Thermal phototactic bioconvection in an isotropic porous medium heated from above

TL;DR

This work addresses thermal phototactic bioconvection in an isotropic porous medium by coupling Darcy–Brinkman fluid dynamics with a phototactic cell flux and an energy equation. The authors perform a linear stability analysis around a steady phototactic state using a fourth-order finite-difference scheme and NRK iterations to obtain neutral stability curves in the $(k,R)$ plane, accounting for both rigid-free and rigid-rigid top boundaries. Key findings show that increasing the thermal Rayleigh number $R_T$ stabilizes the suspension (increasing the critical bioconvective Rayleigh number $R^c$), while increasing the Lewis number $Le$ promotes instability (decreasing $R^c$); the boundary conditions also influence the onset and can induce oscillations when the phototactic sublayer resides near three-quarters of the height. These results have potential implications for bioengineering applications involving phototactic microorganisms in porous supports and for understanding natural bioconvection under coupled light and thermal fields.

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.

Figures (5)

• Figure 1: The spatial configuration of the proposed problem.
• Figure 2: Neutral curves for different values of the thermal Rayleigh number, where the other parameters $V_c=10,\tau_H=0.5,G_c=0.63,\phi=0.76,Da=0.1$, and $Le=0.4$ are fixed. Here, the top wall is assumed to be stress free.
• Figure 3: Neutral curves for different values of the Lewis number, where the other parameters $V_c=10,\tau_H=0.5,G_c=0.63,\phi=0.76,Da=0.1$, and $R_T=50$ are fixed. Here, the top wall is assumed to be stress free.
• Figure 4: Neutral curves for different values of the thermal Rayleigh number, where the other parameters $V_c=10,\tau_H=0.5,G_c=0.63,\phi=0.76,Da=0.1$, and $Le=0.4$ are fixed. Here, the top wall is assumed to be rigid.
• Figure 5: Neutral curves for different values of the Lewis number, where the other parameters $V_c=10,\tau_H=0.5,G_c=0.63,\phi=0.76,Da=0.1$, and $R_T=50$ are fixed. Here, the top wall is assumed to be rigid.