The paper deals with the investigation of convective filtration near a solid inclusion in a porous medium saturated with a fluid heated from above. The inclusion is a horizontal cylinder of circular cross-section. Its thermal conductivity is assumed to be much greater than the thermal conductivity of the saturated porous medium. Far from inclusion the temperature gradient is vertical and the convective flow is absent. Near inclusion the conditions for mechanical equilibrium are disturbed, the temperature gradient has a horizontal component, so the buoyancy convection inevitably arises. The study is based on the Darcy-Boussinesq equations, assuming constant fluid properties. The impermeability condition is imposed on the cylinder surface. A two-dimensional flow uniform along the cylinder axis is considered. Approximation similar to the Oseen approximation in the streaming flow problems is used, with the difference that quasi-linearization is applied to the nonlinear terms in the energy equation and not in the momentum equation. The compensating flow does not have jet type. In a similar manner, the problem is considered for a finite thermal conductivity of the inclusion. In this case, there is an additional parameter: the ratio of thermal conductivities of inclusion and saturated porous medium. Analytical results obtained for this case show that in the leading order, at small values of Rayleigh number, the structure of convective flow does not depend on the ratio of thermal conductivities, varying only in intensity. When the thermal conductivity of the inclusion coincides with the thermal conductivity of the surrounding medium, convection is absent. In the case when the thermal conductivity of the inclusion is lower than that of the medium, the sign of the convective circulation is changed, so that in the horizontal plane passing through the cylinder axis the fluid moves towards the inclusion.
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