5-4 - CHAP 5 Finite Elements for Heat Transfer Problems 283...

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CHAP 5 Finite Elements for Heat Transfer Problems 283 4. Determine the temperature distribution (nodal temperatures) of the structure shown in the figure using two equal length, linear finite elements with the cross-sectional area of 1 m 2 . The thermal conductivity is 10 W/m ºC. The left side is maintained at 300 ºC. The right side is subjected to heat loss by convection with h = 1 W/m 2 ºC and T f = 30 ºC. All other sides are insulated. Solution: Element 1: 1 1 1 2 2 11 0.5 q T kA T q L         Element 2: 22 2 3 33 () 0.5 f T qq T q hAT T L      2 2 2 3 1 1 0 0 1 1 0 0.5 f T q hA T hAT L     Assembling: 2 3 1 1 0 1 2 1 0 0 1 2 f Tq T T hAT  
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