HEAT TRANSFER QUESTION (PHYSICS)

Question

Two different metal plates A and B are joined together as shown. The temperature on the side of metal A is at 150oC, while the temperature on the side of metal B is at 40oC. If Metal A has a thermal conductivity of 206 W/m-K, and metal B has a thermal conductivity of 390 W/m-K, determine the temperature between the two metal plates.

Answer 1

You need the thickness of the plates if they are side by side.

The expression for the heat flux (J/m²s) = -k_i ΔT/t_i where t is thickness of the plate and i = A or B

The flux is steady: -k_A(T_C - 150)/t_A = -k_B(40 - T_C)/t_B with T_C being the temperature between the two metals.

If t_A = t_B then k_A(140 -T_C) = k_B(T_C-40) and multiply out, group terms, and isolate T_C