A large steel plate having a thickness of L = 4 in, thermal conductivity of k= 7.2 Btu/h·ft. °F, and an emissivity of ε = 0.7 is lying on the ground. The exposed surface of the plate at x = L is known to exchange heat by convection with the ambient air at T∞ = 90°F with an average heat transfer coefficient of h = 12 Btu/h·ft².°F as well as by radiation with the open sky with an equivalent sky temperature of Tsky =480 R. Also, the temperature of the upper surface of the plate is measured to be 80°F. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the plate, (b) obtain a relation for the variation of temperature in the plate by solving the differential equation, and (c) determine the value of the lower surface temperature of the plate at x = 0. Tsky h, To Convection Radiation XA 80°F L E Plate 0 Ground

The temperature of a cylindrical tank containing liquid nitrogen is -10 ° C. Tank diameter is 16 cm. The amount of heat lost by convection and radiation from the tank to the environment is 65.5 W / m. Calculate the temperature of the environment where the tank is located: h = 4.35 W / m2K, ∈ = 1.

The thermal conductivities of human tissues vary greatly. “Fat” and “skin” have conductivities of approximately 0.200 W /m 0K and 0.0200 W /m 0K, respectively, while other “tissues” inside the body have conductivities of approximately 0.500 W /m 0 Assume that between the core region of the body and the skin surface lies a “skin” layer of 1.00mm, a “fat” layer of 0.500 cm., and 3.20 cm. layer of other “tissues”. A)Find the R-factor for each of these three layers, and the R-factor for all layers taken together

= A processing plant is convectively heating a solid half-sphere of radius of 12 cm made of pure aluminum (k 237 W/m-K) by placing it on an insulated surface as shown in Fig. 1. It is exposed to hot exhaust gas at 300°C with a convection coefficient of 180 W/m².K. Is the lumped capacitance approximation valid? Figure 1: Half-sphere