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Unformatted text preview: ME 608 Numerical Methods in Heat, Mass, and Momentum Transfer Solution to Assignment No: 1 Due Date: January 24, 2011 Instructor: J. Murthy 1. The governing equation for unsteady flow of a Newtonian fluid is: t ( u )+ x ( uu )+ y ( vu )+ z ( wu ) = P x + b x + x parenleftbigg parenleftbigg 2 u x parenrightbigg 2 3 V parenrightbigg + y parenleftbigg parenleftbigg u y + v x parenrightbiggparenrightbigg + z parenleftbigg parenleftbigg u z + w x parenrightbiggparenrightbigg (a) Comparing with general scalar transport equation, =u, = and S = P x + b x + x parenleftbigg u x parenrightbigg + y parenleftbigg v x parenrightbigg + z parenleftbigg w x parenrightbigg 2 3 x ( V ) (b) When = constant and = constant, = u, = . Since V =0, we can show that S = P x + b x (c) When negationslash = constant and = constant, =u, = and S = P x + b x + x parenleftbigg u x parenrightbigg + y parenleftbigg v x parenrightbigg + z parenleftbigg w x parenrightbigg (d) When = constant and negationslash = constant, =u, = and S = P x + b x 2 3 x ( V )+ x ( V ) = P x + b x 2. (a) Source integration:2....
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