTION

FIGURE 5: HEAT SINK FIN ARRANGEMENT
A passive heat sink would normally have the base plate which would be the one attached to the central processing unit where it would absorb the heat generated by the central processing unit through conduction.

The base plate of the heat sink would provide the conduction needed so that the heat produced by the central processing unit could be transferred to its fins so that the heat would be transferred to the surrounding air by the process of convection and radiation. There are still factors affecting the heat sink and these factors may be more similar to the fin’s factors as one may think as the base plate of the heat sink would have the factors:
Dimension or Area as this is repeatedly mentioned as the key reason why fins are used in the heat transfer topic this as well is a factor for the base plate of the heat sink as this component uses the conduction as its heat transfer process. The rate of conduction of heat process is proportional to the area of heat sink thus increasing the rate of heat transfer between the heat sink and the central processing unit.

Material is important in the effects of a base plate to the central processing unit as the base plate is the one that makes direct contact with central processing unit in the heat sink it’s material is key as the material of a heat sink would determine its thermal conductivity which was discussed before on what is the pros and cons of materials for heat sinks with aluminum being the chosen one for the heat sink by the young man with it being within the budgetfor his custom built computer. With thermal conductivity being proportional to heat transfer rate this would be another key factor in the base plate of a heat sink
Another component of a heat sink would be the fins where it increases the surface area of the fin resulting into a better heat transfer rate for the heat sink as this type of heat sink has many fin arrangements from the simple plate type fin base arrangement used in aluminum passive heat sinks to the pin type heat sinks.
The plate type heat sink has said before six geometrical parameters that is needed in designing for one for it to have the best effect in the regulation of heat in a central processing unit this plate type heat sinks are regularly rectangular and extended from the base plate of the heat sink this form of heat sink tend to have a better height than the pin fin arrangement heat sink where it could be both advantage and disadvantage as modern times would prefer the smaller and more compact pin fin arrangement on a heat sink than the plate type fin arrangement on a heat sink.
Another form of a heat sink would be the skived fin heat sink where in it would be called a skived heat sink because of its most prominent feature which is being skived this skived process is where the fins are generally made by the skiving process where the general and most used material would be copper which has generally better thermal conductivity than the aluminum material which is also commonly used and cheaper the skiving process could be called as a process that slices of the fins not rolling for a heat but slicing it precisely with a slicing tool that from the skiving machine.
Then comes the radial heat sink which provides a better surface area with the lower volume needed in this modern age of electronics where devices get smaller and smaller as new advancements of technology are made every day to make it more compact and portable.
The addition of a heat sink that has a tapered fin which means that the fin is reducing as it goes to the top as tapered means to reduce in thickness in one end this type of heat sink tends to look like pin type heat sink except for the part where it reduces its radius as it grows higher this type of heat sink fin tend to be better than pin type heat sink and has better heat characteristics than any other pin type arrangements for a heat sink.

The heat sinks ability to transfer heat thanks to its components is very apparent when observing the design of a heat sink as one of the best examples to be used when discussing the heat transfer process conduction, convection and radiation as each demonstrates this heat transfer one way from another the base plate would demonstrate the conduction and the heat sink’s fins would provide the demonstration of convection and radiation in a heat sink
USES
Heat Sinks works as a heat regulator of the central processing unit where it absorbs the heat generated by the central processing unit provides when operation as this heat sink would have different components and the use of these components are the base in which is normally attached to the central processing unit itself this component would tend to be bigger than the central processing unit to cover it more and providing a bigger surface area for the heat generated by the central processing unit to go through this process would be called the conduction in the heat sink and can be observed as heat sinks are sometimes used in mechanical engineering heat transfer problems.

The next component of the heat sink and one of the most prominent features in heat transfer would be the extended surfaces or also known as the fins which would be used as the medium of convection and radiation in a heat sink. These extended surfaces have already been discussed in prior sections in this paper but to summarize the process of this fins we could say that the fins would take advantage of the surface area of the heat sink to propel the heat transfer rate to a better standing as this fins would also take advantage of the crevices between the fins to be more efficient in its use thus providing the heat sink a better convection and radiation heat transfer process.

