The unsteady penetration of free convection flows caused by heating and cooling flat surfaces in a porous media (Q1276713)

Free convection flow is generated in a porous medium adjacent to a vertical or horizontal flat surface which is suddenly heated and cooled, sinusoidally along its length. An approximate analytical solution, which is valid for small times and for any value of the Rayleigh number, \(Ra\), is obtained by matching inner and outer expansions. A numerical solution is also obtained which matches the small time analytical solution to the ultimate steady-state solution when such a solution exists. In both configurations the flow pattern is that of a row of counter rotating cells situated close to the surface.