Transport mechanism in chemically reactive hybrid nanofluidflow containing gyrotactic micro-organisms overa curved oscillatory surface

doi:10.1007/s10483-025-3208-7

Abstract

Abstract:

This paper examines the transport analysis, including both heat transfer and mass transfer, in hybrid nanofluid flow containing gyrotactic microorganisms towards a curved oscillatory surface. The influence of magnetic fields is also inspected in terms of their physical characteristics. To depict the phenomena of transport, modified versions of both Fick's and Fourier's laws are used. Additionally, the characteristics of both heterogeneous and homogeneous chemical reactions are also incorporated. Utilizing a curvilinear coordinate system, the flow problem is formulated as partial differential equations (PDEs) for momentum, concentration, microorganism field, and energy. An analytical solution to the obtained flow equations is achieved utilizing the homotopy analysis method (HAM). The effects of significant flow parameters on the pressure and microorganism fields, velocity, oscillation velocity, concentration, and temperature distributions are shown via graphs. Furthermore, the variations in skin friction, mass transfer rate, heat transfer rate, and local motile number due to different involved parameters are presented in tables and are analyzed in detail. Graphical results indicate that the curves of velocity and temperature fields are enhanced as the values of the solid volume fraction variables increase. It is also verified that the concentration rate field decreases as the values of the homogeneous reaction strength parameter and the radius of curvature parameter increase, and it increases with the Schmidt number and the heterogeneous reaction strength parameter. Tabular outcomes show a favorable response of the motile number to advanced values of the Peclet number, the Schmidt number, the microorganism difference parameter, and the bio-convective Lewis number.

Key words: hybrid nanofluid, oscillating curved stretchable sheet, gyrotactic microorganism, Cattaneo-Christov heat and mass flux, chemical reaction, analytical solution

2010 MSC Number:

O368

M. NAVEED, M. IMRAN, T. ASGHAR, Z. ABBAS. Transport mechanism in chemically reactive hybrid nanofluidflow containing gyrotactic micro-organisms overa curved oscillatory surface. Applied Mathematics and Mechanics (English Edition), 2025, 46(1): 177-192.

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Figures/Tables 12

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Table 1

Comparison of the numerical results of g″(0,τ) with the existing results for divergent values of τ when S=1.0, M=12, φ1=0.0, φ2=0.0, and R0→∞"

$τ$	Ref. [7]	Ref. [27]	Present result
$32 π$	11.678 656	11.678 656	11.678 656
$112 π$	11.678 706	11.678 706	11.678 706
$192 π$	11.678 655	11.678 656	11.678 655

