Closed-Form Analytical Solution for Laminar Natural Convection Heat Transfer for a Vertical Circular Plate

Abstract A closed-form analytical solution is proposed to predict the average Nusselt numbers for laminar natural convection heat transfer from a vertical circular plate. The analytical solution is derived by adapting the integral analysis for semi-infinite vertical plates to a circular plate geometry through the assumption of laterally invariant heat transfer coefficient across the width of the circular plate. The analytical solution is presented for an isothermal plate as well as for the isoflux plate. The analytical solution was compared against a validated three-dimensional computational fluid dynamics (CFD) solution for 104 ≤ Ra ≤ 109 and 0.05 ≤ Pr ≤ 10, and the agreement was found to be within 6.9% and 9.4% for the isothermal and the isoflux conditions, respectively. Furthermore, the analytical solution was compared against available experimental data for air, and the two agreed to within 8.7% and 6.6% for the isothermal and the isoflux conditions, respectively. The proposed analytical solution is compact and simple to use and would be of value to thermal equipment designers to predict heat transfer from vertical circular plate geometries which are commonly present in many engineering designs, such as those occurring on ends of cylindrical storage tanks and reactors, disk antennas, etc.