Natural and mixed convection in a vertical water-flow chamber in the presence of solar radiation

Abstract

Natural and mixed convection in a vertical plane channel in the presence of solar radiation are analytically studied. The physical problem under consideration simulates water flow and heat transfer in a chamber with transparent rigid boundaries exposed to solar radiation. The intensity of the volumetric heat source across the channel declines exponentially as described by the Beer–Lambert law for light absorption in near-infrared and visible spectra. The flows are assumed laminar and fully-developed. The properties of the liquid are considered constant except for the variation of density defining the Boussinesq term in the momentum equation. For both natural and mixed convection it is possible to observe one, two or no reverse flows and the conditions for the existence of reverse flows are derived. Heat fluxes across the chamber as well as the power outlet and the bulk liquid temperature are calculated for values of the Reynolds number between zero and 500 and the Prandtl number for water. It is shown that the solar heat source in combination with the liquid heating from the chamber walls has a pronounced effect on the flow behavior and the heat transfer.

Keywords

• Vertical channel
• Viscous liquid
• Laminar natural and mixed convection
• Reverse flow
• Light absorption
• Non-uniform heat source