A hot fluid at 35°C is to be transported through a tube horizontally positioned in quiescent air at 25°C. Which of the tube shapes, each of equal cross-sectional area, would you use in order to minimize heat losses to the ambient air by free convection?

Use the following correlation of Lien hard (Int. J. Heat Mass Transfer, 16, 2121, 1973) to approximate the laminar convection coefficient for an immersed body on which the boundary layer does not separate from the surface, Nu₁ = 0.52Ra_l^1/4. The characteristic length / is the length of travel of the fluid in the boundary layer across the shape surface. Compare this correlation to that given for a sphere to test its utility.

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40 mm 20 mm 20 mm 22.56 mm * 10 - mm (1) (2) (3) (4)