Chapter 3, Problem 3.85P

Consider a plane composite wall that is composed of three materials (materials A, B, and C are arranged left to right) of thermal conductivities $k_A=0.24\text{W/m}\cdot \text{K,}{k}_B=0.13\text{W/m}\cdot \text{K,}$ and $k_C=0.50\text{W/m}\cdot \text{K}\text{.}$ The thicknesses of the three sections of the wall are $L_A=20\text{mm,}{L}_B=13\text{mm,}$ and $L_C=20\text{mm}\text{.}$ A contact resistance of $R_{t,c}={10}^{-2}{\text{m}}^{\text{2}}\cdot \text{K/W}$ exists at the interface between materials A and B, as well as at the interface between materials B and C. The left face of the composite wall is insulated, while the right face is exposed to convective conditions characterized by $h=10\text{}{\text{W/m}}^{\text{2}}\cdot \text{K,}{T}_{\infty }=20°\text{C}\text{.}$ For Case 1, thermal energy is generated within material A at the rate ${\stackrel{.}{q}}_A=5000{\text{W/m}}^{\text{3}}.$ For Case 2, thermal energy is generated within material C at the rate ${\stackrel{.}{q}}_C=5000{\text{W/m}}^{\text{3}}.$

1. Determine the maximum temperature within composite wall under steady-state conditions for Case 1.
2. Sketch the steady-state temperature distribution on $T-x$ coordinates for Case 1.
3. Sketch the steady-state temperature distribution for Case 2 on the same $T-x$ coordinates used for Case 1.