Solve This Problem I Made

[AHaskin14]

So I'm a 3rd Year Mechanical Engineering Student. My Heat Transfer Professor asked us to write our own problem for homework. Seeing as though I liked computers, here's my submission. Note that all the material properties are completely made up. Enjoy! Post your answer if you're actually capable!

 

Intel’s flagship i7-6950X processor has a TDP of 140 W. After purchasing this $1750 processor Adam can only afford a small heat sink and has no money left over for thermal compound. Adam researches online to find that toothpaste can work as a substitute thermal compound as it has a thermal resistivity of only R=.25 K/W. Wanting to be better safe than sorry, Adam finds a cheap thermal paste online that claims a thermal resistivity of R=.2 K/W. Adam scours product pages to find that his heat sink has 40 different fins that are 45 cm^2 and is capable of a convection coefficient of h=60 W/m^2K. He then determines through the BIOS and sensors on his motherboard that the ambient temperature of his case is Tinf= 38'C . If Intel advises maintaining your CPU below 85'C and most people like to stay below 80'C for safety, is the thermal compound a worthwhile purchase? Ignore Radiation and conduction through the heat sink.

 

BTW don't missinterpret this as I don't know the answer at all. I made the problem based on answers I created beforehand, I want to see if you've got the guts.

[Mira Yurizaki]

Whether or not the cooling system is capable of keeping the processor within temperature is entirely up to how much load you're putting on it. And if we assume power consumption = TDP.

[AHaskin14]

4 minutes ago, M.Yurizaki said:

Whether or not the cooling system is capable of keeping the processor within temperature is entirely up to how much load you're putting on it. And if we assume power consumption = TDP.

A system would theoretically only fail if pushed to its limit

[Guest]

13 minutes ago, AHaskin14 said:

snip

My answer is that Adam should have bought a cheaper CPU to buy thermal paste. Or not have bought both Toothpaste and Thermal paste to find alternatives to thermal paste.  

[dany_boy]

16 minutes ago, AHaskin14 said:

thermal resistivity of only R=.25 K/W. Wanting to be better safe than sorry, Adam finds a cheap thermal paste online that claims a thermal resistivity of R=.2 K/W.

Don't you need to know the thermal conductivity and not the thermal resistance? Also you would need to know the thickness of the interface material between your heat source and your heat sink. I may be wrong though

[AHaskin14]

2 minutes ago, dany_boy said:

Don't you need to know the thermal conductivity and not the thermal resistance? Also you would need to know the thickness of the interface material between your heat source and your heat sink. I may be wrong though

You're absolutely right. You would need a lot more information to get a real and precise answer. This is just a more simplified approach.

 

[AHaskin14]

3 minutes ago, dany_boy said:

Don't you need to know the thermal conductivity and not the thermal resistance? Also you would need to know the thickness of the interface material between your heat source and your heat sink. I may be wrong though

And I used thermal resistance to make it an easy equivalent circuit problem

[MorganO]

the headtsink comes with thermal paste? most do

[AHaskin14]

1 minute ago, KOMTechAndGaming said:

the headtsink comes with thermal paste? most do

Well this one was so cheap that it didn't.

[dany_boy]

I just love how everyone is trying to pick apart your problem like they have never taken a physics class Nobody is actually trying to solve it or to comment on the phenomenon

[Guest]

5 minutes ago, dany_boy said:

I just love how everyone is trying to pick apart your problem like they have never taken a physics class Nobody is actually trying to solve it or to comment on the phenomenon

I took a physics class I just didn't learn this in it.

[dany_boy]

2 minutes ago, fpo said:

I took a physics class I just didn't learn this in it.

Neither did I, but at some point in basic thermodynamics I got curious and investigated into heat propagation and dissipation. I still remember some basic stuff

[CostcoSamples]

What a cool problem!  I have completely forgotten all of this stuff.  What equations should I be looking for?  Conceptually, the rate of heat transfer depends on the steady state temperature gradient across the system.  I'm pretty sure this involves a bit of calculus to solve.

[Guest]

3 minutes ago, dany_boy said:

Neither did I, but at some point in basic thermodynamics I got curious and investigated into heat propagation and dissipation. I still remember some basic stuff

I just took a basic physics class in HS. I don't think we got to thermal dynamics. If OP provided an equation to use I would have been able to try but I am not an engineering/physics student so I have no idea how to solve this.

[AHaskin14]

2 hours ago, CostcoSamples said:

What a cool problem!  I have completely forgotten all of this stuff.  What equations should I be looking for?  Conceptually, the rate of heat transfer depends on the steady state temperature gradient across the system.  I'm pretty sure this involves a bit of calculus to solve.

Finally someone who has some idea. It's set up so that you have two resistors in series. The first resistor is the different thermal solutions, the second is the convection from the heat sink, represented by the equation 1/hA where A is the total surface area of the radiator. Combine to make an equivalemt resistance, and solve using the equation q=(delta T) / (Req). Simple enough,

[AHaskin14]

2 hours ago, fpo said:

I just took a basic physics class in HS. I don't think we got to thermal dynamics. If OP provided an equation to use I would have been able to try but I am not an engineering/physics student so I have no idea how to solve this.

I see your point in not having equations provided. Unfortunately it's a nothing from high school, but rather a 400 level college course, so our professor expects us to have all relevant equations memorized. Certainly not common knowledge.

[Guest]

58 minutes ago, AHaskin14 said:

I see your point in not having equations provided. Unfortunately it's a nothing from high school, but rather a 400 level college course, so our professor expects us to have all relevant equations memorized. Certainly not common knowledge.

Yeah that's what I figured. This stuff is really complex; at least for me.

[Beef Boss]

4 hours ago, AHaskin14 said:

You're absolutely right. You would need a lot more information to get a real and precise answer. This is just a more simplified approach.

 

Well if there's less resistance,  there's more conductivity,  is there not? 

[AHaskin14]

1 minute ago, BadluckBrian said:

Well if there's less resistance,  there's more conductivity,  is there not? 

correct