- #1

roldy

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**1. Problem statement**

I've already posted this question in the advanced calculus help but it was suggested that I ask this in the physics forum. I can upload the pdf of my work again so I'll link to it https://www.physicsforums.com/attachment.php?attachmentid=31702&d=1296270924" from my other post. Two homogeneous rods have the same cross section, specific heat c, and density LaTeX Code: \\rho but different heat conductivities LaTeX Code: \\kappa 1 and LaTeX Code: \\kappa 2. Let kj=LaTeX Code: \\kappa j/(cLaTeX Code: \\rho ) be their diffusion constants. They are welded together so that the temperature u and the heat flux LaTeX Code: \\kappa ux at the weld are continuous. The left-hand rod has its left end maintained at temperature zero. The right-hand rod has its right end maintained at temperature T degrees.

Find the equilibrium temperature distribution in the composite rod.

## Homework Equations

q

_{x}=-kA[tex]\frac{dT}{dx}[/tex]

## The Attempt at a Solution

Solution is in linked above as a pdf with picture because it was easier to put the equations together using an external tool.

Equilibrium temperature distribution just means find the governing equation for the temperature of the rod, right?If that's the case then I just equate both q's and solve for T2. Another question I had about this problem is the specific heat c. Where does this come into play for solving this problem? Thanks for any help with this topic. It's been a little while since I've done any heat transfer stuff.

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