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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

The Effect of Thermal Modulation on Weakly Nonlinear Bio-convection in a Porous Medium

Journal of Applied Nonlinear Dynamics 15(2) (2026) 439--456 | DOI:10.5890/JAND.2026.06.013

Palle Kiran, M. Amarnath, P. Suresh

Department of Mathematics, Chaitanya Bharathi Institute of Technology, Hyderabad, Telangana-500755, India

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Abstract

This study focuses on investigating the effects of time-periodic thermal modulation on Darcy-Brinkman bio-convection in a porous medium saturated with a Newtonian fluid containing gyrotactic microorganisms. A weak nonlinear stability analysis is performed to analyze the stationary mode of bioconvection with low modulation amplitude. The heat transport measured by the mean Nusselt number, which is governed by a Ginzburg-Landau equation (GLE). The GLE is derived by solvability condition at lowest order of perturbed parameter. The results are presented graphically, illustrating the impact of the system parameters on heat transfer. The results show that both Vadasz number and modulation amplitude have dual effect (either increase or decrease) on heat transfer. On the other hand, an increase in the modified bioconvection Rayleigh number and cell eccentricity leads to a decrease in heat transfer. It is found that only OPM/LBM are effective modulations on heat transfer. This highlights the effectiveness of external modulation to control heat transport in the system. Further, it is found that, the convective heat transfer process may be slow, due to asymmetries and irregularities ($\alpha \neq 0$) of microorganisms than spherical-shaped microorganisms ($\alpha = 0$).

Acknowledgments

The authors PK and AM would like to thank the management of Chaitanya Bharathi Institute of Technology for providing research benefits. R and D CBIT is funding this work as part of the Internal Seed Grant (CBIT/PROJ-IH/1056/Maths/D005/2024) for the academic year 2024–2025. The authors are grateful to the unknown referees for their valuable comments.

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