Thermal phototactic bioconvection in an isotropic porous medium heated from above

This study investigates thermal phototactic bioconvection in an isotropic porous medium using the Darcy-Brinkman model. The top boundary of the medium is exposed to normal collimated light and subjected to heating. A linear analysis of bio-thermal convection is performed using a fourth-order accurate finite difference scheme, employing Newton-Raphson-Kantorovich iterations for both rigid-free and rigid-rigid boundary conditions. The effects of the Lewis number, Darcy number, and thermal Rayleigh number on bioconvective processes are examined and presented graphically. The findings reveal that increasing the thermal Rayleigh number stabilizes the suspension, whereas a higher Lewis number enhances instability.