Free convection from a heated vertical cylinder embedded in a fluid-saturated porous medium

We consider the free convection boundary layer now induced by a heated vertical cylinder which is embedded in a fluid-saturated porous medium. The surface of the cylinder is maintained at a temperature whose value above the ambient temperature of the surrounding fluid varies as the n(th) power of the distance from the leading edge. Asymptotic analyses and numerical calculations are presented for the governing nonsimilar boundary layer equations and it is shown that, when n < 1, the asymptotic flowfield far from the leading edge of the cylinder takes on a multiple-layer structure. However, for n > 1, only a simple single layer is present far downstream, but a multiple layer structure exists close to the cylinder leading edge. We have shown that the fully numerical and asymptotic calculations are in satisfactory agreement especially for exponents n close to zero. Comparisons of the present numerical solutions obtained using the Keller-box method with previous numerical solutions using local methods are also given.