Then comes in the much needed heat sink of the young man who is looking for heat sink that would provide him the efficiency he needs as the material of aluminum is already determined he is looking towards the efficiency of passive aluminum heat sink as copper and an active heat sink is already outside of his budget range which in turn reduces the efficiency of fins with it being now a passive heat sink without the aid of a fan resulting into having to use natural convection in his heat sink he would need to use this aluminum heat sink as the aluminum would have lower thermal conductivity than copper but would still efficient in its conduction when the aluminum base plate has direct contact on the heat sink or he could consider a copper heat sink if their efficiencies are too great from each other . The heat sink would have also aluminum fins to be used but still would have the benefits of surface area provided by a heat sink.

EVALUATION
Overview
The evaluation of the design was done in ANSYS software where it was intended to discover how much the heat sink he bought from the store would have heat flux go through it and what maximum temperature the heat sink may experience.
The software has features for the evaluator that simulates the figure given to provide values involved in heat transfer like the steady-state thermal feature which is used to determine the temperature , heat flux and etc. that it can provide to help the evaluator discover which data’s would result with the given he has.
As the cheap man bought most of his things on his to do list he still had a problem with his central processing unit missing a heat sink in hopes of finding the most cheapest and efficient one he could find he looked for the perfect design of a heat sink that would satisfy all of his needs.
First knowing that he would assume that the room wherein his desktop computer will be placed to be an air conditioned room with an ambient temperature of 23 degrees Celsius and has hopes of having a base of 77 mm x 77 mm for the heat sink. He went ahead and checked on the internet what his central processing unit’s maximum temperature to which it will start to break to be 100 degrees Celsius plus assuming the power dissipated to be 25 W he then went ahead to look for the design of his heat sink.
With these known and assumptions we can compute for a design of a heat sink:
Properties of Dry Air at 23 ? . (Dry Air Properties. (2018).
K (thermal conductivity) = 0.025362
?= 1.8394 E-5
v= 1.5436 E -5
Pr = 0.73012
?= 1.8394 E-5
?= 1.192
First to Compute the Design of Heat Sink we first compute for the Rayleigh Number
Ra = (9.81 (2669)(373-296)(0.0773)(0.73012)1.8394 E-5)Ra = 2.224731822×106
After computing for the Rayleigh Number we can now compute for the Optimum Fin Spacing.

Sopt= 2.174 x 0.1524(2.224731822×106)0.25Sopt = 8.578771297 mm
Then we compute for the Number of Fins the Heat Sink would have
Number OF Fins = 772+8.578771297mmNumber of Fins = 7.278728109
Number of fins = 8 Fins
Then we compute for the Height of The Heat Sink’s Fins
254(77)= 2 x 8 x 0.077 x H+ 0.077 x 0.077 H= 61.07129153 mm
With him computing for heats sink that could handle his AMD Athlon 5350 APU he computed for a design that would enable his central processing unit without the need of a fan while having a base of 77 x 77 mm. He eventually was able to design a passive aluminium heat sink that could handle total dissipated power of 25 watts which would have 8 fins and a fin height of 61.07129153 mm.

Analysis and Results
With the calculations done we can now simulate the designed heat sink with two types of material on the ANSYS software:

FIGURE 6: CONDITIONS SURROUNDING THE HEAT SINK
Steady-State thermal analysis is the feature in ANSYS software where you solve for temperatures and overall heat flux of the heat sink. The figure above shows the stated conditions for both the aluminum and copper heat sink. As the conditions shown in the figure above is applied to the heat sink here we see the heat sink designed by the cheap man to be affected by the surface temperature of 100 degrees Celsius and a power dissipated of 25 W below the base plate of the heat sink where it will be attached to the central processing unit. We can also see the convection on the heat sink in the figure where there are two types of convection but with the same conditions they will have the same heat transfer coefficient of 4W /m2 0C and ambient temperature given before of a 23 degrees Celsius. The figure above illustrates the boundary conditions of the heat sink showing that there are 4 heat transfer phenomena occurring around the heat sink and the reason for the two convections are the directions of heat transfer these convection process is doing from the first convection with a horizontal direction to the second convection which has sideward direction in which the convection would be going through which the face is facing.

