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hw05soln - 1 A furnace of cubical shape with external...

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1. A furnace of cubical shape with external dimensions of 0.35 m is constructed from a refractory brick having thermal conductivity k=1.15 W/m•K. If the wall thickness is 50 mm, the inner surface temperature is 600°C, and the outer surface temperature is 75°C, calculate the heat loss from the furnace. 0.35 m 0.05 m L Plane wall 25 . 1 05 . 0 ) 25 . 0 )( 25 . 0 ( L A S W = = = m Edge 135 . 0 ) 25 . 0 )( 54 . 0 ( L 54 . 0 S E = = = m Corner 0075 . 0 ) 05 . 0 )( 15 . 0 ( t 15 . 0 S C = = = m ) T T )( S 8 S 12 S 6 ( k ) T T ( kS q 2 1 C E W 2 1 - + + = - = = ) 75 600 )( 0075 . 0 8 135 . 0 12 ) 25 . 1 6 )( 15 . 1 ( - × + × + × =5.5 kW 2. A solid having volume V, surface area A s , and thermal conductivity k is exposed to a fluid with convective heat transfer coefficient h and ambient temperature T . For Biot number Bi<<1, (a) The solid’s spatial temperature distribution is uniform (isothermal) at each instant in time. Why??? (b) For an initial solid temperature T i , derive the temperature in the solid as a function of time and the total heat transfer rate. (a) The temperature gradient in the solid is small compared to the fluid. Relative to
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