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# hw4-addit_prob_a - Calculate using the numerical finite...

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∆x ˙ q, k ˙ q ∆x=L/4 Calculate, using the numerical finite difference procedure for one dimensional conduction, the steady state temperature in a long flat plate of 1m thickness (and also 1m width) with a uniform energy generation of 4 x 10 4 W/m 3 The surface at x = 0 is at a constant temperature of 120C, and the surface at x = L = 1 m loses heat by convection to air at 40C with a heat transfer coefficient h = 100 W / m 2 K . The plate thermal conductivity is k = 100 W/mk .. There is no heat transfer in the y or z directions. Take 5 points (nodes), T 0 , T 1 , T 3 , and T 4 with T0 = 120C = 393 K . Solve numerically for T 1 , T 2 , T 3 and T 4 . Doing an energy balance around node m=1, 2, or 3 E in - E ou t + E g = E st 0 for steady state L R st q q qV E - + = = & ( 29 1 1 ( ) ( ) 0 m m m m c c c T T T T kA kA q dxA x x - + - - � � - - - + = � � � � & ( 29 2 1 1 2 m m m q T T T x k + - + - = & x L T 0 T , h 0 1 2 3 4 m q L q R

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∆x/2 ˙ q Doing an energy balance around node m=4 E in - E ou t + E g = E st 0 for steady state cond conv st q q qV E - + = = & ( 29 ( ) 0 2 c c s c T dx kA hA T T q A x
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