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Thermal analysis of chemically reactive and radiative hybrid nanofluid flow by a curved stretchable surface with bioconvection

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Abstract

Hybrid nanofluids are advanced heat transfer fluids that combine the benefits of traditional nanofluids with additional features to enhance their performance. These fluids have the potential to reduce energy consumption, improve heat transfer proficiency, and enhance the performance of thermal systems in diverse applications. Current work analyzes bioconvective Darcy–Forchheimer hybrid nanofluid flow by porous curved stretched surface. The thermal field is modeled accounting the effects of dissipation and thermal radiation. Chemical reaction and Arrhenius kinetics are accounted in the mass concentration field. Influence of the magnetic field is considered. Bioconvection phenomenon is taken into account to control the random motion of solid tiny particles of copper (Cu) and aluminum oxide (Al2O3) in hybrid base fluid water (H2O)–Ethylene glycol (C2H6O2). Cylindrical nanoparticles with shape factor \(\left( {m = 4.9} \right)\) are considered. Boundary layer norms are utilized to acquire the flow governing dimensional equations. Appropriate transformations are utilized to alter the dimensional system into non-dimensional one. Runge–Kutta–Fehlberg (RKF-45) method in Mathematica is implemented to explore the effective consequences of involved variables on hybrid nanofluid velocity, motile density, thermal, and concentration fields. Surface drag force, mass, density, and heat transfer rates are tabulated and analyzed. The acquired results depict that the velocity field of hybrid fluid decays through porosity variable and Hartmann number. Motile density of microorganisms diminished versus bioconvection Lewis and Peclet numbers. Intensity of heat transfer boosts via Eckert number and thermal radiation parameter.

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All data generated or analyzed during this study are included in this published article.

Abbreviations

\(u,\;v\) :

Velocity components \(\left( {{\text{m}}\;{\text{s}}^{ - 1} } \right)\)

\(F_{{\text{e}}} \left( { = \frac{{C_{{\text{b}}} }}{{sk_{{\text{p}}} }}} \right)\) :

Inertial coefficient \(\left( {{\text{kg}}\;{\text{m}}^{2} } \right)\)

\(P\) :

Pressure \(\left( {{\text{N}}\;{\text{m}}^{ - 2} } \right)\)

\(B_{0}^{2}\) :

Magnitude of magnetic field \(\left( {{\text{kg}}\;{\text{s}}^{ - 2} \;{\text{A}}^{ - 1} } \right)\)

\(r,\;s\) :

Cartesian coordinates \(\left( {\text{m}} \right)\)

\(k^{*}\) :

Mean absorption coefficient \(\left( {{\text{m}}^{ - 1} } \right)\)

\(K_{{\text{p}}}\) :

Permeability of porous medium \(\left( {{\text{m}}^{2} } \right)\)

\({\text{Rd}}\) :

Thermal radiation parameter

\(\sigma\) :

Electrical conductivity \(\left( {{\text{kg}}^{ - 1} \;{\text{m}}^{ - 3} \;{\text{s}}^{3} \;{\text{A}}^{2} } \right)\)

\(\nu\) :

Kinematic viscosity of fluid \(\left( {{\text{m}}^{2} \;{\text{s}}^{ - 1} } \right)\)

\(\sigma^{*}\) :

Stefan Boltzmann constant \(\left( {{\text{J}}\;{\text{s}}^{ - 1} \;{\text{m}}^{ - 2} \;{\text{K}}^{ - 4} } \right)\)

\(n_{1}\) :

Fitted rate constant

\(N_{\infty } ,\;N_{{\text{w}}}\) :

Ambient and surface concentration of microorganisms

\(\rho\) :

Density of base fluid \(\left( {{\text{kg}}\;{\text{m}}^{ - 3} } \right)\)

\(D_{{\text{B}}}\) :

Diffusion coefficient \(\left( {{\text{m}}^{2} \;{\text{s}}^{ - 1} } \right)\)

\(K\) :

Thermal conductivity \(\left( {{\text{W}}\;{\text{m}}^{ - 1} \;{\text{K}}^{ - 1} } \right)\)

\(b\) :

Chemotaxis constant \(\left( m \right)\)

\({\text{Ec}}\) :

Eckert number

\(\Pr\) :

Prandtl number

\(T_{\infty } ,\;T_{{\text{w}}}\) :

Ambient and surface fluid temperatures \(\left( {\text{K}} \right)\)

