In an experiment a porous plate of silicon carbide (ksiC = 490 W/m-K), with a heat transfer area of 0.5 m2, 15cm thick is cooled by a cryogenic fluid. Assume that the cryogenic fluid's volume is small and does not effect the material properties of the SiC plate. The cryogenic fluid acts like a heat sink in the plate with some volumetric heat rate (W/m3). The walls of the plate are insulated, 5-cm thick on each side and kin = 0.05 W/m-K. On the outside of the insulation flows a fluid at 300oC and an h=1500 W/m2-K. The plate is symmetric about the centerline. Use the thermal resistance methodology to determine your answers.
1. What is the thermal resistance of the SiC plate, the insulation and the convective boundary layer.
2. Determine the volumetric heat rate provided by the cryogenic coolant that will maintain the SiC plate's centerline temperature at 0oC.
3. Determine the temperature at the interface of the SiC plate and the insulation.
4. Determine the temperature at the outer edge of the insulation.
5. What is the temperature change across the boundary layer?