Laminar free convection from a uniformly heated sphere.

概要

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The steady convection flow around an isothermal sphere, which is placed in an infinitely vast incompressible viscous fluid otherwise at rest is numerically investigated at high Grashof numbers using the patching ADI method previously proposed by the authors. In the method, to facilitate the solution procedure the whole flow field is partitioned expediently into two sections : a boundary layer region over the sphere surface and a plume region along the upper stagnation axis. In these two regions the governing Navier-Stokes and energy equations (in the stream function, vorticity and temperature version) with false transient term are discretised by Davis' scheme and solved alternately until a solution which can be continuated smoothly across the virtual boundary is attained. The fluid flow with Pr=0.72 is calculated and the velocity and temperature distributions are determined for Grd=8×105, 8×106 and 8×107. Therefrom the Nusselt numbers are evaluated, and correspondingly Nud= 14.25, 23.90 and 41.09 are found, where Pr is the Prandtl number and Grd the Grashof number based on the diameter of sphere and the temperature difference from the ambient fluid.
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