Chapter 12, Problem 12.69P

An opaque, horizontal plate has a thickness of $L=21mm$ and thermal conductivity $k=25W/m\cdot K$ . Water flows adjacent to the bottom of the plate and is at a temperature of $T_{\infty ,w}={25}^{\circ }C$ . Air flows above the plateat $T_{\infty ,\alpha }={260}^{\circ }C$ withha $h_a=40W/m^2$ . The top of the plate is diffuse and is irradiated with $G=1450W/m^2$ ,of which $435W/m^2$ is reflected. The steady-state top and bottom plate temperatures are $T_t={43}^{\circ }C{\text{ and T}}_b={35}^{\circ }C$ , respectively. Determine the transmissivity, reflectivity, absorptivity, and emissivity of the plate. Is the plate gray? What is the radiosity associated with the top of the plate? What is the convection heat transfer coefficient associated with the water flow?