$5-37$ Consider a $2-m-$long and $0\mathrm{.}7-$m$-$wide stainless$-$steel plate whose thickness is $0\mathrm{.}1$ m $.$ The left surface of the plate is exposed to a uniform heat flux of $2000\frac{W}{m^2}$ while the right surface of the plate is exposed to a convective environment at $0C$ with $h=400\frac{W}{m^2}*K.$ The thermal conductivity of the stainless steel plate can be assumed to vary linearly with temperature range as $k(T)=k_0(1+T)$ where $k_0=48\frac{W}{m}*K$ and $=9\mathrm{.}21{10}^{-4}{C}^{-1}.$ The stainless steel plate experiences a uniform volumetric heat generation at a rate of $8{10}^5\frac{W}{m^3}.$ Assuming steady state one$-$dimensional heat transfer, determine the temperature distribution along the plate thickness.