problem4-56 - PROBLEM 4.56 KNOWN Rectangular air ducts...

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PROBLEM 4.56 KNOWN: Rectangular air ducts having surfaces at 80 ° C in a concrete slab with an insulated bottom nd upper surface maintained at 30 ° C. a FIND: Heat rate from each duct per unit length of duct, q . SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional conduction, (3) No internal olumetric generation, (4) Constant properties. v P ROPERTIES: Concrete (given): k = 1.4 W/m K. ANALYSIS: Taking advantage of symmetry, the nodal network, using the suggested grid spacing Δ x = 2 Δ y = 37.50 mm Δ y = 0.125L = 18.75 mm where L = 150 mm, is shown in the sketch. To evaluate the heat rate, we need the temperatures T 1 , T 2 , T 3 , T 4 , and T 5 . All the nodes may be treated as interior nodes ( considering symmetry for those nodes on insulated boundaries), Eq. 4.29. Use matrix notation, Eq. .48, [A][T] = [C], and perform the inversion. 4 The heat rate per unit length from the prescribed section of
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