How to Calculate Temperature Distribution in a Composite Cylinder?

[Tezzador]

Homework Statement

I have a cylinder that's made up of three sections, brass, stainless steel, brass. There's a heat source at the top and a heat sink at the bottom. I know the overall heat transfer coefficient, power supplied to the heater, length, diameter, cross-sectional area of the cylinder. I also know the temperature of the heat sink, heat source and the average surface temperature. How do I go about it roughly?

Homework Equations

q" = -k * (dT/dx)

q = A * q" = (k/L) * A * (TL - TR)

L/Keq = L1/k1 + L2/k2 + L3/k3

The Attempt at a Solution

Can't figure it out.

 

[gabbagabbahey]

Hi Tezzador, welcome to PF!

What exactly is the question asking you to find?

Assuming you are asked to find the temperature at any given time everywhere inside the cylinder, you'll need to solve the 3D heat conduction equation, subject to the boundary conditions you are given. Start by choosing a coordinate system (I recommend cylindrical coordinates for obvious reasons!)...write your boundary conditions (temperature of the heat sink/source and average surface temp) and your heat conduction equation in that coordinate system, and then solve away!