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Sample Problem

EIT Certification Heat Transfer

Cooling a CPU

#062

A square silicon chip (k = 150 W/m∙K) is of width w = 7 mm on a side and of thickness t = 2 mm. The chip is mounted in a substrate such that its side and back surfaces are insulated, while the front surface is exposed to a coolant. If 60 W are being dissipated in circuits mounted to the back surface of the chip, what is the steady-state temperature difference between back and front surfaces?

Hint

Fourier's law:

P=q=kAΔTtP=q=kA\frac{\Delta T}{t}

Solution

Assumptions: (1) Steady state conditions, (2) Constant properties, (3) Uniform heat dissipation, (4) Negligible heat loss from back and sides, (5) One-dimensional conduction chip.

All the electrical power dissipated at the chip's back surface is transferred by conduction. From Fourier's law:

P=q=kAΔTtP=q=kA\frac{\Delta T}{t}

Rearranging the formula to solve for the temperature difference:

ΔT=t⋅Pkw2=0.002m⋅60W150W/m⋅K(0.007m)2=16.33K\Delta T=\frac{t\cdot P}{kw^{2}}=\frac{0.002m\cdot 60W}{150W/m\cdot K(0.007m)^{2}}=16.33K

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Hi, I'm Kevin!

Mechanical Engineer based in Los Angeles, California. 10+ years of combined experience across multiple Fortune 100 companies, designing and building fighter/commercial jets, nuclear missiles, robots, classified weapon systems, NASA space vehicles, and more!

I'll be your instructor for this small passion project of mine. Always found the lack of MechE interview prep resources frustrating, especially compared to our coding counterparts. So, I created this centralized solution to practice for my own technical interviews, and to continually refresh the undergrad fundamentals that aren't always used while in industry. ¯\_(ツ)_/¯

Figured others could benefit, so please join me! No strings attached, seriously. I just enjoy optimizing designs/processes, building products, & trying new things :)

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