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A plane wall (k = 10 W/m °C) of thickness 50 cm has its exterior surface subjected to a convection environment of 30 °C with a surface heat transfer coefficient of 600 W/m2 °C. Determine the temperature distribution in the plane wall using
(a) four linear elements
(b) one quadratic element and
(c) one modified quadratic element with only two nodes. Compare the results with the analytical solution. If the heat transfer coefficient increases to 10,000 W/m2 °C, what happens to the temperature of the exterior surface?
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