In this work the non-homogeneous model for the nanofluid flow is formulated to examine the consequences of Fick’s and Fourier’s laws on bioconvective MHD couple-stress nanoliquid flows across a stretching surface under the significances of multiple stratified conditions and activation energy. Both the concentrations of motile microbes and solid nanoparticles are unified flow system. Furthermore, the collective effects of the Cattaneo–Christov (CC) heat flux and thermal radiation are also analyzed. To remove the complexity from the mathematical model, the similarity conversions are presented properly to change the resulting system of PDEs into a nonlinear set of ODEs. The transform set of ODEs is then numerically solved through the parametric continuation method (PCM) in MATLAB software. To validate our results, the outcomes are compared with bvp4c package. It can be perceived that the fluid velocity decreases with the impact of mixed convection and magnetic effects. The energy field enriches with the variation of thermophoresis effect, thermal radiation, buoyancy ratio factor, and Rayleigh number. Furthermore, the mass profile diminishes under the consequences of Lewis number, whereas enhanced with the effect of thermophoresis factor and concentration stratification Biot number.
PlattJR. Bioconvection patterns in cultures of free-swimming organisms. Science1961; 133(3466): 1766–1767.
2.
AreekaraSMaboodFSabuAS, et al. Dynamics of water conveying single-wall carbon nanotubes and magnetite nanoparticles subject to induced magnetic field: a bioconvective model for theranostic applications. Int Commun Heat Mass Transf2021; 126: 105484.
3.
TayyabMSiddiqueIJaradF, et al. Numerical solution of 3D rotating nanofluid flow subject to Darcy–Forchheimer law, bio-convection and activation energy. South Afr J Chem Eng2022; 40: 48–56.
4.
KhanASaeedATassaddiqA, et al. Bio-convective micropolar nanofluid flow over thin moving needle subject to Arrhenius activation energy, viscous dissipation and binary chemical reaction. Case Stud Therm Eng2021; 25: 100989.
5.
GangadharKSreeTSWakifA, et al. Stefan blowing impact and chemical response of Rivlin–Reiner fluid through rotating convective disk. Pramana2024; 98(4): 1–16.
6.
AnjumNKhanWAHobinyA, et al. Numerical analysis for thermal performance of modified Eyring Powell nanofluid flow subject to activation energy and bioconvection dynamic. Case Stud Therm Eng2022; 39: 102427.
7.
GangadharKNaga ChandrikaGDinarvandS.Simulation of radiative nonlinear heat dynamism on Buongiorno-modeled nanoliquid through porous inclined plate with adjustable chemical response. Mod Phys Lett B2024; 38(34): 2450347.
8.
ShahSAAAhammadNAAliB, et al. Significance of bio-convection, MHD, thermal radiation and activation energy across Prandtl nanofluid flow: a case of stretching cylinder. Int Commun Heat Mass Transf2022; 137: 106299.
9.
HabibDSalamatNAbdalS, et al. On time dependent MHD nanofluid dynamics due to enlarging sheet with bioconvection and two thermal boundary conditions. Microfluid Nanofluid2022; 26(2): 1–15.
10.
UsmanMGulTKhanA, et al. Electromagnetic couple stress film flow of hybrid nanofluid over an unsteady rotating disc. Int Commun Heat Mass Transf2021; 127: 105562.
11.
WaseemMGulTKhanI, et al. Gravity-driven hydromagnetic flow of couple stress hybrid nanofluid with homogenous-heterogeneous reactions. Sci Rep2021; 11(1): 1–12.
12.
UllahMZAbuzaidDAsmaM, et al. Couple stress hybrid nanofluid flow through a converging-diverging channel. J Nanomater2021; 8: 1–13.
13.
GangadharKMary VictoriaEWakifA.Irreversibility analysis for the EMHD flow of silver and magnesium oxide hybrid nanofluid due to nonlinear thermal radiation. Mod Phys Lett B2024; 38(33): 2450337.
14.
DhlaminiMMondalHSibandaP, et al. Numerical analysis of couple stress nanofluid in temperature dependent viscosity and thermal conductivity. Int J Appl Comput Math2021; 7(2): 1–14.
15.
WaqasHWakifAAl-MdallalQ, et al. Significance of magnetic field and activation energy on the features of stratified mixed radiative-convective couple-stress nanofluid flows with motile microorganisms. Alex Eng J2022; 61(2): 1425–1436.
16.
AzizSKolsiLAhmadI, et al. Thermal stability and bioconvection investigation for couple stress nanofluid due to a three-dimensional accelerated frame. Waves Random Complex Media2022; 35(3): 1–22.
17.
MukherjeeSShitGC.Mathematical modeling of electrothermal couple stress nanofluid flow and entropy in a porous microchannel under injection process. Appl Math Comput2022; 426: 127110.
18.
HameedNNoeiaghdamSKhanW, et al. Analytical analysis of the magnetic field, heat generation and absorption, viscous dissipation on couple stress Casson hybrid nano fluid over a nonlinear stretching surface. Results Eng2022; 16: 100601.
