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Numerical investigation of MHD tangent hyperbolic nanofluid flow across a vertical stretching surface subject to activation energy

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Abstract

We analyze numerically the consequence of gyrotactic microbes on the MHD (magnetohydrodynamics) steady tangent hyperbolic nanofluid (THNF) flow over a nonlinearly elongating surface. The thickness of the sheet is not uniform. The effect of magnetic field, thermal conductivity, heat source/sink and thermal radiation are observed on the THNF. The modeled equations are reformed into a non-dimensional system of ODEs by using appropriate similarity variables. The simplified form of set of ODEs is further numerically calculated through the bvp4c code (MATLAB package). The comparative estimation is performed to confirm the validity of the results. It has been observed that the influence of Rayleigh number and Brownian motion all result in an acceleration of the energy field. The mass dissemination rate upsurges with the impact of activation energy, whereas declines with the chemical reactions. By varying the magnetic factor from 0.5 to 1.5, the skin friction rises by up to 8.13%. However, the rate of energy transference drops by 5.92%. The upshot of thermal radiation rises the flow velocity and energy propagation rate by 13.39% and 11.25%, respectively.

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Abbreviations

\(B_{0}\) :

Magnetic field

\(\varepsilon \left( x \right)\) :

Variable thickness

\(\sigma\) :

Electrical conductivity

\(Q_{0}\) :

Heat source term

\(\rho_{{\text{f}}}\) :

Density

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

Activation energy

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

Thermal conductivity

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

Specific heat

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

Thermophysical variables properties

C :

Nanoparticle concentration

Le:

Lewis number

\({\text{Wc}}\) :

Weissenberg number

Rb:

Rayleigh number

\(\lambda\) :

Mixed convection

Rd:

Radiation term

\(\chi\) :

Wall thickness

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

Chemical reaction factor

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

Surface temperature

G :

Gravitational force

M :

Power law index

2D:

Two dimensional

\(\nu\) :

Kinematic viscosity

\(k_{{\text{r}}}^{2}\) :

2Nd-order chemical reaction

\(\tau\) :

Nanoparticles capacities ratio

\(\beta\) :

Thermal expansion factor

N :

Motile microbes density

T :

Temperature

M :

Magnetic term

Qr:

Thermal radiation

Pr:

Prandtl number

Nr:

Buoyancy factor

Pe:

Peclet number

Lb:

Lewis number

\(\Omega\) :

Motile microorganisms density

References

  1. Elsebaee FAA, Bilal M, Mahmoud SR, Balubaid M, Shuaib M, Asamoah JK, et al. Motile micro-organism based trihybrid nanofluid flow with an application of magnetic effect across a slender stretching sheet: Numerical approach. AIP Adv. 2023. https://doi.org/10.1063/5.0144191.

    Article  Google Scholar 

  2. Bilal M, Ali A, Hejazi HA, Mahmuod SR. Numerical study of an electrically conducting hybrid nanofluid over a linearly extended sheet. ZAMM-J Appl Math Mech Zeitschrift für Angewandte Math Mech. 2023;103(5):e202200227.

    Article  Google Scholar 

  3. Goud BS, Madhu JV, Shekar MR. MHD viscous dissipative fluid flows in a channel with a stretching and porous plate with radiation effect. Int J Innov Technol Explor Eng. 2019. https://doi.org/10.35940/ijitee.K2086.0981119.

    Article  Google Scholar 

  4. Wang F, Asjad MI, Rehman SU, Ali B, Hussain S, Gia TN, et al. MHD Williamson nanofluid flow over a slender elastic sheet of irregular thickness in the presence of bioconvection. Nanomaterials. 2021;11(9):2297.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  5. Hussain F, Hussain A, Nadeem S. Thermophoresis and Brownian model of pseudo-plastic nanofluid flow over a vertical slender cylinder. Math Probl Eng. 2020;2020:1–10.

    Google Scholar 

  6. Raizah Z, Alrabaiah H, Bilal M, Junsawang P, Galal AM. Numerical study of non-Darcy hybrid nanofluid flow with the effect of heat source and hall current over a slender extending sheet. Sci Rep. 2022;12(1):16280.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Reddy YD, Goud BS, Nisar KS, Alshahrani B, Mahmoud M, Park C. Heat absorption/generation effect on MHD heat transfer fluid flow along a stretching cylinder with a porous medium. Alex Eng J. 2023;64:659–66.

    Article  Google Scholar 

  8. Asogwa KK, Goud BS, Shah NA, Yook S-J. Rheology of electromagnetohydrodynamic tangent hyperbolic nanofluid over a stretching riga surface featuring dufour effect and activation energy. Sci Rep. 2022;12(1):14602.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  9. Shankar Goud B, Dharmendar Reddy Y, Mishra S. Joule heating and thermal radiation impact on MHD boundary layer Nanofluid flow along an exponentially stretching surface with thermal stratified medium. Proc Inst Mech Eng Part N J Nanomater Nanoeng Nanosyst. 2022. https://doi.org/10.1177/23977914221100961.

