Quiz 2 - fluid T ∞ DERIVATION METHODOLOGY 1 Starting with...

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Wright State University Spring 2014 Department of Mechanical and Materials Engineering ME 3360/5360 HEAT TRANSFER: QUIZ 2 Open Book, Closed Notes, DO NOT Write on this Sheet Show All Work for Partial Credit Problem 1 (20 points): Heat is generated uniformly at a rate of ̇ in a solid ball of constant thermal conductivity k and radius r o . The ball is exposed to a fluid with a heat transfer coefficient of h . Neglecting the effects of thermal radiation, derive the following by using the methodology outlined below: a) The steady state surface temperature of the ball ( T s ) with respect to the free-stream temperature within the fluid ( T ). b) The steady state center temperature of the ball ( T o ) with respect to the free-stream temperature within the
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Unformatted text preview: fluid ( T ∞ ). DERIVATION METHODOLOGY: 1. Starting with the conservation of energy equation given below, cancel the appropriate terms using the appropriate assumptions. 2. Integrate the energy equation twice and apply the appropriate boundary conditions to evaluate integration constants. One of the boundary conditions to be used is that the surface temperature is T s . 3. Relate the surface temperature to the free-stream temperature within the fluid by performing a surface energy balance. ANSWERS: ´ µ ¶ ´ · ¸ ¹ º ̇ ±²³ »¼ ´ º ¶ ´ · ¸ ̇ ±²³ ( ¹ º »¼ ¸ ¹ º ½ ¾¿ ) CONSERVATION OF ENERGY EQUATION: Rectangular Coordinate System: Cylindrical Coordinate System: Spherical Coordinate System:...
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