journal article·2026-01-23Open access

Heat and mass transfer impact on bio-convective Maxwell fluid flow driven by Darcy–Forchheimer media under activation energy and pollutant discharge effects

Sudha Mahanthesh Sachhin, Kenchappa Nagegowda, Ulavathi Shettar Mahabaleshwar, Gabriella Vadaszne Bognar, David Laroze

Nanotechnology Reviews· Volume 15· Issue 1

Abstract

Abstract The present article examines the waste discharge impact on concentration which influences fluid flow by changing its viscosity, which can slow the flow and result in pressure fluctuations. In wastewater treatment, elevated waste concentrations can cause clogging and decrease flow efficiency, ultimately affecting overall execution. The authors noticed that there was a deficit investigation on Bio-convective Maxwell equations in the circumstances of waste discharge concentration, magnetic field, activation energy, thermophoresis, and Brownian diffusions. The authors utilized the research gap. Governing equations are solved to ordinary differential equations by utilizing similar variables. Additionally, examining the entropy production and Bejan number were later solved using the numerical shooting method. Outcomes of the current analysis reveal that upsurging external pollutant and external source variation factors enhance the concentration profile. Enhancing the Peclet bio-Lewis number 1 to 4 reduces the microbial field by 20 %. Raising the porosity and magnetic field reduces the Bejan number. Enhancing the Brownian diffusion 1 to 2 reduces the concentration profile by 25 %. The accuracy achieved in this work is in close agreement with that observed in prior studies, supporting the validity of our methodology. Our investigation is considered original, as no prior studies have employed the same framework; moreover, the present results show strong agreement with previously published findings in terms of accuracy.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Nanofluid Flow and Heat Transfer · Heat and Mass Transfer in Porous Media · Thermoelastic and Magnetoelastic Phenomena

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Department of Studies in Mathematics , Davangere University , Shivagangothri, 577007 , Davangere , India

Institute of Machine and Product Design, University of Miskolc , 3515 , Miskolc-Egyetemváros , Hungary

Instituto de Alta Investigación, Universidad de Tarapacá , Casilla 7 D, 1000000 , Arica , Chile

References (47)

