problem4-45 - PROBLEM 4.45 KNOWN: Steady-state temperatures...

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PROBLEM 4.45 K NOWN: Steady-state temperatures (K) at three nodes of a long rectangular bar. FIND: (a) Temperatures at remaining nodes and (b) heat transfer per unit length from the bar using nodal temperatures; compare with result calculated using knowledge of q. ± SCHEMATIC: A SSUMPTIONS: (1) Steady-state, 2-D conduction, (2) Constant properties. ANALYSIS: (a) The finite-difference equations for the nodes (1,2,3,A,B,C) can be written by inspection using Eq. 4.35 and recognizing that the adiabatic boundary can be represented by a symmetry plane. () 2 73 2 2 neighbors i 5 10 W/m 0.005m qx T 4T q x / k 0 and 62.5K. k2 0 W / m K × Δ −+ Δ = = = ± ± Node A (to find T 2 ): 2 2BA 2T 2T 4T q x / k 0 + Δ = ± 2 1 T 2 374.6 4 398.0 62.5 K 390.2K 2 = ×+ ×− = < Node 3 (to find T 3 ): 2 c2B 3 TTT 3 0 0 K 4 Tq x / k0 + ++ + Δ = ± 3 1 T 348.5 390.2 374.6 300 62.5 K 369.0K 4 = +++ + = < Node 1 (to find T 1 ): 2 C2 1 300 2T T 4T q x / k 0 + +− + Δ = ± 1 1 T 300 2 348.5 390.2 62.5 362.4K 4 =+ × + + = < (b) The heat rate out of the bar is determined by calculating the heat rate out of each control volume around the 300 K nodes. Consider the node in the upper left-hand corner; from an energy balance in out g a a,in g g E E E 0 or q q E where
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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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