Heat conduction through a layers of different materials

AI Thread Summary
The discussion revolves around understanding heat conduction through layers of different materials, specifically focusing on the equations governing heat transfer. The user initially struggles with the placement of area in the heat conduction equation, questioning why it appears in the numerator in the provided solution. They explore the implications of equal areas and conductivities, suggesting that if they were equal, adjustments could be made to the equation. The conversation indicates a need for clarification on algebraic manipulation in the context of thermal conductivity. Overall, the thread highlights the complexities of applying heat conduction principles in layered materials.
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Homework Statement


Question C(ii)
23513252_1863108113702914_1119620298_n.jpg

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Homework Equations


dQ/dt =-kA(dθ/dx)
dQ/dt = (θ1-θ2)/ ((lx/kxAx)+ (ly/kyAy))

The Attempt at a Solution


So the first time I tried at this question, I was using the second equation provided above,but when I check the answer, they put the area on the numerator. which left me wonder, how did they make it on top, I've check my textbook but none of it give any clues. If area is on the numerator with θ, I think k should be too isn't it?
 

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If Ax = Ay = A, you can multiply numerator and denominator by A, so A will appear in the numerator and not the denominator. You can do the same with k if kx = ky, but that is not the case in this problem.
 
I’ve moved this to the precalculus math forum where they can help you learn algebra.
 
mjc123 said:
If Ax = Ay = A, you can multiply numerator and denominator by A, so A will appear in the numerator and not the denominator. You can do the same with k if kx = ky, but that is not the case in this problem.
I see, thanks for your answer
 

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