Thermal phototactic bioconvection in an isotropic porous medium heated from above

TL;DR

This paper explores how thermal and phototactic effects influence bioconvection in an isotropic porous medium heated from above, using numerical analysis to understand stability and instability conditions.

Contribution

It introduces a detailed numerical analysis of thermal phototactic bioconvection in porous media, considering various physical parameters and boundary conditions.

Findings

Increasing thermal Rayleigh number stabilizes the suspension.

Higher Lewis number enhances bioconvective instability.

Boundary conditions significantly affect bioconvection patterns.

Abstract

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.