An integral treatment for coupled heat and mass transfer by natural convection from a radiating vertical thin needle in a porous medium

In the present paper, an analytical study of the effects of radiation on the buoyancy induced heat and mass transfer by natural convection from an isothermal vertical thin needle embedded in a saturated porous medium has been done in case of linear temperature and concentration distribution. For the analysis of the problem, an integral method of Von Karman type has been used. The governing parameters for the problem under study are the buoyancy ratio (N), Lewis number (Le) and radiation parameter (Rd). The computed results have covered a wide range of the governing parameters e.g.  −1 < N < 10, 0 < Le < 50 and 1.4≤Rd*≤10. It has been concluded that the local Nusselt number decreases while the local Sherwood number increases along with N > 0 for increasing Lewis number. But an opposite trend is observed for N < 0 (i.e. for N = −1). The local Nusselt number decreases while the local Sherwood number increases for increasing values of the radiation parameter for N > 0. An opposing trend is observed for N < 0.