Analysis of Bioconvective Steady Darcy Forchhemier Nanofluid Flow with Arrhenius Chemical Kinetics and Energy Transition over a Permeable Vertical Plate


Published: 2024-01-24

Page: 59-76

Matilukuro O. M. *

Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

Olanrewaju P. O.

Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

Amoo S. A.

Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

Nwaokolo M. A.

Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

*Author to whom correspondence should be addressed.


In the realm of renewable energy, Darcy-Forchheimer nanofluids are considered for use in solar collectors and thermal energy storage systems. Magnetohydrodynamics Bioconvective Unsteady Darcy Forchhemier Nanofluid flow with arrhenius chemical kinetics and energy transition over a permeable vertical plate was considered. The Darcy Forchheimer porosity medium was considered for the flow analysis. The impressions of thermal radiation, viscous dissipation, heat generation, activation energy, Soret and Dufour effects are taken to investigate the transference analysis of heat and mass rate. The flow equations are in the form of partial differential equations (PDEs) and we utilize suitable similarity transformations to convert them into ordinary differential equations (ODEs). The thermophysical characteristics of the gyrostatic microorganisms conducting flow with energy transition were analysed numerically using Chebyshev Collocation Method (CCM – Hybrid Numerical method) and analytically, using Galarking Weighted Residual Method (GWRM – Analytical technique) with help of MATHEMATICA software. The findings from this research were analyzed in the form of graphs and tables. The following is a list of some key observations from this parametric research: The chemical reaction thermophoresis and Brownian motion parameter reduces the mass concentration, while large values of activation energy have the opposite effect. The mounting values of Péclet numbers (Pe) and bioconvection Lewis numbers reduce the motile microorganism profile. The results obtained showed a perfect agreement with the existing literature and have further applications in fluid dynamic.

Keywords: Bioconvective, darcy forchhemier, nanofluid, arrhenius chemical kinetics

How to Cite

Matilukuro O. M., Olanrewaju P. O., Amoo S. A., & Nwaokolo M. A. (2024). Analysis of Bioconvective Steady Darcy Forchhemier Nanofluid Flow with Arrhenius Chemical Kinetics and Energy Transition over a Permeable Vertical Plate . Asian Journal of Pure and Applied Mathematics, 6(1), 59–76. Retrieved from


Download data is not yet available.


Maxwell JC. Electricity and Magnetism. Clarendon Press, Oxford, UK; 1873.

Yu W, Choi SUS. The role of interfacial layers in the enhanced thermal conductivity of Nanofluids: A Renovated Maxwell Model. Journal of Nanoparticle Research. 2003;5:167–171.

Yu SM. Effect of Nanoparticles on Critical Heat Flux of water in Pool Boiling Heat Transfer. Applied Physics Letters. 2003;83:3374-3376.

Sreelakshmy KR, Aswathy S Nair, Vidhya KM, Saranya TR, Sreeja C Nair. Overview of Recent Nanofluid Research. International Research Journal Pharm. 2014;5(4):1-5. DOI: 10,7897/2230 – 8407, 050451

Maatoug S, Babu KH, Deepthi VVL, Ghachem K, Raghunath K, Ganteda C, Khan SU. Variable chemical species and thermo-diffusion Darcy–Forchheimer squeezed flow of Jeffrey nanofluid in horizontal channel with viscous dissipation effects. Journal of the Indian Chemical Society. 2023;100(1):100831.

Gaffar SA, Prasad VR, Beg OA. Numerical study of flow and heat transfer of non-Newtonian tangent hyperbolic fluid from a sphere with Biot number effects, Alex. Eng. J. 2015;54:829–841.

Ali A, Asghar S. Analytic solution for oscillatory flow in a channel for Jeffrey fluid, J. Aero. Eng. 2012;27:644–651.

Sharma BD, Yadav PK, Filippov AA. Jeffrey-fluid model of blood flow in tubes with stenosis. Colloid J. 2017;79:849–856.

Seddeek MA. Influence of viscous dissipation and thermophoresis on Darcy Forchheimer mixed convection in a fluid saturated porous media, J. Colloid Interface Sci. 2006;293:137–142.

Kuznetsov AV. The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms. International Communications in Heat and Mass Transfer. 2010;37(10):1421-1425.

Kuznetsov AV. Nanofluid bioconvection in water-based suspensions containing nanoparticles and oxytactic microorganisms: Oscillatory instability. Nanoscale Research Letters. 2011;6:1-13.

Khan M, Salahuddin T, Malik MY, Mallawi FO. Change in viscosity of Williamson nanofluid flow due to thermal and solutal stratification. International Journal of Heat and Mass Transfer. 2018;941-948. DOI: 10.1016/j.ijheatmasstransfer.2018.05.074

Kazi SN, Hussein T. An experimental and numerical investigation of heat and mass transfer enhancement for graphic nanoplatelets nanofluids in turbulent flow conditions. Journal of Heat and Mass Transfer. 2015;41-51.

