New analytical solution for natural convection of Darcian fluid in porous media prescribed surface heat flux

A new analytical method called He's variational iteration method is introduced to be applied to solve non-linear equations. In this method, general Lagrange multipliers are introduced to construct correction functional for the problems. It is strongly and simply capable of solving a large class of linear or non-linear differential equations without the tangible restriction of sensitivity to the degree of the non-linear term and also is very user friend because it reduces the size of calculations besides; its iterations are direct and straightforward. In this paper the powerful method called variational iteration method is used to obtain the solution for a non-linear ordinary differential equations that often appear in boundary layers problems arising in heat and mass transfer which these kinds of the equations contain infinity boundary condition. The boundary layer approximations of fluid flow and heat transfer of vertical full cone embedded in porous media give us the similarity solution for full cone subjected to surface heat flux boundary conditions. The obtained variational iteration method solution in comparison with the numerical ones represents a remarkable accuracy.