Numerical Modelling of Convective Heat and Mass Transfer in Spherical Coordinates

Abstract

The aim of the research is to construct a discrete analogue of the generalized differential equation describing convection in a viscous incompressible fluid in spherical coordinates. The mathematical model of convective heat and mass transfer in a viscous incompressible fluid is given by a system of differential equations derived from the equations of hydrodynamics, heat and mass transfer. These equations satisfy the generalized conservation law, which is described by a differential equation for the generalized variable. The control volume method is used to obtain a discrete analogue of the differential equation. The computational domain is divided into a multiplicity of control volumes with a node in each of them. As a result, a discrete analogue is obtained that relates the value of the generalized variable at the node point to its values at neighboring nodes. The method guarantees strict compliance of conservation laws both in the entire calculation area and in any part of it. To apply the best approximation of the profiles of the generalized variable, there are exact solutions of the conservation equation separately for each coordinate. The physical meaning of exact solutions is briefly explained. As a result, a discrete analogue is constructed for the generalized differential equation using the obtained analytical solutions.