\(C_{{\text{w}}} ,\;C_{\infty }\) :

Surface and ambient concentration of nanoparticles

\(c_{{\text{p}}}\) :

Specific heat \(\left( {{\text{J}}\;{\text{kg}}^{ - 1} \;{\text{K}}^{ - 1} } \right)\)

\(\mu\) :

Dynamic viscosity \(\left( {{\text{kg}}\;{\text{m}}^{ - 1} \;{\text{s}}^{ - 1} } \right)\)

\(R\) :

Radius of curved surface \(\left( {\text{m}} \right)\)

\(C,\;N\) :

Nanofluid temperature, concentration and microorganisms concentration

\(W_{{\text{c}}}\) :

Cell swimming speed \(\left( {{\text{m}}\;{\text{s}}^{ - 1} } \right)\)

\({\text{Kr}}^{2}\) :

Rate of reaction \(\left( {{\text{s}}^{ - 1} } \right)\)

\(E_{{\text{a}}}\) :

Activation energy \(\left( {{\text{kg}}\;{\text{m}}^{2} \;{\text{s}}^{ - 2} } \right)\)

\(\eta\) :

Dimensionless variable \(\left( - \right)\)

\(D_{{\text{m}}}\) :

Microorganisms diffusivity \(\left( {{\text{m}}^{2} \;{\text{s}}^{ - 1} } \right)\)

\(\kappa\) :

Boltzmann constant \(\left( {{\text{J}}\;{\text{s}}^{ - 1} \;{\text{m}}^{ - 2} \;{\text{K}}^{ - 4} } \right)\)

\(\phi\) :

Volume fraction of nanoparticles

\(j_{{\text{w}}}\) :

Mass flux \(\left( {{\text{kg}}\;{\text{m}}^{ - 2} \;{\text{s}}^{ - 1} } \right)\)

\(\theta ,\;\phi ,\;\xi\) :

Dimensionless temperature, concentration and motile density

\(f^{\prime}\) :

Fluid velocity

\(\alpha\) :

Curvature variable

\(k_{1}\) :

Porosity parameter

\({\text{Sc}}\) :

Schmidt number

\(E_{1}\) :

Activation energy parameter

\(h_{{\text{w}}}\) :

Density flux \(\left( {{\text{W}}\;{\text{m}}^{ - 2} \;{\text{K}}^{ - 1} } \right)\)

\(u_{{\text{w}}} (s)\) :

Sheet stretching rate \(\left( {{\text{m}}\;{\text{s}}^{ - 1} } \right)\)

\(\gamma\) :

Chemical reaction variable

\(\delta_{1}\) :

Temperature difference ratio parameter

\({\text{Lb}},\;{\text{Pe}}\) :

Bioconvection Lewis and Peclet numbers

\({\text{Fr}}\) :

Darcy Forchheimer variable

\(q_{{\text{w}}}\) :

Surface heat flux \(\left( {{\text{J}}\;{\text{s}}^{ - 2} } \right)\)

\(\tau_{{\text{w}}}\) :

Surface shear stress \(\left( {{\text{W}}\;{\text{m}}^{ - 2} } \right)\)

\({\text{Ha}}\) :

Hartmann number

\(T\) :

Nanofluid temperature \(\left( K \right)\)

\({\text{hnf}}\) :

Hybrid nanofluid

\({\text{bf}}\) :

Base fluid

References

  1. Shalchi-Tabrizi A, Seyf HR. Analysis of entropy generation and convective heat transfer of Al2O3 nanofluid flow in a tangential micro heat sink. Int J Heat Mass Transf. 2012;55(15):4366–75.

    Article  CAS  Google Scholar 

  2. Rostami MN, Dinarvand S, Pop I. Dual solutions for mixed convective stagnation-point flow of an aqueous silica–alumina hybrid nanofluid. Chin J Phys. 2018;56(5):2465–78.

    Article  CAS  Google Scholar 

  3. Algehyne EA, Gamaoun F, Lashin MMA, Al-Duais FS, Singh S, Kumar RN. Blasius and Sakiadis flow of a Casson hybrid nanofluid over a moving plate. Waves Random Complex Media. 2022. https://doi.org/10.1080/17455030.2022.2077470.

    Article  Google Scholar 

  4. Haq I, Naveen Kumar R, Gill R, Madhukesh JK, Khan U, Raizah Z, et al. Impact of homogeneous and heterogeneous reactions in the presence of hybrid nanofluid flow on various geometries. Front Chem. 2022. https://doi.org/10.3389/fchem.2022.1032805.

