Heat transfer between a circular free impinging jet and a solid surface with non-uniform wall temperature or wall heat flux—1. Solution for the stagnation region

Abstract

In this, the first part of a two-part analytical study of the heat transfer between an axisymmetrical free impinging jet and a solid flat surface with non-uniform wall temperature or wall heat flux, both the exact energy equation and the boundary layer energy equation are solved asymptotically in the vicinity of the stagnation point. The results show that the nonuniformity of wall temperature or wall heat flux has a considerable effect on the stagnation point Nusselt number. Increasing the wall temperature or wall heat flux with the radial distance reduces the stagnation point Nusselt number while decreasing the wall temperature or wall heat flux with r enhances the heat transfer at the stagnation point. For the special case of constant wall temperature or wall heat flux, the result is essentially the same as that of Sibulkin, and the difference in Nusselt number is less than 0.3% for Pr ⩾ 0.7.