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The aim of the present analytical study is to investigate a thermally developing forced convective heat transfer inside a channel filled with a porous medium whose walls are imposed to a constant heat flux (i.e. the iso-flux thermal boundary condition). The Darcy’s law of motion and the two-energy equation (i.e. local thermal non-equilibrium, LTNE) model are considered. A perturbation analysis is conducted to avoid using any model for the iso-flux thermal boundary condition. Thermally developing forced convection inside a porous-filled channel has previously not been analyzed without implementing a heuristic model for the iso-flux thermal boundary condition. The temperature difference between the fluid and solid phases (called the LTNE intensity) is analytically obtained. Results concerning the LTNE intensity is compared with the available models of the iso-flux thermal boundary condition. In addition, the Nusselt number of a thermally developing convection through a porous material is obtained for the LTNE condition. Also, an expression representing the developing length, i.e. the dimensionless axial location at which the flow becomes fully developed, for a porous-filled channel is proposed for the first time. [ABSTRACT FROM AUTHOR]

In this article the finite volume method (FVM) is carried out to simulate the flow around and through a two-dimensional porous cylinder. An external magnetic field is used to control the wake behind the bluff body and also to suppress the vortex shedding phenomena. The Darcy–Brinkman–Forchheimer model has been used for modeling the flow in the porous medium. Effects of Stuart ( N ), Reynolds ( Re ) and Darcy ( Da ) numbers on the flow behavior have been investigated. The results show that the critical Stuart number for suppress vortex shedding decreases with increasing the Darcy numbers. Also, the Stuart number for disappearance the re-circulating wake increases with increased Reynolds number for both porous and solid cylinders. [ABSTRACT FROM AUTHOR]