5-8 - CHAP 5 Finite Elements for Heat Transfer Problems 289...

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CHAP 5 Finite Elements for Heat Transfer Problems 289 8. Consider heat conduction in a uniaxial rod surrounded by a fluid. The right end of the rod is attached to a wall and is at temperature T R . One half of the bar is insulated as indicated. The free stream temperature is T f . There is convective heat transfer across the un-insulated surface of the rod as well as over the left end face. Use two equal-length elements to determine the temperature distribution in the rod. Use following numerical values: L = 0.2 m, k = 200 W/m/ o C, h = 36 W/m 2 / o C, T R = 600 o C, T f = 300 o C, A = 10 -4 m 2 , and P = 0.04 m. Solution: Write conduction matrices, convection matrix, and thermal loads due to convection: 12 (1) (2) (1) 23 (1) 11 (1) 2 1 1 .2 .2 .2 .2 [ ] , [ ] 1 1 .2 .2 .2 .2 2 1 .048 .024 1 21.6 [ ] , { } 1 2 .024 .048 2 21.6 62 TT f h kA L hPLT hPL T      
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5-8 - CHAP 5 Finite Elements for Heat Transfer Problems 289...

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