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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 phasechange cooling electronics. For the purposes of this problem, phase change may be ignored. Typical twotemperature 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 surfacetovolume ratio of the porous medium (1...
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