problem4-55 - PROBLEM 4.55 KNOWN: Flue of square cross...

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PROBLEM 4.55 KNOWN: Flue of square cross section with prescribed geometry, thermal conductivity and inner and uter surface convective conditions. o FIND: (a) Heat loss per unit length, q , by convection to the air, (b) Effect of grid spacing and onvection coefficients on temperature field; show isotherms. c SCHEMATIC: Schematic (a) ASSUMPTIONS: (1) Steady-state, two-dimensional conduction, (2) Constant properties. ANALYSIS: (a) Taking advantage of symmetry, the nodal network for a 75 mm grid spacing is shown in schematic (a). To obtain the heat rate, we need first to determine the temperatures T i . Recognize that there are four types of nodes: interior (4-7), plane surface with convection (1, 2, 8-11), internal corner with convection (3), and external corner with convection (12). Using the appropriate relations from Table 4.2, the finite-difference equations are Node Equation 1 () ii 422 , i 1 2h x h x 2 TTT T 2 2 T kk ΔΔ ++ + + = ⎛⎞ ⎜⎟ ⎝⎠ 0 4.42 2 531 , i 2 x h x 2T T T T 2 2 T 0 + + = 4.42 3 66 22 , i 3 x h x 2T T T T T 23 T 0 ++++ −+ = 4.41 4 8515 4 TTTT 4 T 0 +++ = 4.29 5 9624 5 TTTT 4 T0 = 4.29 6 1 0735 6 TT T T4 T = 0 0 4.29 7 11 11 6 6 7 T +− = 4.29 8 oo 499 , o 8 x h x 2T T T T 2 2 T 0 +
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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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problem4-55 - PROBLEM 4.55 KNOWN: Flue of square cross...

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