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

We consider the free convection boundary layer flow 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.