Thermal interaction between free convection and forced convection along a vertical conducting wall

TL;DR

This paper presents a theoretical analysis of conjugate heat transfer involving free and forced convection along a vertical conducting wall, using a non-similarity transformation and numerical solutions to explore heat transfer effects.

Contribution

It introduces a novel numerical approach to solve the conjugate heat transfer problem with non-similarity transformation and investigates the effects of resistance parameters and Prandtl numbers.

Findings

Heat transfer characteristics depend on resistance parameters.

Countercurrent boundary layers form on both sides of the wall.

Numerical solutions effectively handle singular points in the equations.

Abstract

A theoretical study is presented in this paper to investigate the conjugate heat transfer across a vertical finite wall separating two forced and free convection flows at different temperatures. The heat conduction in the wall is in the transversal direction and countercurrent boundary layers are formed on the both sides of the wall. The governing equations of this problem and their corresponding boundary conditions are all cast into a dimensionless form by using a non-similarity transformation. These resultant equations with multiple singular points are solved numerically using a very efficient singular perturbation method. The effects of the resistance parameters and Prandtl numbers on heat transfer characteristics are investigated.