FIGURE 7: TEMPERATURE OF ALUMINUM ALLOY HEAT SINK

FIGURE 8 : TEMPERATURE OF COPPER ALLOY HEAT SINK
Temperature is a the degree of how hot and cold an object is usually measured by a thermometer. This temperature measured by the aluminum and copper heat sink both maintain the maximum temperature condition of 100 degrees celsius but noticably has a slight difference in the minimum temperature which has copper heat sink having a 98.339 degrees celsius and the minimum temperature of the aluminum heat sink goes to show a temperature of 96.053 degrees celsius. This small difference between the two materials goes to show how the thermal conductivity of the heat sink of the copper and the aluminum produces small change in the temperature distribution of the heat sink which would be illustrated in both figures as in both figures one would observe that the temperature is concentrated at the base for both the aluminum and the copper heat sinks the reason for this is that the surface in which the central processing unit is attached to is the base of the heat sink resulting in direct contact between them plus the power dissipate by the processor would indeed increase temperature concentrated at the base of the heat sink. Here as shown in Table 2 below we have a temperature increase in copper of 2.38 % which signifies how small is the difference in performance between a aluminum heat sink and a copper heat sink showing that their biggest difference could be their ability to retain heat as stated before because copper does indeed absorb the temperature much better than the aluminum heat sink causing it to heat up fast thus needing a fan to help it cool faster while retaining the hot temperature truly endangering the heat sink from overheating.

FIGURE 9: TOTAL HEAT FLUX OF COPPER ALLOY HEAT SINK

FIGURE 10 : TOTAL HEAT FLUX OF ALUMINUM ALLOY HEAT SINK
Here we could compare the total heat flux flowing through both heat sinks with noticable differences in maximum value and minimum value this is with the same design and boundary conditions applied to both in the simulation with the only glaring difference is the material of each heat sink. Heat Flux is how much heat rate flows through the heat sink per unit of area per unit of time which shows how much heat flows through the heat sink as noticeable in the figures above the heat flux tends to concentrate on the roots of the fins the reason for this would be that the heat source is near the base of the plate and heat flow would be high towards that area where convection would happen as the air conditioned room with 23 degrees celsius would have heat flowing through it. Another noticeble difference is that the change in heat flux is also minimal like that of the temperature experienced of a heat sink at 1 s direct contact with the maximum surface temperature possible with these results one can assume that aluminum and copper heat sink’s almost perform similarly but other factors affect it the most. As shown in the table below the highest percent increase between the copper and the aluminum would be its minimum total heat flux with a approximately 4% increase in the heat flux which signifies that the copper even with its highest % increase is still a slight increase thus concluding that copper and aluminum will perform the same way in most factors in designing a heat sink and their most major difference is their ability to retain heat and the higher thermal conductivity of copper.

Results Copper Aluminum % increase in copper
Max Temp. 100 100 No Increase
Min Temp. 98.339 96.053 2.3799360769575144%
Max. Total Heat Flux 19728 19308 2.175264139216905%
Min. Total Heat Flux 289.79 278.43 4.080020112775209%
TABLE 2 : RESULTS OF STEADY STATE THERMAL ANALYSIS
Assesment
The Aluminum Heat Sink design would be more beneficial to than the copper heat sink because even with the way the heat sink was designed it made the differences between the aluminum and the copper heat sink minimal and the fact that a copper heat sink has a weakness of being able to retain heat as stronger than aluminum heat sink making copper heat sink’s the most common among all heat sinks to be used as an active heat sink which makes the already expensive copper heat sink more expensive.
Thus recommending the aluminum passive heat sink design is much more viable compared to the copper passive heat sink as shown in the temperature distribution of the aluminum and copper heat sink we could observe that the copper heat sink does indeed have better thermal conductivity but only raises this at a small amount , but with a aluminum heat sink which has better heat retention properties compared to the copper heat sink.

