Влияние числа Прандтля на естественную конвекцию тепловыделяющей жидкости в полуцилиндрической полости в условиях переменной вязкости

Abstract

The study presents a numerical analysis on natural convection of a heat generating fluid having variable viscosity within a semi-cylindrical cavity. It is assumed that the top wall is adiabatic, and the bottom one is isothermal. The simulation is conducted to discover the influence of the Prandtl number on the average Nusselt number at the bottom wall when the dynamic viscosity of the fluid decreases exponentially. The natural convection in the cavity is described by the system of equations in the Boussinesq approximation. The problem has been formulated in terms of non-primitive variables in a dimensionless form. The governing equations have been solved using the finite difference method. As a result of the numerical simulation, we have obtained time dependencies of the average Nusselt number when the Prandtl number is equal to 7.0, 70 and 700, and the Rayleigh number is varied from 104 to 106.