Correlating convection heat transfer for Falkner-Skan flow

Abstract

Forced convection heat transfer in a laminar Falkner-Skan boundary layer flow with constant wall temperature is considered over a wide range of pressure gradient parameter β and entire range of Prandtl number Pr. A new asymptotic behavior for the Nusselt number Nux for large β and arbitrary Pr is discovered by examining the dependence of the ratio of the heat transfer for arbitrary Pr to its small Pr limit on Pr/β. Correlations for Nux are developed for −0.19883774 ≤ β < ∞ and all Pr for boundary layer flows without flow reversal. The thermal boundary layer for point-sink flow, which is the limiting case of Falkner-Skan problem as β → ∞, is analyzed. The peculiar behavior of Nux = 0 as β → ∞ in the Falkner-Skan thermal problem is caused by the loss of self-similarity for the solution of boundary layer temperature in the point-sink flow.