Mixed convection flow in a vertical tube filled with porous material with time-periodic boundary condition: steady-periodic regime

Abstract

An analytical study is reported on the hydrodynamic and thermal behaviour of a fully developed mixed convective flow in a vertical tube filled with isotropic porous material having time-periodic boundary condition. The analysis is performed for fully developed parallel flow and steady-periodic regime. The momentum and energy equations presented in dimensionless form along with the constraint equations for the present physical situation are solved exactly. Closed form solution are expressed in terms of modified Bessel function of first kind. The solution obtained is graphically represented and the effect of the Prandtl number $$Pr$$ , the dimensionless frequency $$\Omega $$ , and the Darcy number $$Da$$ on the flow is investigated. It is discovered that velocity is maximum at two different locations in the flow domain, one near the surface of the tube and another at the axis of the tube.