A wall subject to intense radiative and convective heating is to be protected by sweat cooling. For this purpose water is injected onto the surface through a porous stainless steel plate at a rate sufficient to keep it wetted and to keep the surface temperature at \(360 \mathrm{~K}\). Bone-dry air at \(840 \mathrm{~K}\) and \(1 \mathrm{~atm}\) flows past the surface and causes a convective transport to the surface. In addition there is a radiation of \(461 \mathrm{~W} / \mathrm{m}^{2}\) impinging on the surface. The heat and mass transfer coefficients are estimated from the boundary layer. We use the following values: \(k_{\mathrm{m}}=0.02 \mathrm{~m} / \mathrm{s}\) and \(h=250 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\).

(i) Calculate the water flow rate needed to keep the surface at the desired temperature.

(ii) If the water comes from a cold reservoir, find the water temperature in this reservoir which would be required in order to maintain a steady state.