problem4-43 - PROBLEM 4.43 KNOWN Two-dimensional network...

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PROBLEM 4.43 KNOWN: Two-dimensional network with prescribed nodal temperatures and thermal conductivity of he material. t FIND: Heat rate per unit length normal to page, q . SCHEMATIC: Node T i ( ° C) 1 120.55 2 120.64 3 121.29 4 123.89 5 134.57 6 150.49 7 147.14 ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional heat transfer, (3) No internal olumetric generation, (4) Constant properties. v ANALYSIS: Construct control volumes around the nodes on the surface maintained at the uniform temperature T s and indicate the heat rates. The heat rate per unit length is a b c d q q q q q q e = + + + + r in terms of conduction terms between nodes, o 1 2 3 4 5 7 q q q q q q q = + + + + + . Each of these rates can be written in terms of nodal temperatures and control volume dimensions using ourier’s law, F 1 s 2 s 3 s 4 s 5 s 7 s T T T T T T T T x q k k x k x k x 2 y y y y T T
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