Homotopy analysis solution of free convection flow on a horizontal impermeable surface embedded in a saturated porous medium

In this paper, the analytic solution of the buoyancy-driven flow over a horizontal impermeable flat plate embedded in a saturated porous medium is derived using the newly developed analytic method, namely the homotopy analysis method (HAM). The HAM results show great agreement comparing with numerical results. HAM contains an auxiliary parameter ℏ that provides a simple way of controlling and adjusting the convergence region. The resultant analytic solution is valid for all acceptable values of the temperature exponent parameter λ.