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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Interaction of Time-periodic Surface Modulation and Oscillatory Bio-convection in a Porous Medium

Discontinuity, Nonlinearity, and Complexity 15(3) (2026) 365--380 | DOI:10.5890/DNC.2026.09.006

Palle Kiran, M. Amarnath, G. Narsimlu

Department of Mathematic, Chaitanya Bharathi Institute of Technology, Hyderabad, Telangana-500075, India

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Abstract

This work investigates the effects of thermal modulation on Darcy-Brinkman bio-convection in a porous medium saturated with a Newtonian fluid containing gyrotactic microorganisms. We investigate the oscillatory bioconvection with low modulation amplitude using a weak nonlinear stability analysis. The heat transfer is measured by the mean Nusselt number governed by a complex Ginzburg-Landau equation (CGLE). The CGLE 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 Vadaszs number and modulation amplitude have a progressive effect on heat transfer. On the other hand, upon increase in the modified bio-Rayleigh number and cell eccentricity leads to a decrease in heat transfer. It is found that only OPM/LBM are effective on controlling heat transfer than IPM. This highlights the effectiveness of external modulation in controlling heat transport within the system. Further, it is found that the convective heat transfer process may be delayed, 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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