Table 1

References 47

[1]	SANNI, K. M., ASGHAR, S., JALIL, M., and OKECHI, K. M. Flow of viscous fluid along a nonlinearly stretching curved surface. Results in Physics, 7, 1–4 (2017)
[2]	OKECHI, N. F., JALIL, M., and ASGHAR, S. Flow of viscous fluid along an exponentially stretching curved surface. Results in Physics, 7, 2851–2854 (2017)
[3]	HAYAT, T., RASHID, M., ALSAEDI, A., and AHMED, B. Flow of nanofluid by nonlinear stretching velocity. Results in Physics, 8, 1104–1109 (2018)
[4]	NAVEED, M., ABBAS, Z., SAJID, M., and HASNAIN, J. Dual solution in hydromagnetic viscous fluid flow past a shrinking curved surface. Arabian Journal for Science and Engineering, 43, 1189–1194 (2018)
[5]	WANG, C. Y. Nonlinear streaming due to the oscillatory stretching of a sheet in a viscous fluid. Acta Mechanica, 72(3), 261–268 (1988)
[6]	ABBAS, Z., WANG, Y., HAYAT, T., and OBERLACK, M. Hydromagnetic flow in a viscoelastic fluid due to the oscillatory stretching surface. International Journal of Non-Linear Mechanics, 43(8), 783–793 (2008)
[7]	KHAN, S. U., SHEHZAD, S. A., and NASIR, S. Unsteady flow of chemically reactive Oldroyd-B fluid over oscillatory moving surface with thermo-diffusion and heat absorption/generation effects. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(2), 72 (2019)
[8]	IMRAN, M., ABBAS, Z., NAVEED, M., and SALAMAT, N. Impact of Joule heating and melting on time dependent flow of nanoparticles due to an oscillatory stretchable curved wall. Alexandria Engineering Journal, 60(4), 4097–4113 (2021)
[9]	HASNAIN, J., ABID, N., ALANSARI, M. O., and ULLAH, M. Z. Analysis on Cattaneo-Christov heat flux in three-phase oscillatory flow of non-Newtonian fluid through porous zone bounded by hybrid nanofluids. Case Studies in Thermal Engineering, 35, 102074 (2020)
[10]	CASTRO, A. R., CHABANON, M., and GOYEAU, B. Numerical analysis of the fluid-solid interactions during steady and oscillatory flows of non-Newtonian fluid through deformable porous media. Chemical Engineering Research and Design, 193, 38–53 (2023)
[11]	RAUF, A., SHEHZAD, S. A., ABBAS, Z., and HAYAT, T. Unsteady three-dimensional MHD flow of the micropolar fluid over an oscillatory disk with Cattaneo-Christov double diffusion. Applied Mathematics and Mechanics (English Edition), 40(10), 1471–1486 (2019) https://doi.org/10.1007/s10483-019-2530-6
[12]	ABBAS, Z., IMRAN, M., and NAVEED, M. Time-dependent flow of thermally developed viscous fluid over an oscillatory stretchable curved surface. Alexandria Engineering Journal, 59(6), 4377–4390 (2020)
[13]	NAVEED, M., IMRAN, M., and ABBAS, Z. Curvilinear flow of micropolar fluid with Cattaneo-Christov heat flux model due to oscillation of curved stretchable sheet. Zeitschrift für Naturforschung A, 76(9), 799–821 (2021)
[14]	IMRAN, M., NAVEED, M., and ABBAS, Z. Dynamics of Soret and Dufour effects on oscillatory flow of couple stress fluid due to stretchable curved surface. Advances in Mechanical Engineering, 15(2), 16878132231156742 (2023)
[15]	WÖHLISCH, E. Adolf Fick und die heutige physiologie. Naturwissenschaften, 26(36), 585–591 (1938)
[16]	FOURIER, J. B. J. Théorie Analytique de la Chaleur, Gauthier-Villars, Paris (1888)
[17]	CATTANEO, C. Sulla conduzione del calore. Atti dei Seminari della Facoltà di Matematica, Fisica, Chimica e Geologia dell. Università di Modena, 3, 83–101 (1948)
[18]	CHRISTOV, C. I. On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction. Mechanics Research Communications, 36(4), 481–486 (2009)
[19]	BILAL, S., SHAH, M. I., KHAN, N. Z., AKGÜL, A., and NISAR, K. S. Onset about non-isothermal flow of Williamson liquid over exponential surface by computing numerical simulation in perspective of Cattaneo Christov heat flux theory. Alexandria Engineering Journal, 61(8), 6139–6150 (2022)
[20]	HAFEEZ, A. and KHAN, M. Flow of Oldroyd-B fluid caused by rotating disk featuring the Cattaneo-Christov theory with heat generation/absorption. International Communications in Heat and Mass Transfer, 123, 105179 (2021)
[21]	IMRAN, M., ABBAS, Z., and NAVEED, M. Flow of Eyring-Powell liquid due to oscillatory stretchable curved sheet with modified Fourier and Fick's model. Applied Mathematics and Mechanics (English Edition), 42(10), 1461–1478 (2021) https://doi.org/10.1007/s10483-021-2779-9
[22]	FAROOQ, U., WAQAS, H., MAKKI, R., ALI, M. R., ALHUSHAYBARI, A., MUHAMMAD, T., and IMRAN, M. Computation of Cattaneo-Christov heat and mass flux model in Williamson nanofluid flow with bioconvection and thermal radiation through a vertical slender cylinder. Case Studies in Thermal Engineering, 42, 102736 (2023)
[23]	MEHRYAN, S. A. M., IZADPANAHI, E., GHALAMBAZ, M., and CHAMKHA, A. J. Mixed convection flow caused by an oscillating cylinder in a square cavity filled with Cu-Al₂O₃/water hybrid nanofluid. Journal of Thermal Analysis and Calorimetry, 137(3), 965–982 (2019)
[24]	NADEEM, S., ABBAS, N., and MALIK, M. Y. Inspection of hybrid based nanofluid flow over a curved surface. Computer Methods and Programs in Biomedicine, 189, 105193 (2020)
[25]	SAEED, A., ALGHAMDI, W., MUKHTAR, S., SHAH, S. I. A., KUMAM, P., GUL, T., NASIR, S., and KUMAM, W. Darcy-Forchheimer hybrid nanofluid flow over a stretching curved surface with heat and mass transfer. PLOS One, 16(5), e0249434 (2021)