19.
SridharVRameshKTripathiD, et al. Analysis of thermal radiation, Joule heating, and viscous dissipation effects on blood–gold couple stress nanofluid flow driven by electroosmosis. Heat Transf2022; 51(5): 4080–4101.
20.
ZuhraSRajaMAZShoaibM, et al. Numerical analysis of Cattaneo–Christov heat flux model over magnetic couple stress Casson nanofluid flow by Lavenberg–Marquard backpropagated neural networks. Waves Random Complex Media2022; 15: 1–28.
21.
GangadharKPrameelaMChamkhaAJ, et al. Evaluation of homogeneous–heterogeneous chemical response on Maxwell-fluid flow through spiraling disks with nonlinear thermal radiation using numerical and regularized machine learning methods. Int J Model Simul2024; 16: 1–23.
22.
GangadharKSujana SreeTChamkhaAJ.Binary chemical interaction and nonlinearity radiative flux of Williamson fluidic flow through Riga plate. Int J Model Simul2024; 45(6): 2184–2198.
23.
ShiQHHamidAKhanMI, et al. Numerical study of bio-convection flow of magneto-cross nanofluid containing gyrotactic microorganisms with activation energy. Sci Rep2021; 11(1): 1–15.
24.
XiaWFHaqFSaleemM, et al. Irreversibility analysis in natural bio-convective flow of Eyring–Powell nanofluid subject to activation energy and gyrotactic microorganisms. Ain Shams Eng J2021; 12(4): 4063–4074.
25.
ChuYMKhanMIWaqasH, et al. Numerical simulation of squeezing flow Jeffrey nanofluid confined by two parallel disks with the help of chemical reaction: effects of activation energy and microorganisms. Int J Chem React Eng2021; 19(7): 717–725.
26.
IrfanMRafiqKKhanM, et al. Theoretical analysis of new mass flux theory and Arrhenius activation energy in Carreau nanofluid with magnetic influence. Int Commun Heat Mass Transf2021; 120: 105051.
27.
BabuBHRaoPSReddyMG, et al. Numerical modelling of activation energy and hydromagnetic non-Newtonian fluid particle deposition flow in a rotating disc. Proc Inst Mech Eng E J Process Mech Eng2021; 237(2): 095440892110459.
28.
RazaQQureshiMZAKhanBA, et al. Insight into dynamic of mono and hybrid nanofluids subject to binary chemical reaction, activation energy, and magnetic field through the porous surfaces. Mathematics2022; 10(16): 3013.
FourierJBJ. Théorie analytique de la chaleur. Didot, 1822.
31.
CattaneoC.Sulla conduzione del calore. Atti Semin Mat Fis Univ Modena Reggio Emilia1948; 3: 83–10.
32.
ChristovCI.On frame indifferent formulation of the Maxwell–Cattaneo model of finite-speed heat conduction. Mech Res Commun2009; 36: 481–486.
33.
TurkyilmazogluM.Heat transfer enhancement feature of the non-Fourier Cattaneo–Christov heat flux model. J Heat Transf2021; 143(9): 1671.
34.
GireeshaBJShankaralingappaBMPrasannakumarBC, et al. MHD flow and melting heat transfer of dusty Casson fluid over a stretching sheet with Cattaneo–Christov heat flux model. Int J Ambient Energy2022; 43(1): 2931–2939.
35.
ReddyPSSreedeviPChamkhaAJ.Heat and mass transfer analysis of nanofluid flow over swirling cylinder with Cattaneo–Christov heat flux. J Therm Anal Calorim2022; 147(4): 3453–3468.
BilalMSaeedASelimMM, et al. Comparative numerical analysis of Maxwell’s time-dependent thermo-diffusive flow through a stretching cylinder. Case Stud Therm Eng2021; 27: 101301.
39.
ZhangXHA AlgehyneEG AlshehriM, et al. The parametric study of hybrid nanofluid flow with heat transition characteristics over a fluctuating spinning disk. PLoS One2021; 16(8): e0254457.
40.
HouEWangFKhanMN, et al. Flow analysis of hybridized nanomaterial liquid flow in the existence of multiple slips and Hall current effect over a slendering stretching surface. Crystals2021; 11(12): 1546.
41.
SitholeHMondalHGoqoS, et al. Numerical simulation of couple stress nanofluid flow in magneto-porous medium with thermal radiation and a chemical reaction. Appl Math Comput2018; 339: 820–836.
42.
ShuaibMShahRADurraniI, et al. Electrokinetic viscous rotating disk flow of Poisson–Nernst–Planck equation for ion transport. J Mol Liq2020; 313: 113412.
43.
ShuaibMShahRABilalM.Variable thickness flow over a rotating disk under the influence of variable magnetic field: an application to parametric continuation method. Adv Mech Eng2020; 12(6): 1687814020936385.
44.
ZhangLBilalMUllahS, et al. Couple-stress nanofluid flow comprising gyrotactic microbes subject to convective boundary conditions: numerical solution. AIP Adv2024; 14(5): 55222.
