final - ME 364 Elementary Heat Transfer Summer 2006 Final...

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ME 364: Elementary Heat Transfer Summer 2006 Final Examination Time: 2 Hours, 30 minutes Total Points: 40 Open Book, Open Notes and Open Homework. No other printed/photocopied material. 1. Short answer questions/problems. (a) (3 points) A slab of width L has thermal conductivity that varies according to the law ( 29 T k k α + = 1 0 , where k 0 is a reference value, α is a positive constant, and T is the temperature (in other words, the conductivity is higher where the temperature is higher). Sketch the temperature profile within the slab if it experiences 1-dimensional steady state conduction without internal generation. Assume T ( x = 0) = T 1 , T ( x = L ) = T 2 , T 1 > T 2 . Briefly explain the shape of the profile you sketch. (b) (2 points) In a particular application involving airflow over a heated surface, the boundary layer temperature distribution may be approximated as - - = - - ν y u T T T T s s Pr exp 1 where y is the distance normal to the surface. Assume Pr = 0.7, T = 400 K, T s = 300 K, and u = 5000 m -1 . Assume air conductivity equal to 0.026 W/m-K. Calculate the surface heat flux and the heat transfer coefficient.
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(c) (3 points) Calculate the percentage increase in the average heat transfer coefficient for a vertical isothermal plate if the initial plate height, L = 1 m, is doubled. The
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