Heat Transfer From a Wedge to Fluids at Any Prandtl Number Using the Asymptotic Model

Abstract

Heat transfer from a wedge to fluids at any Prandtl number can be predicted using the asymptotic model. In the asymptotic model, the dependent parameter Nux/Rex1/2 has two asymptotes. The first asymptote is Nux/Rex1/2Pr→0 that corresponds to very small value of the independent parameter Pr. The second asymptote is Nux/Rex1/2Pr→∞, that corresponds to very large value of the independent parameter Pr. The proposed model uses a concave downward asymptotic correlation method to develop a robust compact model. The solution has two general cases. The first case is β ≠ −0.198838. The second case is the special case of separated wedge flow (β = −0.198838) where the surface shear stress is zero, but the heat transfer rate is not zero. The reason for this division is Nux/Rex1/2 ∼ Pr1/3 for Pr ⪢ 1 in the first case while Nux/Rex1/2 ∼ Pr1/4 for Pr ⪢ 1 in the second case. In the first case, there are only two common examples of the wedge flow in practice. The first common example is the flow over a flat plate at zero incidence with constant external velocity, known as Blasius flow and corresponds to β = 0. The second common example is the two-dimensional stagnation flow, known as Hiemenez flow and corresponds to β = 1 (wedge half-angle 90 deg). Using the methods discussed by Churchill and Usagi (1972, “General Expression for the Correlation of Rates of Transfer and Other Phenomena,” AIChE J., 18(6), pp. 1121–1128), the fitting parameter in the proposed model for both isothermal wedges and uniform-flux wedges can be determined.