Abstract
Combined, forced, and free flow in a vertical circular duct filled with a porous medium is investigated according to the Darcy–Boussinesq model. The effect of viscous dissipation is taken into account. It is shown that a thermal boundary condition compatible with fully developed and axisymmetric flow is either a linearly varying wall temperature in the axial direction or, only in the case of uniform velocity profile, an axial linear-exponential wall temperature change. The case of a linearly varying wall temperature corresponds to a uniform wall heat flux and includes the uniform wall temperature as a special case. A general analytical solution procedure is performed, by expressing the seepage velocity profile as a power series with respect to the radial coordinate. It is shown that, for a fixed thermal boundary condition, i.e., for a prescribed slope of the wall temperature, and for a given flow rate, there exist two solutions of the governing balance equations provided that the flow rate is lower than a maximum value. When the maximum value is reached, the dual solutions coincide. When the flow rate is higher than its maximum, no axisymmetric solutions exist.
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E. Magyari is on leave from the Institute of Building Technology, ETH—Zürich.
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Barletta, A., Magyari, E., Pop, I. et al. Buoyant Flow with Viscous Heating in a Vertical Circular Duct Filled with a Porous Medium. Transp Porous Med 74, 133–151 (2008). https://doi.org/10.1007/s11242-007-9192-6
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DOI: https://doi.org/10.1007/s11242-007-9192-6