Tzeng SC, Lim CW, Huang KD. Heat Transfer Enhancement of Nanofluids in Rotary Blade Coupling of Four-Wheel-Drive Vehicles. Acta Mechanica. 2005;179:11-23.

Vassallo, Peter, Kumar Ranganathan, D’Amico Stephen. Pool boiling heat transfer experiments in Silica-Water NanoFluids. International Journal of Heat and Mass Transfer. 2004;47:407-411.

Sabet FA. Nanofluid-based sensors and their applications in detection of chemical and biological species: A review. Microchimica Acta. 2018;185(3):213-220.

Farooq U, Tahir M, Waqas H, Muhammad T, Alshehri A, Imran M. Investigation of 3D flow of magnetized hybrid nanofluid with heat source/sink over a stretching sheet, Scientific Reports. 2022;12:12254.

Gandhi R, Sharma B. Combined effects of Joule heating and non-uniform heat source/sink on unsteady MHD mixed convective flow over a vertical stretching surface embedded in a Darcy-Forchheimer porous medium. Propulsion and Power Research. 2022;11(2):276-292.

Gautam AK, Rajput S, Bhattacharyya K, Pandey AK, Chamkha AJ, Begum M. Comparative study of two non-newtonian fluids with bioconvective induced MHDflow in presence of multiple slips, heat source/sink and nonlinear thermal radiation. Chemical Engineering Journal Advanves. 2022;12:100365.

Jawad M, Mebarek-Oudina F, Vaidya H, Prashar P. Influence of bioconvection and thermal radiation on MHD Williamson non casson fluid flow with the swimming of gyrotactic microorganisms due to porous stretching sheet. J. Nanofluids. 2022;11(4):500-509.

Asogwa KK, Goud BS, Reddy YD, Ibe AA. Suction effect on the dynamics of MHD casson nanofluid over an induced stagnation point flow of stretchable electromagnetic plate with radiation and chemical reaction, Results in Engineering. 2022;15:100-518.

Eswaramoorthi S, Thamaraiselvi S, Loganathan K. Exploration of darcy-forchheimer flows of non-newtonian casson and Williamson conveying tiny particles experiencing binary chemical reaction and thermal radiation: comparative analysis. Maths. Comput. Appl. 2022;27:52.

Jawad M, Saeed A, Gul T, Bariq A. MHD Darcy-Forchheimer flow of Casson nanofluid due to a rotating disk with thermal radiation and Arrhenius activation energy. Journal of Physics Communications. 2021;5(2):025008.

Nadab H, Amoo SA, Olopade IA. Heat and mass transfer analysis of magnetohydrodynamic (MHD) thermosolutal nanofluid flow over vertical and inclined porous media. International Journal of Mathematical Analysis and Modelling. 2023;6(2).

Yusuf TA, Mabood F, Prasannakumara BC, Sarris IE. Magneto-Bioconvection Flow of Williamson Nanofluid over an Inclined Plate with Gyrotactic Microorganisms and Entropy Generation . Fluids. 2021;6(3):109-120. DOI: 10.3390/fluids603010

Abdel MS, Mahantesh M, Nandeppanava K, Sharanagouda B, Malipatil A. Heat transfer in a second grade fluid through a porous medium from a permeable stretching sheet with non-uniform heat source/sink. International Journal of Heat and Mass Transfer. 2010;53(9-10):205-217.

Srinivas S, Kalyan Kumar C, Badeti S, Reddy AS. MHD Flow of Casson Nanofluid over an inclined porous stretching surface. In Recent Advances in Applied Mathematics and Applications to the Dynamics of Fluid Flows: 5th International Conference on Applications of Fluid Dynamics (ICAFD) 2020 (pp. 155-165). Singapore: Springer Nature Singapore; 2022, October.

Srinivas S, Challa KK, Badeti S, Kumar PB. Pulsatile powell-eyring nanofluid flow in a channel with inclined magnetic field and chemical reaction. Engineering Transactions. 2023;71(4):519-535.

Srinivas S, Kumar CK, Reddy AS. Dufour and Soret effects on pulsatile hydromagnetic flow of Casson fluid in a vertical non-Darcian porous space. Nonlinear Analysis: Modelling and Control. 2022;27(4):669-683.

Algehyne EA, Areshi M, Saeed A, Bilal M, Kumam W, Kumam P. Numerical simulation of bioconvective Darcy Forchhemier nanofluid flow with energy transition over a permeable vertical plate. Scientific Reports. 2022;12(1):3228.

Makinde OD, Aziz A. Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. International Journal of Thermal Sciences. 2011;50:1326-1332.

Khan W, Pop I. Boundary-layer flow of a nanofluid past a stretching sheet. International Journal of Heat. 2010;53:2477-2483.

Abolbashari MH, Freidoonimehr N, Nazari F, Rashidi MM. Analytical modeling of entropy generation for Casson nano-fluid flow induced by a stretching surface. J Advanced Powder Technology. 2015;26:542-552.