Show source-provided references
1. Mkhatshwa, M. Triple-diffusive bioconvection flow of sutterby nanofluid over an oscillatory stretchable surface immersed in a Darcy–Forchheimer porous medium. BioNanoScience 2024;14:495–516. https://doi.org/10.1007/s12668-023-01230-x.10.1007/s12668-023-01230-x ↗
2. Baithalu, R, Oluwaseun, F, Agbaje, TM, Mishra, SR, Panda, S. Thermophoretic particle deposition in a mixed convective bioconvection nanofluid with thermal radiation and chemical reaction over an exponential stretching sheet. Multiscale Multidiscip Model Exp Des 2025;8:220. https://doi.org/10.1007/s41939-025-00805-3.10.1007/s41939-025-00805-3 ↗
3. Narsimulu, G, Gopal, D, Udaikumar, R. Numerical approach for enhanced mass transfer of bio-convection on Magneto-hydrodynamic Carreau fluid flow through a nonlinear stretching surface. Mater Today Proc 2022;1;2267–75. https://doi.org/10.1016/j.matpr.2021.09.341. GC-RASM 202149.10.1016/j.matpr.2021.09.341 ↗
4. Li, Y, Leng, Y, Baazaoui, N, Arain, MB, Ijaz, N, Hassan, A. Exploring the dynamics of active swimmers microorganisms with electromagnetically conducting stretching through endothermic heat generation/assimilation flow: observational and computational study. Case Stud Therm Eng 2023;51:103560. https://doi.org/10.1016/j.csite.2023.103560.10.1016/j.csite.2023.103560 ↗
5. Ajala, OA, Adegbite, P, Obalalu, AM, Abbas, A, Owolabi, AO, Ojewola, OB. Bio-convective flow of micropolar nanofluids over an inclined permeable stretching surface with radiative activation energy. J Biomimet, Biomater Biomed Eng 2024;65:1–13. https://doi.org/10.4028/p-c79R3Y.10.4028/p-c79R3Y ↗
6. Nandeppanavar, MM, Basha, H, Udgiri, S. Analysis of bio-convective gyrotactic microorganisms swim in a buongiorno’s dissipative Prandtl–Eyring nanofluid flow about a stretching sheet with inclined magnetic field and radiation effects under chemical reaction. Hybrid Adv 2025;8:100382. https://doi.org/10.1016/j.hybadv.2025.100382.10.1016/j.hybadv.2025.100382 ↗
7. Sarma, N, Paul, A. Thermophoresis and brownian motion influenced bioconvective cylindrical shaped Ag–CuO/H2O ellis hybrid nanofluid flow along a radiative stretched tube with inclined magnetic field. BioNanoScience 2024;14:1266–92. https://doi.org/10.1007/s12668-023-01280-1.10.1007/s12668-023-01280-1 ↗
8. Mishra, NK, Sharma, BK, Sharma, P, Muhammad, T, Pérez, LM. Entropy generation optimization of cilia regulated MHD ternary hybrid Jeffery nanofluid with Arrhenius activation energy and induced magnetic field. Sci Rep 2023;13:14483. https://doi.org/10.1038/s41598-023-41299-8.10.1038/s41598-023-41299-8 ↗
9. Pal, D, Mondal, S. Lie group analysis and SQLM of entropy generation of MHD nonlinear radiative micropolar nanofluid flow with thermophoresis and Brownian motion. Numer Heat Transf A Appl 2025;0:1–30. https://doi.org/10.1080/10407782.2024.2359055.10.1080/10407782.2024.2359055 ↗
10. Rajkumar, D, Subramanyam Reddy, A, Chamkha, AJ. Entropy generation of magnetohydrodynamic pulsating flow of micropolar nanofluid in a porous channel through Cattaneo–Christov heat flux model with Brownian motion, thermophoresis and heat source/sink. Waves Random Complex Media 2025;0:1–26. https://doi.org/10.1080/17455030.2022.2124467.10.1080/17455030.2022.2124467 ↗
11. Das, UJ, Patgiri, I. Entropy analysis on thermophoretic magnetohydrodynamic Couette flow over a deformable porous channel with temperature-dependent viscosity and thermal conductivity. Heat Transfer 2024;53:2556–72. https://doi.org/10.1002/htj.23053.10.1002/htj.23053 ↗
