A non-Boussinesq integral method for laminar free convection between vertical flat plates subject to a uniform wall heat flux

An integral method is developed to analyze laminar free convection between large aspect ratio, vertical, parallel plate channels subject to a uniform, symmetric, heat flux and varying fluid properties. The flow is assumed to be fully developed, which is a good assumption for channels with large aspect ratios. This is a heat transfer problem characterized by high temperature ratios, thereby rendering the commonly applied Boussinesq approximation invalid. The method developed is general and, therefore, can be used to calculate natural circulation of gases or liquids. Sample calculations are included for air between 300 and 1100 K.