Chapter 2, Problem 2.67P

A composite one-dimensional plane wall is of overall thickness 2L. Material A spans the domain $-L\le x<0$ and experiences an exothermic chemical reaction leading to a uniform volumetric generation rate of $q_A.$ Material B spans the domain $0\le x\le L$ and undergoes an endothermic chemical reaction corresponding to a uniform volumetric generation rate of ${\stackrel{.}{q}}_B=-{\stackrel{.}{q}}_A$ . The surfaces at $x=\pm L$ are insulated. Sketch the steady-state temperature and heat flux distributions $T\left(x\right)$ and respectively, over the domain $-L\le x\le L$ for $k_A=k_B,k_A=0.5k_B,$ and $k_A=2k_B.$ Point out the important features of the distributions you have drawn. If ${\stackrel{.}{q}}_B=-2{\stackrel{.}{q}}_A,$ can you sketch the steady-state temperature distribution?