The fire brick of Example 12.10 is used to construct the walls of a brick oven. The irradiation on the inte- rior surface of the wall is G = 50,000 W/m2 and has a spectral distribution proportional to that of a black- body at 2000 K. The temperature of the gases adjacent to the inner wall of the oven is 500 K, and the convec- tion heat transfer coefficient is 25 W/m2. Find the wall surface temperature if the heat loss through the wall is negligible. If the brick wall is 0.1 m thick and of thermal conductivity kb = 1.0 W/m · K, and is insulated with a 0.1-m-thick layer of thermal conductivity ki = 0.05 W/m · K, what is the steady-state interior
(a) Determine the total emissivity s of the sample.
(b) Determine the total absorptivity a of the sample for irradiation from the enclosure walls.
(c) Perform an energy balance on the sample and determine the laser irradiation, Glaser, required to maintain the sample at Ts = 2000 K.
(d) Consider a cool-down process, when the laser and the inert gas flow are deactivated. Sketch the total emissivity as a function of the sample temperature, Ts(t), during the process. Identify key features, including the emissivity for the final condition (t l 00).
(e) Estimate the time to cool a sample from its operat- ing condition at Ts(0) = 2000 K to a safe-to-touch temperature of Ts(t) = 40°C. Use the lumped capacitance method and include the effect of con- vection to the inert gas with h = 50 W/m2 · K and T00 = Tenc = 300 K. The thermophysical properties of the sample material are p = 3900 kg/m3, cp = 760 J/kg · K, and k = 45 W/m · K.