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Unformatted text preview: ME 608 Numerical Methods in Heat, Mass, and Momentum Transfer Assignment No: 3 Due Date: February 21, 2011 Instructor: J. Murthy Unless otherwise stated, use the finite volume method for discretization . Please submit an appropriately annotated printout of any code you write. 1. Consider unsteady conduction in a metallic foam (m) impregnated with a solid material such as a paraffin (p) . This type of material is sometimes used in phase-change cooling electronics. For the purposes of this problem, phase change may be ignored. Typical two-temperature formulations employ separate energy equations for the metal and the paraffin with a heat exchange term to model heat transfer between the two media. This is typically obtained from experimental correlations. The governing equations in 2D are: ( 1- ) m C pm T m t = x parenleftbigg ( 1- ) k m T m x parenrightbigg + y parenleftbigg ( 1- ) k m T m y parenrightbigg + hA s ( T p- T m ) p C pp T p t = x parenleftbigg k p T p x parenrightbigg + y parenleftbigg k p T p y parenrightbigg + hA s ( T m- T p ) Here, T m and T p are the temperatures of the metal and the paraffin respectively, is the porosity, h is the interfacial heat transfer coefficient ( W / m 2 K ), and A s is the surface-to-volume ratio of the porous medium (1...
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