    Article  PubMed  PubMed Central  Google Scholar 

  5. Nagapavani M, Kanuri VR, Fareeduddin M, Thanesh Kumar K, Kolli UC, Sunitha M, et al. Features of the exponential form of internal heat generation, Cattaneo-Christov heat theory on water-based graphene–CNT–titanium ternary hybrid nanofluid flow. Heat Transf. 2023;52(1):144–61.

    Article  Google Scholar 

  6. Madhukesh JK, Naveen Kumar R, Khan U, Gill R, Raizah Z, Elattar S, et al. Analysis of buoyancy assisting and opposing flows of colloidal mixture of titanium oxide, silver, and aluminium oxide nanoparticles with water due to exponentially stretchable surface. Arab J Chem. 2023;16(4): 104550.

    Article  CAS  Google Scholar 

  7. Alzahrani HAH, Alsaiari A, Madhukesh JK, Naveen Kumar R, Prasanna BM. Effect of thermal radiation on heat transfer in plane wall jet flow of Casson nanofluid with suction subject to a slip boundary condition. Waves Random Complex Media. 2022. https://doi.org/10.1080/17455030.2022.2030502.

    Article  Google Scholar 

  8. Varun Kumar RS, Kumar RN, Ben Ahmed S, Madhu J, Verma A, Punith Gowda RJ. Unsteady flow of a ternary nanofluid over a slow-rotating disk subject to uniform suction and backpropagated neural network. Numer Heat Transf Part B Fundam. 2023. https://doi.org/10.1080/10407790.2023.2269610.

    Article  Google Scholar 

  9. Turkyilmazoglu M. Thermal management of parabolic pin fin subjected to a uniform oncoming airflow: optimum fin dimensions. J Therm Anal Calorim. 2021;143(5):3731–9.

    Article  CAS  Google Scholar 

  10. Bouselsal M, Mebarek-Oudina F, Biswas N, Ismail AAI. Heat transfer enhancement using Al2O3-MWCNT hybrid-nanofluid inside a tube/shell heat exchanger with different tube shapes. Micromachines. 2023;14(5):1072.

    Article  PubMed  PubMed Central  Google Scholar 

  11. Mebarek-Oudina F, Preeti SAS, Vaidya H, Lewis RW, Areekara S, et al. Hydromagnetic flow of magnetite–water nanofluid utilizing adapted Buongiorno model. Int J Mod Phys B. 2024;38(01):2450003.

    Article  CAS  Google Scholar 

  12. Paul A, Sarma N, Patgiri B. Mixed convection of shear-thinning hybrid nanofluid flow across a radiative unsteady cone with suction and slip effect. Mater Today Commun. 2023;37: 107522.

    Article  CAS  Google Scholar 

  13. Islam MS, Islam S, Siddiki MN-AA. Numerical simulation with sensitivity analysis of MHD natural convection using Cu–TiO2–H2O hybrid nanofluids. Int J Thermofluids. 2023;20: 100509.

    Article  CAS  Google Scholar 

  14. Ali A, Mebarek-Oudina F, Barman A, Das S, Ismail AI. Peristaltic transportation of hybrid nano-blood through a ciliated micro-vessel subject to heat source and Lorentz force. J Therm Anal Calorim. 2023;148(14):7059–83.

    Article  CAS  Google Scholar 

  15. Iskandarov S, Komartsova E. On the influence of integral perturbations on the boundedness of solutions of a fourth-order linear differential equation. TWMS J Pure Appl Math. 2022;1(13):3–9.

    Google Scholar 

  16. Mebarek-Oudina F, Chabani I, Vaidya H, Ismail AAI. Hybrid-nanofluid magneto-convective flow and porous media contribution to entropy generation. Int J Numer Meth Heat Fluid Flow. 2024;34(2):809–36.

    Article  Google Scholar 

  17. Hamidoğlu A, Taghiyev M, Weber G. On construction of pursuit-evasion games in discrete control models. Appl Comput Math. 2022;21(1):52–60.

    Google Scholar 

  18. He CH, Liu C, He JH, Sedighi HM, Shokri A, Gepreel KA. A fractal model for the internal temperature response of a porous concrete. Appl Comput Math. 2022;21(1):71–7.

