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 1Heat 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. PropertiesThe thermal conductivity is given to be k= 45 W/m⋅°C. Analysis The nodal spacing is given to be Δx=Δx=l=0.05 m, and the general finite difference form of an interior node for steady two-dimensional heat conduction is expressed as TTTTTglklefttoprightbottomnodenode+++−+=402&h, T∞Insulated••••••••••••••••240200°C3502603052903125 cm325Convectiongwhere C5.93CW/m214)m05.0)(W/m108(236202node°=°⋅×==klgklg&&The finite difference equations for boundary nodes are obtained by applying an energy balance on the volume
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