Instability of the mixed convection flow in a heated porous channel with an adiabatic upper wall

This paper presents a linear stability analysis of horizontal throughflow in a saturated po- rous channel bounded by parallel impermeable walls with heating provided from below and an insulated top. The linear stability analysis is carried out for longitudinal rolls, leading to an eigenvalue problem for determining critical values for the Rayleigh number as a function of the Péclet number and the wavenumber. This problem is then solved using the Generalized Integral Transform Technique. The results give critical values of the Darcy-Rayleigh number that lead to unstable solutions for different Péclet numbers.