Question

consider the following 1-D heat conduction problem. Two slabs of different width and materials are in contact with one another. Slab B is generating heat at a rate of $\dot{q}$ per unit volume. The temperature of the left boundary is T1 and the temperature of the right boundary is T2. Assume 1-D and steady state. The properties are listed as follows.

Constant properties:
T1 =300K, T2 =350K, k1 =200W/mK, k2 =400W/mK, $\dot{q}$ =1000W/m, L1=L2 =0.2m

Using the finite-difference approach, we can treat materials A and B as one combined computational domain and re-formulate the problem as:

Using grid points I= 1, 2, ..., 7 solve for the temperature at each grid point analytically

T2 2 T2 2

Answer 1