Chapter 1, Problem 1.53P

In one stage of an annealing process, 304 stainless steel sheet is taken from 300 K to 1250 K as it passes through an electrically heated oven at a speed of $V_s=10\text{mm/s}\text{.}$ The sheet thickness and width are $t_s=8\text{mm}$ and $W_s=2\text{m,}$ respectively, while the height, width, and length of the oven are $H_o=2\text{m,}{W}_o=2.4\text{m,}$ and $L_o=25\text{m,}$ respectively. The top and four sides of the oven are exposed to ambient air and large surroundings, each at 300 K, and the corresponding surface temperature, convection coefficient, and emissivity are $T_s=350\text{K,}h=10{\text{W/m}}^{\text{2}}\cdot \text{K,}$ and ${\epsilon }_s=\mathrm{0.8.}$ The bottom surface of the oven is also at 350 K and rests on a 0.5-m-thick concrete pad whose base is at 300 K. Estimate the required electric power input, $P_{\text{elec}},$ to the oven.