Non-Darcy mixed convection in a vertical pipe filled with porous medium

The present paper reports an analytical as well as numerical investigation of fully developed mixed convective flow in a vertical pipe filled with porous medium. The motion in the pipe is induced by external pressure gradient and buoyancy force. The non-Darcy Brinkman–Forchheimer-extended model has been considered. The Chebyshev spectral-collocation method has been used to solve the coupled differential equations numerically. A comprehensive investigation on the dependency of mixed convective flow on governing parameters indicates that depending on the values of other parameters the velocity profile possess point of inflection beyond a threshold value of Rayleigh number (Ra). In the case of buoyancy-opposed flow, the velocity profile may contain point of inflection in the center zone and point of separation at the vicinity of the wall. The appearance of point of separation causes the back flow near the wall. In contrast to buoyancy-opposed case, where enhancement of Ra increases the magnitude of the center velocity as well as temperature till the distortion appears on both profiles, in buoyancy-assisted case both velocity as well as temperature decrease on increasing Ra at the center. The points of separation as well as inflection die out on reducing the media permeability or increasing magnitude of the form drag coefficient. Further, it was observed that for buoyancy-opposed flow the velocity as well as temperature profiles have a kind of distortion beyond a threshold value of Ra, which is also a function of other governing parameters. In this situation, the heat transfer rate varies abruptly as a function of Ra.