Convection induced by the selective absorption of radiation is investigated, for the case of an internal heat source that is modelled quadratically with respect to concentration. The growth rate for the linearised system is shown to be real, and a linear instability analysis is performed. To establish conditional and unconditional nonlinear stability results, both the Darcy and Forchheimer models are employed to describe fluid flow. Due to the presence of significant regions of potential subcritical instabilities, the results indicate that linear theory may only be accurate enough to predict the onset of convective motion when the model for the internal heat source is predominantly linear.
Hill, A. A., & Hill, A. A. (2004). Conditional and unconditional nonlinear stability for convection induced by absorption of radiation in a porous medium. Continuum Mechanics and Thermodynamics, 16(4), 305-318. https://doi.org/10.1007/s00161-003-0151-3