Derivation process? (Heatsink Fin Heat Conduction Equations)

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Homework Help Overview

The discussion revolves around the derivation process related to heat conduction equations for heatsink fins. Participants are examining the mathematical relationships and assumptions involved in the equations presented.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand the derivation of a specific term in the heat conduction equation and questions the absence of a constant in the temperature variation. They also express confusion regarding the equivalence of heat transfer rates at different points. Other participants suggest corrections to equations and clarify the reasoning behind differentiating temperature with respect to position.

Discussion Status

The discussion is active, with participants providing clarifications and corrections to the original poster's understanding. Some guidance has been offered regarding the differentiation of temperature and the treatment of constants in the equations.

Contextual Notes

There appears to be some confusion regarding the assumptions made in the derivation, particularly concerning the treatment of boundary conditions and constants in the equations. The original poster is working within the constraints of a homework assignment, which may limit the information available for discussion.

EastWindBreaks
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Homework Statement


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I don't understand the derivation of the right side of the last equation.

Homework Equations

The Attempt at a Solution



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I got to this point, I also don't understand why it did not include C_2 for the variation of temp. along the fin.
I am guessing the right side is the rate of heat transfer on the tip? which equals to the rate of heat transfer at x=0 under steady state. but i failed to see how they are equivalent, I don't understand where did sqrt( hpkA)*(Tb-T_inf) came from. any help would be appreciated!

 

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Your second equation should be θb = θ(0) = C1 + C2, instead of 2. and since C1 = 0, C2 = θb. Now when you differentiate θ(x) wrt x and multiply both sides by -kA at x=0, it should work out OK.
 
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Dr Dr news said:
Your second equation should be θb = θ(0) = C1 + C2, instead of 2. and since C1 = 0, C2 = θb. Now when you differentiate θ(x) wrt x and multiply both sides by -kA at x=0, it should work out OK.
thank you, I got it now. the reason we differentiate θ(x) is because T_inf is treated as a constant right? therefore it is same as dT/dx.
 
Last edited:
That is correct.
 
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