Abstract
Natural Convection induced by a heated sphere embedded in an unbounded fluid-saturated porous medium is studied analytically. The temperature of the sphere is assumed to be fluctuating over a non-zero mean value. Solutions for both the velocity and temperature fields are obtained in the form of series expansions in the Rayleigh number based on the permeability of the porous medium and the mean heat flux from the sphere. All discussions are based on the assumption that the flow is governed by Darcy's law and that the thermal Rayleigh number is small. Fluctuating part shows the evolution of different wave patterns. The interaction of the first harmonic fields induce second-order mean components in the velocity and temperature fields, for which analytical expressions are obtained.
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