In one stage of an annealing process, 304 stainless steel sheet is taken from \(300 \mathrm{~K}\) to \(1250 \mathrm{~K}\) as it passes through an electrically heated oven at a speed of \(V_{s}=12 \mathrm{~mm} / \mathrm{s}\). The sheet thickness and width are \(t_{s}=10 \mathrm{~mm}\) and \(W_{s}=\) \(3 \mathrm{~m}\), respectively, while the height, width, and length of the oven are \(H_{o}=3 \mathrm{~m}, W_{o}=3.4 \mathrm{~m}\), and \(L_{o}=30 \mathrm{~m}\), respectively. The top and four sides of the oven are exposed to ambient air and large surroundings, each at \(300 \mathrm{~K}\), and the corresponding surface temperature, convection coefficient, and emissivity are \(T_{s}=350 \mathrm{~K}, h=\) \(10 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), and \(\varepsilon_{s}=0.8\). The bottom surface of the oven is also at \(350 \mathrm{~K}\) and rests on a 0.5-m-thick concrete pad whose base is at \(300 \mathrm{~K}\). Estimate the required electric power input, \(P_{\text {elec }}\), to the oven.

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