12. Sun, SL, Liu, D, Wang, YZ, Qi, YL, Kim, HB. Convective heat transfer and entropy generation evaluation in the Taylor–Couette flow under the magnetic field. Int J Mech Sci 2023;252:108373. https://doi.org/10.1016/j.ijmecsci.2023.108373.10.1016/j.ijmecsci.2023.108373 ↗
13. Makinde, OD, Chinyoka, T. Transient analysis of pollutant dispersion in a cylindrical pipe with a nonlinear waste discharge concentration. Comput Math Appl 2010;60:642–52. https://doi.org/10.1016/j.camwa.2010.05.012.10.1016/j.camwa.2010.05.012 ↗
14. Elattar, S, Khan, U, Zaib, A, Ishak, A, Saleh, W, Abed, AM. Scrutinization of waste discharge concentrations in Eyring–Powell nanofluid past a deformable horizontal plane surface. Water 2023;15:19. https://doi.org/10.3390/w15193419.10.3390/w15193419 ↗
15. Xin, X, Ganie, AH, Alwuthaynani, M, Bonyah, E, El-Wahed Khalifa, HA, Fathima, D, et al.. Parametric analysis of pollutant discharge concentration in non-Newtonian nanofluid flow across a permeable Riga sheet with thermal radiation. AIP Adv 2024;14:045018. https://doi.org/10.1063/5.0200401.10.1063/5.0200401 ↗
16. Nagaraja, KV, Shagolshem, S, Kanabar, B, Kedia, A, Abdulrahman, A, Prakash, C, et al.. Lie symmetry analysis on heat and mass transport aspects of rate type fluid flow with waste discharge concentration: Keller Box approach. Sci Rep 2024;14:28803. https://doi.org/10.1038/s41598-024-80267-8.10.1038/s41598-024-80267-8 ↗
17. Mishra, A. Analysis of waste discharge concentration in radiative hybrid nanofluid flow over a stretching/shrinking sheet with chemical reaction. Mech Time-Dependent Mater 2024;29:7. https://doi.org/10.1007/s11043-024-09752-x.10.1007/s11043-024-09752-x ↗
18. Sachhin, SM, Mahabaleshwar, US, Swaminathan, N, Pérez, LM, Wang, J. Thermal dynamics and magnetohydrodynamics in ferrofluidic wall jet flow: entropy generation in heat and mass transfer. J Mol Liq 2025;427:127449. https://doi.org/10.1016/j.molliq.2025.127449.10.1016/j.molliq.2025.127449 ↗
19. Chu, YM, Khan, MI, Khan, NB, Kadry, S, Khan, SU, Tlili, I, et al.. Significance of activation energy, bio-convection and magnetohydrodynamic in flow of third grade fluid (non-Newtonian) towards stretched surface: a Buongiorno model analysis. Int Commun Heat Mass Tran 2020;118:104893. https://doi.org/10.1016/j.icheatmasstransfer.2020.104893.10.1016/j.icheatmasstransfer.2020.104893 ↗
20. Sowmiya, C, Rushi Kumar, B. MHD Maxwell nanofluid flow over a stretching cylinder in porous media with microorganisms and activation energy. J Magn Magn Mater 2023;582:171032. https://doi.org/10.1016/j.jmmm.2023.171032.10.1016/j.jmmm.2023.171032 ↗
21. Sarma, N, Paul, A, Patgiri, B. Computational study of Jeffrey Hybrid nanofluid flow over on a non-uniformly heated permeable exponentially stretching surface with Arrhenius activation energy and inclined magnetic field. Hybrid Adv 2024;6:100194. https://doi.org/10.1016/j.hybadv.2024.100194.10.1016/j.hybadv.2024.100194 ↗
22. Sarkar, S, Jana, RN, Das, S. Activation energy impact on radiated magneto-Sisko nanofluid flow over a stretching and slipping cylinder: entropy analysis. Multidiscip Model Mater Struct. 2020;16:1085–115. Located at: world. https://doi.org/10.1108/MMMS-09-2019-0165.10.1108/MMMS-09-2019-0165 ↗
23. Lone, SA, Anwar, S, Saeed, A, Bognár, G. A stratified flow of a non-Newtonian Casson fluid comprising microorganisms on a stretching sheet with activation energy. Sci Rep 2023;13:11240. https://doi.org/10.1038/s41598-023-38260-0.10.1038/s41598-023-38260-0 ↗
24. Madan Kumar, R, S Raju ,R Kumar ,M. Anil, and Venkateswarlu, B A numerical study of thermal and diffusion effects on MHD Jeffrey fluid flow over a porous stretching sheet with activation energy. Numer Heat Transf A Appl. 0:1–22. https://doi.org/10.1080/10407782.2024.2319344.10.1080/10407782.2024.2319344 ↗
