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 ${\stackrel{.}{q}}_{\text{A}}.$ Material B spans the domain $0\le x\le L$ and undergoes an endothermic chemical reaction corresponding to a uniform volumetric generation rate of ${\stackrel{.}{q}}_{\text{B}}=-{\stackrel{.}{q}}_{\text{A}}.$ The surfaces at $x=\pm L$ are insulated. Sketch the steady-state temperature and heat flux distributions $T\left(x\right)$ and $q_x^{"}\left(x\right),$ respectively, over the domain $-L\le x\le L$ for $k_{\text{A}}=k_B,k_{\text{A}}=0.5k_B,$ and $k_A=2k_B.$ Point out the important features of the distributions you have drawn. If ${\stackrel{.}{q}}_B=-2{\stackrel{.}{q}}_{\text{A}},$ can you sketch the steady-state temperature distribution?