Numerical study on wall temperature and surface heat flux natural convection equations arising in porous media by rational Legendre collocation approach (Q2918847)

The authors consider the problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers, using the boundary layer approximation and Darcy's law. A numerical solution based on the rational Legendre functions is presented for the third-order nonlinear differential equation corresponding to the similarity solution of the initial problem. These orthogonal functions are proposed to provide an effective but simple way to improve the convergence of the solution by the collocation method. The validity of the method is based on the assumption that it converges by increasing the number of collocation points. The obtained numerical results are compared with those of several other methods.