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Homework Statement
4 rectangular long fins are assembled on a 40x40x6 mm aluminum heat sink with the fins being 30 mm long, t=4 mm in thickness and 40 mm wide. The system generates 3 W and the room temp is maintained at 20 c. What is the temperature of the substrate surface that holds the fins, assuming the system is at steady state? The kinematic viscosity of air v=1.5x10^5 m2/s, specific heat of the gas Cp=1005j/kgk, thermal conductivity of air k=.026w/mk. For the aluminum, k=160w/mk.
hint: you will need to solve this through iterations. Assume a starting temp of substrate surface at 100c.
Homework Equations
This is part of the problem, i'm not sure which equations I need.
The Attempt at a Solution
At first i thought i could approach this using Θ/Θb which equals (ttinfinity)/(tbasetinifinty) with tinfinity being the room temp and setting it equal to e^(nx) where n=sqrt(2h/kt) and using this with q=haΔT but with x=0 to get surface temp, this simplfies to 1, which does not help. Next i tried using a u=1/h with q=uaΔT but i have no second equation to itterate against. I/m also not sure whether to use a qgeneration here because the heat is going through an aluminum block, but in this case I have no temperature for either side of the block and therefore nowhere to start, or if because this is at steady state I can assume q=3W.
I'm not asking anyone to go through and give me the exact number, just enough help to determine equations needed and point me in the right direction.
Thanks a lot for your help.
Homework Statement
Homework Equations
The Attempt at a Solution
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