Natural convection with volumetric energy sources in a fluid bounded by a spherical segment

Natural convection in a heat-generating fluid layer bounded from below by a segment of a sphere and from above by a horizontal surface has been investigated via finite-difference solution of the governing partial differential equations. The effects of both cavity geometry and the thermal boundary conditions on the temperature and flow fields are found to be significant in both developing and steady convection. Steady-state heat transfer coefficients are obtained at the upper boundary and can be correlated in the form Nu = Constant x Ra to the m despite the strong influence of conduction at the edge of the system. Steady-state convection is dominated by a single cell under the assumption of an axisymmetric flow but does not exhibit a truly steady temperature and flow fields.