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problem4-50

# problem4-50 - PROBLEM 4.50 KNOWN Long rectangular bar...

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PROBLEM 4.50 KNOWN: Long rectangular bar having one boundary exposed to a convection process (T , h) while the ther boundaries are maintained at a constant temperature (T s ). o FIND: (a) Using a grid spacing of 30 mm and the Gauss-Seidel method, determine the nodal temperatures and the heat rate per unit length into the bar from the fluid, (b) Effect of grid spacing and onvection coefficient on the temperature field. c SCHEMATIC: ASSUMPTIONS: (1) Steady-state, two-dimensional conduction, (2) Constant properties. ANALYSIS: (a) With the grid spacing Δ x = Δ y = 30 mm, three nodes are created. Using the finite- difference equations as shown in Table 4.2, but written in the form required of the Gauss-Seidel method (see Section 4.5.2), and with Bi = h Δ x/k = 100 W/m 2 K × 0.030 m/1 W/m K = 3, we obtain: Node 1: () ( 12 s 2 2 11 1 T T T BiT T 50 3 100 T 350 Bi 2 5 5 =+ + = + + × = + + ) (1) Node 2: ( 2 1 s3 13 1 T T 2T T T T 2 50 T T 100 44 4 = + + = ++ × = ) (2) Node 3: ( 32 s 2 2 1 T T 3T T 3 50 T 150 4 × ) (3) Denoting each nodal temperature with a superscript to indicate iteration step, e.g.

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problem4-50 - PROBLEM 4.50 KNOWN Long rectangular bar...

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