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Unformatted text preview: show that . ) ( ) ( = R dV dS F F n r 4. (a) Show that . | | ) ( 2 2 T T T T T + = (b) Suppose that at any time t , the temperature distribution ) , , , ( t z y x T over a domain D in 3 R satisfies the heat conduction equation T t T 2 = where the diffusivity is a constant. Suppose D is bounded by the surface . If either T = 0 or = = n T T n on , show that ( 29 . | | 2 2 2 1 dV T dV T t D D -=...
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- Spring '10