as3-sol - ME 608 Numerical Methods in Heat, Mass, and...

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Unformatted text preview: ME 608 Numerical Methods in Heat, Mass, and Momentum Transfer Solution to Assignment No: 3 Due Date: February 21, 2011 Instructor: J. Murthy 1. (a) Non-dimensionalizing the governing equations using m = T m T 1 T 2 T 1 and p = T p T 1 T 2 T 1 , x = x / D , y = y / D , and = m t / D 2 : ( 1 ) m = x parenleftbigg ( 1 ) m x parenrightbigg + y parenleftbigg ( 1 ) m y parenrightbigg + hA s D 2 k m ( p m ) m p p = x parenleftbigg p x parenrightbigg + y parenleftbigg p y parenrightbigg + hA s D 2 k m k m k p ( m p ) The dimensionless parameters governing the problem are , the diffusivity ratio m / p , the conductivity ratio k m / k p , and the interface heat transfer parameter H = hA s D 2 k m . (b) Typical discrete equations for control volumes 1,2 and 3 in Fig. 1 are given below. For the metal: Point 1 a E = k m ( 1 ) y / x ; a W = k m ( 1 ) y / x ; a N = k m ( 1 ) x / y ; a S = k m ( 1 ) x / y a p = m c pm ( 1 ) x y t ; a P = nb a nb + a p + hA s x y ; b = hA s x yT p + a p T m Point 2 a E = k m ( 1 ) y / x ; a W = 0; a N = k m ( 1 ) x / y ; a S = k m ( 1 ) x / y ; a bw = 2 k m ( 1 ) y / x a p = m c pm ( 1 ) x y t ; a P = nb a nb + a bw + a p + hA s x y ; b = hA s x yT p + a bw T m , bw + a p T m Point 3 a E = k m ( 1 ) y / x ; a W = 0; a N = k m ( 1 ) x / y ; a S = 0; a bs = 2 k m ( 1 ) x / y a bw = 2 k m ( 1 ) y / x a p = m c pm ( 1 ) x y t ; a P = nb a nb + a bw + a bs + a p + hA s x y b = hA s x yT p + a bw T m , bw + a bs T m , bs + a p T m For the paraffin: Point 1 a E = k p y / x ; a W = k p y / x ; a N = k p x / y ; a S = k p x / y a p = p c pp x y t ; a P = nb a nb + a p + hA s x y ; b = hA s x yT m + a p T p Point 2 a E = k p y / x ; a W = 0;...
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This note was uploaded on 12/29/2011 for the course ME 608 taught by Professor Na during the Fall '10 term at Purdue University-West Lafayette.

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as3-sol - ME 608 Numerical Methods in Heat, Mass, and...

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