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.

A. Barletta, E. Magyari, I. Pop, L. Storesletten (2008). Buoyant flow with viscous heating in a vertical circular duct filled with a porous medium. TRANSPORT IN POROUS MEDIA, 74, 133-151 [10.1007/s11242-007-9192-6].

Buoyant flow with viscous heating in a vertical circular duct filled with a porous medium

BARLETTA, ANTONIO;
2008

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.
2008
A. Barletta, E. Magyari, I. Pop, L. Storesletten (2008). Buoyant flow with viscous heating in a vertical circular duct filled with a porous medium. TRANSPORT IN POROUS MEDIA, 74, 133-151 [10.1007/s11242-007-9192-6].
A. Barletta; E. Magyari; I. Pop; L. Storesletten
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/62280
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