Chapter 2, Problem 2.10P

A one-dimensional plane wall of thickness $2L=100\text{mm}$ experiences uniform thermal energy generation of $\stackrel{.}{q}=1000{\text{W/m}}^{\text{3}}$ and is convectively cooled at $x=\pm 50\text{mm}$ by an ambient fluid characterized by $T_{\infty }=20°\text{C}\text{.}$ If the steady-state temperature distribution within the wall is $T\left(x\right)=a\left(L^2-x^2\right)+b$ where $a=10°{\text{C/m}}^{\text{2}}$ and $b=30°\text{C,}$ what is the thermal conductivity of the wall? What is the value of the convection heat transfer coefficient, h?