Thermodynamics HW Solutions 436

Thermodynamics HW Solutions 436 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction 5-46 A long solid body is subjected to steady two-dimensional heat transfer. The unknown nodal temperatures and the rate of heat loss from the bottom surface through a 1-m long section are to be determined. Assumptions 1 Heat transfer through the body is given to be steady and two-dimensional. 2 Heat is generated uniformly in the body. 3 Radiation heat transfer is negligible. Properties The thermal conductivity is given to be k = 45 W/m °C. Analysis The nodal spacing is given to be Δ x = Δ x = l =0.05 m, and the general finite difference form of an interior node for steady two-dimensional heat conduction is expressed as TTT T T gl k left top right bottom node node ++ + + = 40 2 & h, T Insulated 240 200°C 350 260 305 290 3 1 2 5 cm 325 Convection g where C 5 . 93 C W/m 214 ) m 05 . 0 )( W/m 10 8 ( 2 3 6 2 0 2 node ° = ° × = = k l g k l g & & The finite difference equations for boundary nodes are obtained by applying an energy balance on the volume
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