problem4-76 - PROBLEM 4.76 KNOWN: Nodal network and...

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PROBLEM 4.76 KNOWN: Nodal network and boundary conditions for a water-cooled cold plate. FIND: (a) Steady-state temperature distribution for prescribed conditions, (b) Means by which operation ay be extended to larger heat fluxes. m SCHEMATIC: A SSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional conduction, (3) Constant properties. ANALYSIS: Finite-difference equations must be obtained for each of the 28 nodes. Applying the nergy balance method to regions 1 and 5, which are similar, it follows that e Node 1: ( ) ( ) ( ) ( ) 26 yxT xyT yx xyT 0 ⎡⎤ ΔΔ +ΔΔ −ΔΔ+ΔΔ = ⎣⎦ 1 Node 5: ( ) ( ) ( ) ( ) 41 0 = 5 Nodal regions 2, 3 and 4 are similar, and the energy balance method yields a finite-difference equation of he form t Nodes 2,3,4: () ( ) ( ) m 1,n m 1,n m,n 1 m,n T 2xyT 2 yx 0 −+ + + ΔΔ − ΔΔ +ΔΔ = Energy balances applied to the remaining combinations of similar nodes yield the following finite- difference equations. Continued. ..
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PROBLEM 4.76 (Cont.) Nodes 6, 14: () ( ) ( ) ( ) [ ] 17 6 xyT yxT xy yx hx kT hx ΔΔ +ΔΔ −ΔΔ+ΔΔ + Δ = −Δ ( ) ( ) ( ) [ ] 19 15 14 x yT y xT x y y x hxk T hxkT
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This note was uploaded on 12/07/2010 for the course MAE Heat Trans taught by Professor Lee,j.s. during the Spring '10 term at Seoul National.

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problem4-76 - PROBLEM 4.76 KNOWN: Nodal network and...

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