Resistor-Network Formulation of Multitemperature Free-Convection Problems

Abstract

In recent work, the resistor-network formulation of forced-convection problems and a technique (dQdT) for evaluating the paired convective resistances that characterize the network were presented. This technique entails solutions of the energy equation with perturbed boundary conditions. In the present paper, the dQdT technique is extended to free convection. The analytical solution to the classical two-temperature problem of free convection at an isothermal vertical flat plate is used to verify the technique. Then, dQdT is applied to the three-temperature problem of free convection in an asymmetrically heated vertical channel based on numerical solutions of the energy equation. Sample results are presented and known limits are discussed to demonstrate the validity of the results. This paper is part of a series on the resistor-network formulation of convection problems.