A similarity solution for laminar forced convection heat transfer from solid spheres

A New analytical solution, based on scale analysis and similarity transformation, is presented to solve a linearized form of the energy equation for the laminar forced convection over a sphere in a spherical coordinate system. Compact expressions for temperature, wall heat flux, and Nusselt number are developed as a function of the Reynolds number (Re-D) and Prandtl number (Pr) for both isothermal and isoflux boundary conditions. A blending method is used to extend the range of the present analytical expression to cover 0 < Re-D < 10(5) and 0.7 < Pr < infinity. The present analysis reveals that the theoretical averaged-Nusselt numbers for the laminar forced convection over isoflux (constant wall heat flux) and isothermal (uniform wall temperature) spheres are identical. The proposed model is verified by comparing the analytical expression with the available experimental data over various Reynolds and Prandtl numbers. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

A new analytical solution is presented for the linearized form of the energy equation for laminar forced convection over a sphere in spherical coordinates. Compact expressions for temperature, wall heat flux, and Nusselt number are developed based on scale analysis and similarity transformation. The range of the analytical expression is extended using a blending method.