(35 points) A horizontal solid plate has simultaneous conduction, convection, and radiation modes of heat transfer....

 

 

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(35 points) A horizontal solid plate has simultaneous conduction, convection, and radiation modes of heat transfer. On the top side of the plate, air is flowing at Too,air = 260C with htop = 40 W/mK. Additionally, the top of the plate is irradiated with G = 1450 W/m, and 435 W/m is reflected from the top surface. On the bottom of the plate, water flows adjacent to the bottom surface of the plate and is at a bulk temperature of T,w = 22C. The plate has thickness L = 21 mm and thermal conductivity k = 25 W/mK. At steady-state, the top and bottom of the plate have constant surface temperatures T = 43C and T = 35C, respectively. The plate is an opaque medium and a diffuse emitter. Evaluate the system at steady state. Heat generation is negligible in the plate. Assume 1-D conduction along the thickness of the plate. Air x Too,air htop Tt L Th Water Too,W hbottom (a) Determine the transmissivity, reflectivity, and absorptivity of the plate. (b) Write the surface energy balance expression for the top surface of the plate. Hint: We must account for conduction in the plate. There are radiation, convection, and conduction components. (c) Using the energy balance in (b), determine the emissivity of the plate. (d) What is the radiosity J associated with the top of the plate? (e) Write the surface energy balance expression for the bottom surface of the plate. (f) Using the energy balance in (e), determine the convection heat transfer coefficient hbottom associated with the water flow at the bottom of the plate? (35 points) A horizontal solid plate has simultaneous conduction, convection, and radiation modes of heat transfer. On the top side of the plate, air is flowing at Too,air = 260C with htop = 40 W/mK. Additionally, the top of the plate is irradiated with G = 1450 W/m, and 435 W/m is reflected from the top surface. On the bottom of the plate, water flows adjacent to the bottom surface of the plate and is at a bulk temperature of T,w = 22C. The plate has thickness L = 21 mm and thermal conductivity k = 25 W/mK. At steady-state, the top and bottom of the plate have constant surface temperatures T = 43C and T = 35C, respectively. The plate is an opaque medium and a diffuse emitter. Evaluate the system at steady state. Heat generation is negligible in the plate. Assume 1-D conduction along the thickness of the plate. Air x Too,air htop Tt L Th Water Too,W hbottom (a) Determine the transmissivity, reflectivity, and absorptivity of the plate. (b) Write the surface energy balance expression for the top surface of the plate. Hint: We must account for conduction in the plate. There are radiation, convection, and conduction components. (c) Using the energy balance in (b), determine the emissivity of the plate. (d) What is the radiosity J associated with the top of the plate? (e) Write the surface energy balance expression for the bottom surface of the plate. (f) Using the energy balance in (e), determine the convection heat transfer coefficient hbottom associated with the water flow at the bottom of the plate?