Thermal radiation and activation energy effects on triple-stratified Darcy-Forchheimer flow of micropolar nanofluid with gyrotactic microorganisms over a porous vertical stretching sheet.
7 affiliations
- 1Postdoctoral Research, Department of Mathematics, SR University, Warangal, 506371, Telangana, India.
- 2Department of Supportive Requirements, Sciences and Mathematics Unit, University of Technology and Applied Sciences, Sultanate of Oman, P.O. Box 608, Salalah, Salalah, PC:211, Sultanate of Oman.
- 3Department of Mathematics and Sciences, Sir Syed University of Engineering and Technology, Gulshan-e-Iqbal, Karachi, 75300, Pakistan.
- 4Faculty of Natural Sciences and Mathematics, Queen Arwa University, P.O. Box: 11586, Sana'a, Yemen. [email protected].
- 5Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia.
- 6Department of Mathematical Sciences, Federal Urdu University Arts, Science and Technology, University Road, Karachi, 75300, Pakistan.
- 7Department of Mathematics, Faculty of Arts and Sciences, Kocaeli University, Kocaeli, 41001, Izmit, Türkiye.
Abstract
This study presents a unified mathematical model for the triple-stratified Darcy-Forchheimer flow of a micropolar nanofluid containing gyrotactic microorganisms over a porous vertical stretching sheet by simultaneously incorporating thermal radiation, viscous dissipation, activation energy, Brownian motion, thermophoresis, mixed convection, and porous medium effects. The mathematical formulation accounts for momentum, thermal, solutal, nanoparticle, and microorganism stratifications together with bioconvection induced by gyrotactic microorganisms. Appropriate similarity transformations are employed to convert the governing nonlinear partial differential equations into a coupled system of ordinary differential equations, which is solved numerically using the MATLAB bvp4c boundary value solver. The coupled effects of the governing parameters on the velocity, microrotation, temperature, nanoparticle concentration, and motile microorganism density distributions are systematically examined. In addition, the variations in the local skin-friction coefficient, local wall couple stress, local Nusselt number, local Sherwood number, and local density number of motile microorganisms are comprehensively analyzed. The numerical results reveal that thermal radiation enhances the fluid temperature and thickens the thermal boundary layer, while activation energy increases nanoparticle concentration by weakening the chemical reaction rate. The Darcy-Forchheimer porous medium parameters suppress the fluid velocity owing to increased flow resistance, whereas triple stratification significantly modifies the thermal and concentration boundary layers, thereby affecting the heat and mass transfer characteristics. Furthermore, micropolar effects and gyrotactic microorganisms substantially influence the flow structure and enhance suspension stability through bioconvection. The present investigation provides new theoretical insights into the coupled momentum, heat, mass, and bioconvective transport mechanisms of micropolar nanofluids in stratified porous media, establishes a reliable benchmark for future experimental and high-fidelity CFD investigations, and offers potential applications in geothermal energy systems, chemical reactors, bioengineering processes, thermal management technologies, and advanced energy conversion systems.Clinical trial registration: Not applicable.
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BibTeX
@article{anjum2026thermal,
title = {{Thermal radiation and activation energy effects on triple-stratified Darcy-Forchheimer flow of micropolar nanofluid with gyrotactic microorganisms over a porous vertical stretching sheet.}},
author = {Asra Anjum and G Swamy Reddy and Syed Sohaib Zafar and Shaima Al-Tamimi and Abdulkafi Mohammed Saeed and Mohammed Faizan Ahmed and Farhan Ali},
journal = {Discover nano},
year = {2026},
month = nov,
doi = {10.1186/s11671-026-05106-3},
url = {https://europepmc.org/article/MED/42972168},
note = {CC BY-NC-ND},
}
RIS
TY - JOUR
TI - Thermal radiation and activation energy effects on triple-stratified Darcy-Forchheimer flow of micropolar nanofluid with gyrotactic microorganisms over a porous vertical stretching sheet.
AU - Asra Anjum
AU - G Swamy Reddy
AU - Syed Sohaib Zafar
AU - Shaima Al-Tamimi
AU - Abdulkafi Mohammed Saeed
AU - Mohammed Faizan Ahmed
AU - Farhan Ali
PY - 2026
DA - 2026/11/02
JO - Discover nano
DO - 10.1186/s11671-026-05106-3
UR - https://europepmc.org/article/MED/42972168
AB - This study presents a unified mathematical model for the triple-stratified Darcy-Forchheimer flow of a micropolar nanofluid containing gyrotactic microorganisms over a porous vertical stretching sheet by simultaneously incorporating thermal radiation, viscous dissipation, activation energy, Brownian motion, thermophoresis, mixed convection, and porous medium effects. The mathematical formulation accounts for momentum, thermal, solutal, nanoparticle, and microorganism stratifications together with bioconvection induced by gyrotactic microorganisms. Appropriate similarity transformations are employed to convert the governing nonlinear partial differential equations into a coupled system of ordinary differential equations, which is solved numerically using the MATLAB bvp4c boundary value solver. The coupled effects of the governing parameters on the velocity, microrotation, temperature, nanoparticle concentration, and motile microorganism density distributions are systematically examined. In addition, the variations in the local skin-friction coefficient, local wall couple stress, local Nusselt number, local Sherwood number, and local density number of motile microorganisms are comprehensively analyzed. The numerical results reveal that thermal radiation enhances the fluid temperature and thickens the thermal boundary layer, while activation energy increases nanoparticle concentration by weakening the chemical reaction rate. The Darcy-Forchheimer porous medium parameters suppress the fluid velocity owing to increased flow resistance, whereas triple stratification significantly modifies the thermal and concentration boundary layers, thereby affecting the heat and mass transfer characteristics. Furthermore, micropolar effects and gyrotactic microorganisms substantially influence the flow structure and enhance suspension stability through bioconvection. The present investigation provides new theoretical insights into the coupled momentum, heat, mass, and bioconvective transport mechanisms of micropolar nanofluids in stratified porous media, establishes a reliable benchmark for future experimental and high-fidelity CFD investigations, and offers potential applications in geothermal energy systems, chemical reactors, bioengineering processes, thermal management technologies, and advanced energy conversion systems.Clinical trial registration: Not applicable.
SN - 2731-9229
ER -