    Google Scholar 

  19. Garg A, Sharma YD, Jain SK. Stability analysis of thermo-bioconvection flow of Jeffrey fluid containing gravitactic microorganism into an anisotropic porous medium. Forces Mech. 2023;10: 100152.

    Article  Google Scholar 

  20. Kada B, Hussain I, Ali Pasha A, Azeem Khan W, Tabrez M, Juhany KA, et al. Significance of gyrotactic microorganism and bioconvection analysis for radiative Williamson fluid flow with ferromagnetic nanoparticles. Therm Sci Eng Progress. 2023;39: 101732.

    Article  CAS  Google Scholar 

  21. Kuznetsov AV. The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms. Int Commun Heat Mass Transf. 2010;37(10):1421–5.

    Article  CAS  Google Scholar 

  22. Neethu TS, Sabu AS, Mathew A, Wakif A, Areekara S. Multiple linear regression on bioconvective MHD hybrid nanofluid flow past an exponential stretching sheet with radiation and dissipation effects. Int Commun Heat Mass Transf. 2022;135: 106115.

    Article  CAS  Google Scholar 

  23. Areekara S, Mabood F, Sabu AS, Mathew A, Badruddin IA. 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 Transfer. 2021;126: 105484.

    Article  CAS  Google Scholar 

  24. Mathew A, Areekara S, Sabu AS. Significance of magnetic field and stratification effects on the bioconvective stagnation-point flow of ferro-nanofluid over a rotating stretchable disk: four-factor response surface methodology. J Indian Chem Soc. 2022;99(8): 100615.

    Article  CAS  Google Scholar 

  25. Madhu J, Baili J, Kumar RN, Prasannakumara BC, Gowda RJP. Multilayer neural networks for studying three-dimensional flow of non-Newtonian fluid flow with the impact of magnetic dipole and gyrotactic microorganisms. Phys Scr. 2023;98(11): 115228.

    Article  Google Scholar 

  26. Haq F, Saleem M, Khan MI. Investigation of mixed convection magnetized Casson nanomaterial flow with activation energy and gyrotactic microorganisms. J Phys Commun. 2021;5(12): 125001.

    Article  CAS  Google Scholar 

  27. Shokri A. The symmetric P-stable hybrid Obrenchkoff methods for the numerical solution of second order IVPs. TWMS J Pure Appl Math. 2012;5:28–35.

    Google Scholar 

  28. Koriko OK, Shah NA, Saleem S, Chung JD, Omowaye AJ, Oreyeni T. Exploration of bioconvection flow of MHD thixotropic nanofluid past a vertical surface coexisting with both nanoparticles and gyrotactic microorganisms. Sci Rep. 2021;11(1):16627.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Haq F, Rahman MU, Khan MI, Abdullaeva BS, Altuijri R. Mathematical modeling and theoretical analysis of bioconvective magnetized sutterby nanofluid flow over rotating disk with activation energy. BioNanoScience. 2023;13(4):1849–62.

    Article  Google Scholar 

  30. Akbay A, Turgay N, Ergüt M. On space-like generalized constant ratio hypersufaces in minkowski spaces. TWMS J Pure Appl Math. 2022;13(1):25–37.

    Google Scholar 

  31. Shokri A. The symmetric two-step P-stable nonlinear predictor-corrector methods for the numerical solution of second order initial value problems. Bull Iran Math Soc. 2015;41(1):201–15.

    Google Scholar 

  32. Saleem M, Haq F, Ullah A, ur Rahman M, Bafakeeh OT. Numerical investigation of irreversibility in bioconvective flow of sisko nanofluid with arrhenius energy. J Comput Biophys Chem. 2022;22(03):295–308.

    Article  Google Scholar 

  33. Hayat T, Aziz A, Muhammad T, Alsaedi A. Numerical study for nanofluid flow due to a nonlinear curved stretching surface with convective heat and mass conditions. Results Phys. 2017;7:3100–6.

    Article  Google Scholar 

  34. Saba F, Ahmed N, Hussain S, Khan U, Mohyud-Din ST, Darus M. Thermal analysis of nanofluid flow over a curved stretching surface suspended by carbon nanotubes with internal heat generation. Appl Sci. 2018;8(3):395.