A weakness of the aluminum heat sink would be its longer time to absorb the heat compared to a copper heat sink which would absorb the heat much faster because of its higher thermal conductivity but the aluminum heat sink used in the design would be an aluminum alloy heat sink which is already documented and stated before to be able to compete with the copper heat sink ‘s ability to absorb heat from the heat source in this case woul be the central processing unit. The heat sink’s design of 8 fins computed by the formulas given before where among the many variants of a passive heat sink thus being available and can be found and bought at a store or at the web where you can order variants of a heat sink.

The heat sink’s design has its strenghts and weaknesses for the design had been computed with assumed varaibles which may change upon the actual testing and not only on testing by ansys software simulation where you would notice that the size of the heat sink or more on the base plate of the heat sink has dimension of 8.92 mm which is pretty thick for a base plate of a heat sink thus heat flux of the heat sink will be lower than expected but still efficient in its own way.

The heat sink’s design of both aluminum and copper as a potential material gives it the benefit of the doubt in weight as both tend to be light and could help the already small and compact new age of central processing units but as it has its own weakness of having a huge height for heat sinks this day and age let alone a passive heat sink which does not use any outside force to force a natural convection instead it uses a fan for the copper design of this heat sink to hide the weaknesses of copper but maintain its strenghts.This design of a heat sink provides a small and compact heat sink that can handle medium powered central processing units but maintain a cheap price because of not needing a fan it is most compatible with the aluminum material and not copper because of aluminum’s ability to release heat much better unlike copper who retains its temperature longer.

References :
Wikipedia Contributors. (n.d). Central Processing Unit. In Wikipedia, The Free Encyclopedia . Retrieved June 23, 2018, from https://en.wikipedia.org/wiki/Central_processing_unit.

Heatsink – Design and Selection, Fin Arrangements. (2018). Retrieved on July 13,2018 from https://www.abl-heatsinks.co.uk/heatsink/heatsink-selection-fin-arrangements.htm
Incropera, F. P., & DeWitt, D. P. (2002). Fundamentals of heat and mass transfer. New York: J. Wiley.

Discover The Benefits of a Precision Forged Heat Sink. (2018). pdf (pp. 1-6). Retrieved on July 15, 2018 from http://www.cooliance.com/pdfs/Discover_the_Benefits_of_A_Precision_Forged_Heatsink.pdf
Wikipedia Contributors.(n.d) Aluminium. In Wikipedia, The Freee Encyclopedia . Retrieved on June 24, 2018 ,from https://en.wikipedia.org/wiki/Aluminium
Reddy, C. S. (2015). Thermal Analysis of A Heat Sink for electric cooling Abstract. International Journal of Mechanical Engineering and Technology, 6(11), 145-153. Retrieved July 18, 2018, from http://www.iaeme.com/IJMET/issues.ajp?JType&VType=6&IType=11
What is a Heat Sink – Types and their Inportance. (2018). Retrieved on June 23, 2018, from https://www.elprocus.com/different-types-of-heat-sinks-and-their-importance/
APPENDIX

ISOMETRIC VIEW OF THE HEAT SINK

DETAILED DIMENSIONS OF THE FRONT VIEW OF THE HEAT SINK

DETAILED DIMESIONS OF THE TOP VIEW OF A HEAT SINK

DETAILE DIMENSIONS OF THE RIGHT SIDE VIEW OF THE HEAT SINK

HEAT SINK AND ITS PARTS