25. Das, TK, Paul, A, Nath, JM. Thermo-convection driven sodium alginate-based Darcy–Forchheimer EMHD Williamson hybrid nanofluid flow with varying thermal distribution. Mod Phys Lett B 2025;39:2450405. https://doi.org/10.1142/S0217984924504050.10.1142/S0217984924504050 ↗
26. Lund, LA, Yashkun, U, Shah, NA. Multiple solutions of unsteady Darcy–Forchheimer porous medium flow of Cu–Al2O3/water based hybrid nanofluid with joule heating and viscous dissipation effect. J Therm Anal Calorim 2024;149:2303–15. https://doi.org/10.1007/s10973-023-12819-5.10.1007/s10973-023-12819-5 ↗
27. Mishra, SR, Panda, S, Ratha, PK. Multi-parameter-based Box–Behnken design for optimizing energy transfer rate of Darcy–Forchheimer drag and mixed convective nanofluid flow over a permeable vertical surface with activation energy. Partial Diff Equat Appl Math 2024;12:101002. https://doi.org/10.1016/j.padiff.2024.101002.10.1016/j.padiff.2024.101002 ↗
28. Mandal, G, Pal, D. Dual solutions for magnetic-convective-quadratic radiative MoS2−SiO2/H2O hybrid nanofluid flow in Darcy–Fochheimer porous medium in presence of second-order slip velocity through a permeable shrinking surface: entropy and stability analysis. Int J Model Simulat 2025;45:517–43. https://doi.org/10.1080/02286203.2023.2222464.10.1080/02286203.2023.2222464 ↗
29. Sharma, BK, Sharma, P, Mishra, NK, Fernandez-Gamiz, U. Darcy–Forchheimer hybrid nanofluid flow over the rotating Riga disk in the presence of chemical reaction: artificial neural network approach. Alex Eng J 2023;76:101–30. https://doi.org/10.1016/j.aej.2023.06.014.10.1016/j.aej.2023.06.014 ↗
30. Paul, A, Patgiri, B, Sarma, N. Darcy–Forchheimer flow of Ag–ZnO–CoFe2O4/H2O Casson ternary hybrid nanofluid induced by a rotatory disk with EMHD. Int J Ambient Energy 2024;45:2313697. https://doi.org/10.1080/01430750.2024.2313697.10.1080/01430750.2024.2313697 ↗
31. Sachhin, SM, Ankitha, PK, Sachin, GM, Mahabaleshwar, US, Shevchuk, IV, Nayakar, SNR, et al.. Chemically reactive micropolar hybrid nanofluid flow over a porous surface in the presence of an inclined magnetic field and radiation with entropy generation. Physics 2024;6:1315–44. https://doi.org/10.3390/physics6040082.10.3390/physics6040082 ↗
32. Hussain, SM, Jamshed, W, Eid, MR. Solar-HVAC thermal investigation utilizing (Cu-AA7075/C6H9NaO7) MHD-driven hybrid nanofluid rotating flow via second-order convergent technique: a novel engineering study. Arab J Sci Eng 2023;48:3301–22. https://doi.org/10.1007/s13369-022-07140-6.10.1007/s13369-022-07140-6 ↗
33. Sharma, RP, Shukla, S, Mishra, SR. Influence of an induced magnetic field and flow behavior of (AA7072–AA7075/water) hybrid nanoliquid in a vertical channel with suction velocity. J Therm Anal Calorim 2023;148:11155–66. https://doi.org/10.1007/s10973-023-12395-8.10.1007/s10973-023-12395-8 ↗
34. Sachhin, SM, Bharath, MS, Mahabaleshwar, US, Bognar, GV, Pérez, LM. Dual modeling of unsteady radiative non-Newtonian fluid flow with Biot boundary conditions using novel time-dependent solutions. Mech Time-Dependent Mater 2026;30:5. https://doi.org/10.1007/s11043-025-09849-x.10.1007/s11043-025-09849-x ↗
35. Thamizharasan, T, Reddy, AS. Entropy generation on pulsatile hydromagnetic flow of Jeffrey nanofluid in a porous channel with Brownian motion, thermophoresis, and heat source/sink using Cattaneo–Christov heat flux. Indian J Pure Appl Phys (IJPAP). 2022;60:8. https://doi.org/10.56042/ijpap.v60i8.63440.10.56042/ijpap.v60i8.63440 ↗
