Chapter 5, Problem 5.35P

A horizontal structure consists of an $L_A=10-$ mm-thick layer of copper and an $L_B=10$ -mm-thick layer of aluminum. The bottom surface of the composite structure receives a heat flux of $q"=100{\text{kW/m}}^{\text{2}},$ while the top surface is exposed to convective conditions characterized by $h=40{\text{W/m}}^{\text{2}}\cdot \text{K,}{T}_{\infty }=25°\text{C}\text{.}$ The initial temperature of both materials is $T_{i,A}=T_{i,B}=25°\text{C,}$ and a
contact resistance of $R_{t,c}^{"}=400\times {10}^{-6}{\text{m}}^{\text{2}}\cdot \text{K/W}$ exists at the interface between the two materials.

1. Determine the times at which the copper and aluminum each reach a temperature of $T_f=90°\text{C}\text{.}$ The copper layer is on the bottom.
2. Repeat part (a) with the copper layer on the top. Hint: Modify Equation 5.15 to include a term associated with heat transfer across the contact resistance. Apply the modified form of Equation 5.15 to each of the two slabs. See Comment 3 of Example 5.2.