Thermal convection from an instantaneous point heat source in a porous medium

Thermal convection in an infinite porous medium due to a source in sphere

“…where U and V are the velocity components in non-dimensional form, given by (U, V) = ({K /ll')(u, »), In the case of the Darcy flow, on the surface of the sphere we need not impose a condition on the tangential velocity [21]. However, in the case of a point heat source in an infinite medium, the origin, being the seat of the point source, is a singular point for the flow field and hence the singularity in P at the origin must be a minimum [6].…”

“…The growing emphasis on effective granular and fibrous insulation systems for the successful containment of the transport of radio-nuclide from deposits of nuclear waste materials has stimulated various studies in fluid-saturated porous media and several results were obtained for the free convection flow around heat sources in the fundamental geometries of both infinite and semi-infinite media. Most of the existing theories [1,[5][6][7][8]16,20,21], with the exception of refs. [5,21], were primarily concerned with the phenomenon of free convection motion wherein the heat source was supposed to be concentrated at one point.…”

Unsteady forced and natural convection around a sphere immersed in a porous medium

“…Several authors [6,7,8,9,10] have already considered the steady natural convection around a sphere with isothermal or non-isothermal surface. Recently, Ganapathy and Purushothaman [11], Ganapathy [12] and Sano and Okihara [13] investigated unsteady natural convection around a sphere. Sano and Okihara obtained asymptotic solutions for small Rayleigh numbers for the case when the sphere is suddenly heated and, subsequently, maintains a constant heat flux over the surface.…”

Thermoconvective flow in a saturated, isotropic, homogeneous porous medium using Brinkman’s model: numerical study

“…A lower rate of heat transfer was predicted with the Brinkman term included. Ganapathy and Purushothaman [22] studied thermal convective flow from an instantaneous point source in a porous domain. They concluded that the boundary friction decelerated the momentum transfer at all times and exerted an influence at radial distances up to order K 1/2 from the source.…”

“…The matrix A can in this way be orchestrated in the form A = LU. Proceeding formally using row by column expansion, the following recurrence relations can be deduced: (22) Keller [33] has shown with rigorous mathematical detail that the Γ j matrix has the same structure as that of the the B j matrix. The ∆ j matrix also has a similar structure to A j .…”