Abstract
In the present work, analytical solutions are developed to simulate the steady mixed convection flow in an annulus partially filled with porous material. Flow formation inside an annulus is due to temperature as well as pressure gradients. The Brinkman-extended Darcy model is used to simulate momentum transfer in the porous region while the Navier–Stokes equation is used to simulate the momentum transfer in the clear fluid region. The clear fluid and porous regions are coupled by equating the velocity, temperature, heat flux and by considering shear stress jump condition at the interface. The goal of the present work is to investigate the impact of dimensionless parameters controlling the present physical situation on the onset of flow reversal at the outer surface of the inner vertical cylinder and the inner surface of the outer vertical cylinder forming the annulus. A dimensionless temperature $$ \theta_{0} $$ is introduced. Moreover, this quantity is related to the usual Gr/Re parameter. Exact solutions for momentum and energy equations are obtained. Expressions for the fully developed velocity, temperature and mass flux are given. The impact of porous thickness and the adjustable coefficient in the stress-jump condition at the interface on flow formation inside the annulus is extensively discussed.
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