Chapter 12, Problem 12.4P

A horizontal semitransparent plate is uniformly irradiated from above and below, while air at $T_{\infty }= 300K$ flows over the top and bottom surfaces, providing a uniform convection heat transfer coefficient of $\text{h = 40 }W/m^2\cdot K$ . The absorptivity of the plate to the irradiation is 0.40. Under steady-state conditions measurements made with a radiation detector above the top surface indicate a radiosity (which includes trans- mission, as well as reflection and emission) of $\text{J = 5000 }W/m^2$ , while the plate is at a uniform temperature of $\text{T = 350K}$ .

Determine the irradiation G and the emissivity of the plate. Is the plate gray ( $\epsilon =\alpha$ ) for the prescribed conditions?