Abstract
A mathematical model is developed for studying the onset of mono-diffusive convective fluid flow in a horizontal porous layer with temperature gradient, internal heat generation, and viscous dissipation effects. Darcy's model is used for the porous medium, which is considered to be isotropic and homogenous. A linear instability analysis is conducted, and transverse or longitudinal roll disturbances are examined. The dimensionless emerging eigenvalue problem is solved numerically with the Runge-Kutta and shooting methods for both cases of disturbances, i.e,. longitudinal and transverse rolls. Critical wave number and critical vertical thermal Rayleigh number <i>R<sub>z</sub></i> are identified. For higher values of Gebhart number, Ge, a significant destabilizing effect of Hadley-Prats flow is computed. Internal heat generation also strongly modifies the critical vertical Rayleigh number. Extensive interpretation of the solutions related to the onset of convection is provided. The study is relevant to geophysical flows and materials processing systems.
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