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hw10soln-typed - 1 The surface of a 1.5-m long flat plate...

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1. The surface of a 1.5-m long flat plate is maintained at 40°C, and water at a temperature of 4°C and a velocity of 0.6 m/s flows over the surface. (a)Using the film temperature T f for evaluation of the thermophysical properties, calculate the heat transfer rate per unit width of the plate, q’. (b) Calculate the error in q’ that would be incurred in part (a) if the thermophysical properties of the water were evaluated at the free stream temperature and the same empirical correlations were used. L = 1.5 m T s = 40 Water T = 4 u = 0.6 m/s q’ x Assumptions: (1) Steady-state conditions. Properties: Table A-6, Water (T =4°C=277 K): ρ f =1000 kg/m 2 , μ f =1560 × 10 -6 N · s/m 2 , ν f = μ f / ρ f =1.560 × 10 -6 m 2 /s, k f =0.577 W/m · K, Pr=11.44; Water (T f =295K): ν =0.961 × 10 -6 m 2 /s, k=0.606 W/m · K, Pr=6.62; Water (T s =40°C=313 K): μ =657 × 10 -6 N · s/m 2 . Analysis: (a) The heat rate is given as q’= h L(T s -T ), and h must be estimated by the proper correlation. First, calculate the Reynolds mumber using properties evaluated at T f 5 2 6 L 10 365 . 9 s / m 10 961 . 0 m 5 . 1 s / m 6 . 0 ν L u Re × = × × = = - . Hence flow is mixed and the appropriate correlation and convection coefficient are [ ] [ ] 2522
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