Free convection from a point source of heat, and heat transfer from spheres at small Grashof numbers
This paper presents an investigation of steady free convection flows due to a point heat source and heated spheres placed in viscous incompressible fluid. The paper starts with the non-dimensionalized formulation of the problem for the point source, and gives numerical solutions for a wide range of Prandtl number. An asymptotic solution is also presented for the temperature, stream function and vorticity near the point source, i.e. for small values of radial coordinate. Other asymptotic solution is obtained for large values of radial coordinate for different Prandtl numbers. The analytical solutions for temperature and flow fields close to the point source include constants which are evaluated numerically, and then are used to describe the flow field around heated spheres for small Grashof numbers, and to perform a correction of Nusselt number, according to the free convection regime, from its pure heat conduction value. This is done by using the matching conditions between the inner heat-conduction-dominated solution and the outer solution for the point heat source. The asymptotic solutions for large and small Grashof numbers allow to derive a correlation equation for Nusselt and Grashof numbers, valid for all values of Grashof number as long as the boundary layer flow is laminar.
scientific article; zbMATH DE number 1436730