36. Sachhin, SM, Granados-Ortiz, FJ, Mahabaleshwar, US, Ortega-Casanova, J, Pérez, LM. Heat and mass transfer analysis of a Bingham ternary nanofluid exposed to radiation over stretching/shrinking sheets and Stefan blowing effect. Alex Eng J 2025;129:515–29. https://doi.org/10.1016/j.aej.2025.06.026.10.1016/j.aej.2025.06.026 ↗
37. Pal, D. Entropy generation and Arrhenius activation energy mechanisms in EMHD radiative Carreau nanofluid flow due to Brownian motion and thermophoresis with infinite shear rate viscosity: solar energy application and regression analysis. Int J Ambient Energy 2024;45:2334401. https://doi.org/10.1080/01430750.2024.2334401.10.1080/01430750.2024.2334401 ↗
38. Khan, WA, Pop, I. Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Tran 2010;53:2477–83. https://doi.org/10.1016/j.ijheatmasstransfer.2010.01.032.10.1016/j.ijheatmasstransfer.2010.01.032 ↗
39. Reddy Gorla, RS, Sidawi, I. Free convection on a vertical stretching surface with suction and blowing. Appl Sci Res 1994;52:247–57. https://doi.org/10.1007/BF00853952.10.1007/BF00853952 ↗
40. Wang, CY. Free convection on a vertical stretching surface. ZAMM - J Appl Math Mech/Z Angew Math Mech 1989;69:418–20. https://doi.org/10.1002/zamm.19890691115.10.1002/zamm.19890691115 ↗
41. Bhatta, DP, Mishra, SR, Dash, JK, Reddy, MG. Squeezing flow analysis of time dependent AA7072 and AA7075 water-based nanofluids through parallel disks with velocity and thermal slip conditions. Proc Inst Mech Eng N. J Nanomater Nanoeng Nanosyst 2023;237:45–58.10.1177/23977914221082888 ↗
42. Ali, B, Jubair, S, Garayev, M, El-Wahid Khalifa, HA, Kumar, A, Shaaban, AA. Energy and mass transfer through hybrid nanofluids flow comprised of AA7072–AA7075 nanoparticles subject to magnetic and thermal radiation on stretching surface. J Radiat Res Appl Sci 2025;18:101250. https://doi.org/10.1016/j.jrras.2024.101250.10.1016/j.jrras.2024.101250 ↗
43. Sachhin, SM, Mahabaleshwar, US, Bognar, GV, Laroze, D, Shevchuk, IV. Mathematical modeling on colloidal mixture of Casson sodium alginate ternary nanofluid suspensions driven by stretching surface with magnetic field and arbitrary power-law velocities: an analytical approach. Eur Phys J A 2025;140:1204. https://doi.org/10.1140/epjp/s13360-025-07135-w.10.1140/epjp/s13360-025-07135-w ↗
44. Yaseen, M, Rawat, SK, Khan, U, Sarris, IE, Khan, H, Negi, AS, et al.. Computational analysis of heat and mass transfer flow of wall jet hybrid nanofluid with irregular heat source/sink effects and waste discharge concentration. J Magn Magn Mater 2023;1:171434. https://doi.org/10.1016/j.jmmm.2023.171434.10.1016/j.jmmm.2023.171434 ↗
45. Khan, U, Zaib, A, Ishak, A, Ghodhbani, R, Elkamchouchi, DH. Insight into the hydrothermal performance for buoyancy flow of a micropolar nanofluid past a stretching/shrinking sheet with viscous dissipation effects. J Therm Anal Calorim 2025;150:8043–58. https://doi.org/10.1007/s10973-025-14217-5.10.1007/s10973-025-14217-5 ↗
46. Elattar, S, Khan, U, Zaib, A, Ishak, A, Alwadai, N, Albalawi, H. Radiative flow of clay nanoparticles on the lubricity of Williamson drilling fluids across a vertical surface in a Darcy–Brinkman porous medium. Chin J Phys 2024;92:701–20. https://doi.org/10.1016/j.cjph.2024.08.031.10.1016/j.cjph.2024.08.031 ↗
47. Nazari, NL, Ishak, A, Khan, U, Zaib, A, Hussain, SM, Elattar, S. The implication of thermal radiation in a mixed convection hybrid nanofluid flow past an inclined stretching/shrinking sheet with mass suction. J Radiat Res Appl Sci 2025;18:101420. https://doi.org/10.1016/j.jrras.2025.101420.10.1016/j.jrras.2025.101420 ↗