The average free convection coefficient for the

Chapter 9, Problem 9.49

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The average free convection coefficient for the exteriorsurfaces of a long, horizontal rectangular duct exposedto a quiescent fluid can be estimated from theHahnDidion (HD) correlation [ASHRAE Proceed-ings, Part 1, pp. 26267, 1972]NuP?0.55Ra1/4P?HP?1/8RaP 107 where the characteristic length is the half-perimeter, P?(w?H), and wand Hare the horizontal width andvertical height, respectively, of the duct. The thermo-physical properties are evaluated at the film temperature.(a) Consider a horizontal 0.15-m-square duct with asurface temperature of 35?C in ambient air at 15?C.Calculate the average convection coefficient and theheat rate per unit length using the HD correlation.(b) Calculate the average convection coefficient andthe heat rate per unit length considering the duct asformed by vertical plates (sides) and horizontalplates (top and bottom). Do you expect this esti-mate to be lower or higher than that obtained withthe HD correlation? Explain the difference, if any.(c) Using an appropriate correlation, calculate the aver-age convection coefficient and the heat rate per unitlength for a duct of circular cross section having aperimeter equal to the wetted perimeter of the rec-tangular duct of part (a). Do you expect this esti-mate to be lower or higher than that obtained withthe HD correlation? Explain the difference, if any