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Unstable mixed convection in an inclined
porous channel with uniform wall heat flux

A. Barletta, M. Celli

 

Fully developed mixed convection in a plane porous channel inclined an angle f to the horizontal is studied. The bounding parallel walls are assumed to be impermeable and subject to a uniform heat flux. The wall heating (or cooling) is symmetric, with the same flux supplied to both walls. A parallel-flow stationary regime is studied, parameterised by the Darcy-Rayleigh number, R, associated with the imposed wall heat flux, by the Péclet number, P, associated with the prescribed through-flow, and by the inclination angle f. Different basic flow regimes exist entailing a net flow either upslope or downslope, with either wall heating or cooling.  The thermo-convective stability of the basic flow is studied versus small-amplitude wavelike perturbations. The resulting eigenvalue problem for normal modes is then solved to obtain the neutral stability dispersion relation. The hybrid analytical-numerical technique adopted in this paper to track and illustrate the parametric changes of the neutral stability curves is Galerkin's method of weighted residuals. Numerical values at specially significant points on the neutral stability curves, as well as the critical values of R and of the wave number of the perturbation, are evaluated by employing a highly accurate Runge-Kutta solver combined with the shooting method.

Porous Medium; Darcy's Law; Convective Instability; Internal Heating; Mixed Convection; Normal Modes