Natural Convection of Heat-Generating Liquid of Variable Viscosity under Wall Cooling Impact

Abstract

This research presents a computational investigation of the thermal convection of a heat-generating liquid having variable viscosity in a semi-cylindrical cavity. The analysis is carried out to obtain the time patterns of the average Nusselt number at the lower border of the chamber and understand the impact of the variable viscosity, the Prandtl number, and the Rayleigh number on this parameter. The natural convection in the cavity is defined by the set of non-dimensional equations based on the Boussinesq approach employing the non-primitive parameters such as vorticity and stream function. These governing equations are worked out numerically based on the finite difference technique. The time dependencies have been obtained at the Rayleigh number equal to 104, 105, and 106 and the Prandtl number taking values of 7.0, 70, and 700. The results obtained for variable and constant viscosity have been compared. Additionally, the paper represents maps of isotherms and streamlines for the mentioned values of the Rayleigh number. The influence of variable viscosity on the parameters of natural convection is poorly studied in closed systems; therefore, this research gives necessary data to understand the general time nature of the average Nusselt number at cooling surface of various parameters. Additionally in this research, the model for simulating the natural convection in non-primitive variables is presented in polar coordinates when the dynamic viscosity varies with temperature. The computational model designed could be used to simulate the free convection in systems with inner heat production such as chemical reactors, inductive metal melting facilities, or corium in-vessel retention to analyze the impact of various factors on the parameters of the natural convection in such systems.