[26]	NAVEED, M., ALI, S., HASNAIN, J., and ABBAS, Z. Analysis of the effect of Joule heating and Hall current on flow of hybrid nanofluid over a curved stretching surface with melting boundary condition. Heat Transfer Research, 52(5), 1–16 (2021)
[27]	IMRAN, M., NAVEED, M., IFTIKHAR, B., and ABBAS, Z. Heat transfer analysis in a curvilinear flow of hybrid nanoliquid across a curved oscillatory stretched surface with nonlinear thermal radiation. Zeitschrift für Angewandte Mathematik und Mechanik, 103(11), e202200600 (2023)
[28]	RAMESH, K., WARKE, A. S., KOTECHA, K., and VAJRAVELU, K. Numerical and artificial neural network modelling of magnetorheological radiative hybrid nanofluid flow with Joule heating effects. Journal of Magnetism and Magnetic Materials, 570, 170552 (2023)
[29]	XU, H. Mixed convective flow of a hybrid nanofluid between two parallel inclined plates under wall-slip condition. Applied Mathematics and Mechanics (English Edition), 43(1), 113–126 (2022) https://doi.org/10.1007/s10483-021-2801-6
[30]	ACHARYA, N., DAS, K., and KUNDU, P. K. Framing the effects of solar radiation on magneto-hydrodynamics bioconvection nanofluid flow in presence of gyrotactic microorganisms. Journal of Molecular Liquids, 222, 28–37 (2016)
[31]	KHAN, W. A., MAKINDE, O. D., and KHAN, Z. H. MHD boundary layer flow of a nanofluid containing gyrotactic microorganisms past a vertical plate with Navier slip. International Journal of Heat and Mass Transfer, 74, 285–291 (2014)
[32]	KHASHIE, N. S., ARFIN, N. M., POP, I., and NAZAR, R. Dual solutions of biconvective hybrid nanofluid flow due to gyrotactic microorganism towards a vertical plate. Chinese Journal of Physics, 72, 461–474 (2021)
[33]	MUHAMMAD, M. Bioconvection and nonlinear thermal extrusion in development of chemically reactive Sutterby nano-material due to gyrotactic microorganisms. International Communications in Heat and Mass Transfer, 130, 105820 (2022)
[34]	ALGEHYNE, E. A., SAEED, A., ARIF, M., BILAL, M., KUMAM, P., and GALAL, A. M. Gyrotactic microorganism hybrid nanofluid over a Riga plate subject to activation energy and heat source: numerical approach. Scientific Reports, 13(1), 13675 (2023)
[35]	YASMIN, H., LONE, S. A., TASSADDIQ, A., RAIZAH, Z., ALRABAIAH, H., and SAEED, A. Numerical analysis of slip-enhanced flow over a curved surface with magnetized water-based hybrid nanofluid containing gyrotactic microorganisms. Scientific Reports, 13(1), 18816 (2023)
[36]	ZUHRA, S., KHAN, N. S., SHAH, Z., ISLAM, S., and BONYAH, E. Simulation of bioconvection in the suspension of second grade nanofluid containing nanoparticles and gyrotactic microorganisms. Aip Advances, 8(10), 105210 (2018)
[37]	KHAN, N. S., KUMAM, P., and THOUNTHONG, P. Renewable energy technology for the sustainable development of thermal system with entropy measures. International Journal of Heat and Mass Transfer, 145, 118713 (2019)
[38]	KHAN, N. S., HUMPHRIES, U. W., KUMAM, W., KUMAM, P., and MUHAMMAD, T. Assessment of irreversibility optimization in Casson nanofluid flow with leading edge accretion or ablation. Zeitschrift für Angewandte Mathematik und Mechanik, 102(10), e202000207 (2022)
[39]	KHAN, N. S., HUSSANAN, A., KUMAM, W., KUMAM, P., and SUTTIARPORN, P. Accessing the thermodynamics of Walter-B fluid with magnetic dipole effect past a curved stretching surface. Zeitschrift für Angewandte Mathematik und Mechanik, 103(8), e202100112 (2023)
[40]	KHAN, N. S., HUMPHRIES, U. W., KUMAM, W., KUMAM, P., and MUHAMMAD, T. Dynamic pathways for the bioconvection in thermally activated rotating system. Biomass Conversion and Biorefinery, 14(7), 8605–8623 (2024)
[41]	KHAN, N. S., SHAH, Q., SOHAIL, A., KUMAM, P., THOUNTHONG, P., and MUHAMMAD, T. Mechanical aspects of Maxwell nanofluid in dynamic system with irreversible analysis. Zeitschrift für Angewandte Mathematik und Mechanik, 101(12), e202000212 (2021)
[42]	HAYAT, T., AYUB, T., MUHAMMAD, T., and ALSAEDI, A. Three-dimensional flow with Cattaneo-Christov double diffusion and homogeneous-heterogeneous reactions. Results in Physics, 7, 2812–2820 (2017)
[43]	IMTIAZ, M., HAYAT, T., and ALSAEDI, A. Convective flow of ferrofluid due to a curved stretching surface with homogeneous-heterogeneous reactions. Powder Technology, 310, 154–162 (2017)
[44]	HAMID, A. Numerical study of temperature dependent thermal conductivity and homogeneous-heterogeneous reactions on Williamson fluid flow. Journal of Physics Communications, 4(8), 085009 (2020)
[45]	WAINI, I., ISHAK, A., and POP, I. Hybrid nanofluid flow with homogeneous-heterogeneous reactions. Computers, Materials & Continua, 68(3), 3255–3269 (2021)
[46]	ABBAS, Z., IMRAN, M., and NAVEED, M. Impact of equally diffusive chemical reaction on time-dependent flow of Casson nanofluid due to oscillatory curved stretching surface with thermal radiation. Arabian Journal for Science and Engineering, 47(12), 16059–16078 (2022)
[47]	LISHA, N. M., KUMAR, A. G. V., and SHAH, N. A. Numerical investigation of homogeneous-heterogeneous reactions in 3D MHD non-Newtonian hybrid nanofluid with heat source and shape factor in permeable media over a stretching sheet. Journal of Thermal Analysis and Calorimetry, 149, 6933–6954 (2023)