Thermal interaction between natural convection on one side of a vertical wall and forced convection on the other side

Abstract

An analysis is made for the conjugate heat transfer problem of natural convection on one side of a vertical wall and forced convection on the other side. The natural convection mode is treated analytically by employing the Oseen linearization approach developed by Gill. The forced convection boundary layer is analyzed on the basis of the integral technique. The two solutions are matched on the separating wall so as to satisfy the continuity of heat flux between the two fluids. The analysis shows that the complexion of this two-fluid problem is governed by a dimensionless conjugate parameter, R, which relates the heat transfer effectiveness of forced convection mode to that of free convection mode. The boundary conditions at the wall are not prescribed in the analysis in advance, rather, determined among the results. The heat transfer and flow characteristics in the two counter-flowing boundary layers are presented graphically. Heat transfer results of engineering importance are determined as a function of the conjugation parameter.