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→âˆ‍, 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 خ²â€‰â‰  −0.198838. The second case is the special case of separated wedge flow (خ²â€‰= −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 âھ¢ 1 in the first case while Nux/Rex1/2 ∼ Pr1/4 for Pr âھ¢ 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 خ²â€‰= 0. The second common example is the twodimensional stagnation flow, known as Hiemenez flow and corresponds to خ²â€‰= 1 (wedge halfangle 90 deg). Using the methods discussed by Churchill and Usagi (1972, “General Expression for the Correlation of Rates of Transfer and Other Phenomena,â€‌ AIChE J., 18(6), pp. 1121–1128), the fitting parameter in the proposed model for both isothermal wedges and uniformflux wedges can be determined.