Numerical analysis of nonsteady-state conjugate natural convection between two concentric spheres

Mathematical modeling of the regimes of free convection heat transfer between two concentric spheres is performed. The temperature of the internal sphere is constant during the whole process; the external sphere with a heat-conducting enclosure of finite thickness is affected by the surrounding medium. The boundary-value problem is formulated based on the mass, momentum, and energy conservation laws in dimensionless stream function-velocity vorticity vector-temperature variables in spherical coordinates. The obtained distributions of temperature and streamlines represent the effect of both energy source and environment on the flow regimes and the heat transfer.