    Article  Google Scholar 

  35. Afridi MI, Wakif A, Qasim M, Hussanan A. Irreversibility analysis of dissipative fluid flow over a curved surface stimulated by variable thermal conductivity and uniform magnetic field: utilization of generalized differential quadrature method. Entropy. 2018;20(12):943.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Shah F, Khan SA, Al-Khaled K, Khan MI, Khan SU, Shah NA, et al. Impact of entropy optimized Darcy-Forchheimer flow in MnZnFe2O4 and NiZnFe2O4 hybrid nanofluid towards a curved surface. ZAMM-J Appl Math Mech. 2022;102(3): e202100194.

    Article  Google Scholar 

  37. Abbas N, Rehman KU, Shatanawi W, Malik MY. Numerical study of heat transfer in hybrid nanofluid flow over permeable nonlinear stretching curved surface with thermal slip. Int Commun Heat Mass Transf. 2022;135: 106107.

    Article  CAS  Google Scholar 

  38. Metwally ASM, Khalid A, Khan AA, Iskakova K, Gorji MR, Ehab M. Radiation consequences on sutterby fluid over a curved surface. J Eng Thermophys. 2022;31(2):315–27.

    Article  Google Scholar 

  39. Naveed M, Abbas Z, Sajid M, Hasnain J. Dual solutions in hydromagnetic viscous fluid flow past a shrinking curved surface. Arab J Sci Eng. 2018;43(3):1189–94.

    Article  Google Scholar 

  40. Hsiao K-L. Combined electrical MHD heat transfer thermal extrusion system using Maxwell fluid with radiative and viscous dissipation effects. Appl Therm Eng. 2017;112:1281–8.

    Article  CAS  Google Scholar 

  41. Hsiao K-L. Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature. Int J Heat Mass Transf. 2017;112:983–90.

    Article  Google Scholar 

  42. Turkyilmazoglu M, Pop I. Induced flow and heat transfer due to inner stretching and outer stationary coaxial cylinders. Int Commun Heat Mass Transf. 2023;146: 106903.

    Article  CAS  Google Scholar 

  43. Turkyilmazoglu M. Exact solutions concerning momentum and thermal fields induced by a long circular cylinder. Eur Phys J Plus. 2021;136(5):483.

    Article  Google Scholar 

  44. Hsiao K-L. To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau-nanofluid with parameters control method. Energy. 2017;130:486–99.

    Article  Google Scholar 

  45. Hsiao K-L. Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet. Appl Therm Eng. 2016;98:850–61.

    Article  CAS  Google Scholar 

  46. Waini I, Ishak A, Groşan T, Pop I. Mixed convection of a hybrid nanofluid flow along a vertical surface embedded in a porous medium. Int Commun Heat Mass Transf. 2020;114: 104565.

    Article  CAS  Google Scholar 

  47. Dharmaiah G, Mebarek-Oudina F, Balamurugan K-S, Vedavathi N. Numerical analysis of the magnetic dipole effect on a radiative ferromagnetic liquid flowing over a porous stretched sheet. Fluid Dyn Mater Process. 2024;20(2):293–310.

    Article  Google Scholar 

  48. Mebarek-Oudina F, Dharmaiah G, Balamurugan KS, Ismail AI, Saxena H. The role of quadratic-linearly radiating heat source with Carreau nanofluid and exponential space-dependent past a cone and a wedge: a medical engineering application and renewable energy. J Comput Biophys Chem. 2023;22(08):997–1011.

    Article  CAS  Google Scholar 

  49. Turkyilmazoglu M. Stagnation-point flow and heat transfer over stretchable plates and cylinders with an oncoming flow: exact solutions. Chem Eng Sci. 2021;238: 116596.

    Article  CAS  Google Scholar 

  50. Devi CDS, Takhar HS, Nath G. Unsteady mixed convection flow in stagnation region adjacent to a vertical surface. Wärme Stoffübertragung. 1991;26(2):71–9.

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. School of Information and Engineering, **gdezhen Ceramic University, **gdezhen, 333403, China

    Nan **ao

  2. Department of Mathematical Sciences, Karakoram International University Main Campus, Gilgit, 15100, Pakistan

    Fazal Haq

  3. Department of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh, 83111-55181, Iran

    Ali Shokri

  4. Department of Mechanical Engineering, College of Engineering and Computer Science, Jazan University, Jazan, Saudi Arabia

    Hassan Ali Ghazwani

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  1. Nan **ao
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**ao, N., Haq, F., Shokri, A. et al. Thermal analysis of chemically reactive and radiative hybrid nanofluid flow by a curved stretchable surface with bioconvection. J Therm Anal Calorim (2024). https://doi.org/10.1007/s10973-024-13366-3

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