A fired heater is designed to produce superheated steam at a temperature of \(300^{\circ} \mathrm{C}\) and a pressure of \(15 \mathrm{~atm}\). The steam is carried in tubes ( \(4 \mathrm{~cm}\) inside diameter) composed of a high temperature alloy \((k=40 \mathrm{~W} / \mathrm{mK}) 3 \mathrm{~mm}\) thick. The tube walls are heated by radiative exchange with the walls of the furnace \(\left(T_{\text {wall }}=1100^{\circ} \mathrm{C}\right)\). What is heat flux into the fluid assuming the inside wall temperature is \(300^{\circ} \mathrm{C}\) ? You will probably have to solve this problem numerically/iteratively. Assume that the heat transfer via radiation obeys:

\[q_{\text {rad }}=\sigma^{r} A_{s}\left(T_{\text {wall }}^{4}-T_{\text {pipe }}^{4}\right)\]