Heat Transfer Between Two Rods in Contact

roldy
1.Two homogeneous rods have the same cross section, specific heat c, and density $$\rho$$ but different heat conductivities $$\kappa$$1 and $$\kappa$$2. Let kj=$$\kappa$$j/(c$$\rho$$) be their diffusion constants. They are welded together so that the temperature u and the heat flux $$\kappa$$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

qx=-kA$$\frac{dT}{dx}$$

The Attempt at a Solution

Solution is in attached 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.

Attachments

• Composite Rod.pdf
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