    Article  Google Scholar 

  10. Goud BS. Heat generation/absorption influence on steady stretched permeable surface on MHD flow of a micropolar fluid through a porous medium in the presence of variable suction/injection. Int J Thermofluids. 2020;7:100044.

    Article  Google Scholar 

  11. Assiri TA, Aziz Elsebaee FA, Alqahtani AM, Bilal M, Ali A, Eldin SM. Numerical simulation of energy transfer in radiative hybrid nanofluids flow influenced by second-order chemical reaction and magnetic field. AIP Adv. 2023. https://doi.org/10.1063/5.0141532.

    Article  Google Scholar 

  12. Devi SA, Prakash M. Temperature dependent viscosity and thermal conductivity effects on hydromagnetic flow over a slendering stretching sheet. J Niger Math Soc. 2015;34(3):318–30.

    Article  Google Scholar 

  13. Haq I, Bilal M, Ahammad NA, Ghoneim ME, Ali A, Weera W. Mixed convection nanofluid flow with heat source and chemical reaction over an inclined irregular surface. ACS Omega. 2022;7(34):30477–85.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Murtaza S, Kumam P, Bilal M, Sutthibutpong T, Rujisamphan N, Ahmad Z. Parametric simulation of hybrid nanofluid flow consisting of cobalt ferrite nanoparticles with second-order slip and variable viscosity over an extending surface. Nanotechnol Rev. 2023;12(1):20220533.

    Article  CAS  Google Scholar 

  15. Srinivasulu T, Goud BS. Effect of inclined magnetic field on flow, heat and mass transfer of Williamson nanofluid over a stretching sheet. Case Stud Thermal Eng. 2021;23:100819.

    Article  Google Scholar 

  16. Murtaza S, Kumam P, Ahmad Z, Seangwattana T, Ali IE. Numerical analysis of newly developed fractal-fractional model of casson fluid with exponential memory. Fractals. 2022;30(05):2240151.

    Article  Google Scholar 

  17. Malik M, Salahuddin T, Hussain A, Bilal S. MHD flow of tangent hyperbolic fluid over a stretching cylinder: using keller box method. J Magn Magn Mater. 2015;395:271–6.

    Article  CAS  Google Scholar 

  18. Ramzan M, Saeed A, Kumam P, Ahmad Z, Junaid MS, Khan D. Influences of Soret and Dufour numbers on mixed convective and chemically reactive Casson fluids flow towards an inclined flat plate. Heat Transfer. 2022;51(5):4393–433.

    Article  Google Scholar 

  19. Zhang C, Zheng L, Zhang X, Chen G. MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction. Appl Math Model. 2015;39(1):165–81.

    Article  Google Scholar 

  20. Alqahtani AM, Bilal M, Usman M, Alsenani TR, Ali A, Mahmuod SR. Heat and mass transfer through MHD Darcy Forchheimer Casson hybrid nanofluid flow across an exponential stretching sheet. ZAMM-J Appl Math Mech Zeitschrift Angewandte Math Mech. 2023. https://doi.org/10.1002/zamm.202200213.

    Article  Google Scholar 

  21. Goud BS, Reddy YD, Rao VS, Khan ZH. Thermal radiation and joule heating effects on a magnetohydrodynamic casson nanofluid flow in the presence of chemical reaction through a non-linear inclined porous stretching sheet. J Naval Archit Marine Eng. 2020. https://doi.org/10.3329/jname.v17i2.49978.

    Article  Google Scholar 

  22. Murtaza S, Ahmad Z, Ali IE, Akhtar Z, Tchier F, Ahmad H, et al. Analysis and numerical simulation of fractal-fractional order non-linear couple stress nanofluid with cadmium telluride nanoparticles. J King Saud Univ Sci. 2023;35(4):102618.

    Article  Google Scholar 

  23. Shakunthala S, Nandeppanavar M. Boundary layer flow and Cattaneo-Christov heat flux of a nonlinear stretching sheet with a suspended CNT. Nanosci Nanotechnol Asia. 2019;9(4):494–503.

    Article  CAS  Google Scholar 

  24. Gaffar SA, Prasad VR, Bég 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(4):829–41.

    Article  Google Scholar 

  25. Nagendramma V, Leelarathnam A, Raju C, Shehzad S, Hussain T. Doubly stratified MHD tangent hyperbolic nanofluid flow due to permeable stretched cylinder. Results Phys. 2018;9:23–32.

    Article  Google Scholar 

  26. Kumar PP, Goud BS, Malga BS. Finite element study of Soret number effects on MHD flow of Jeffrey fluid through a vertical permeable moving plate. Partial Differ Equ Appl Math. 2020;1:100005.

    Article  Google Scholar 

  27. Ali U, Gul T, Khan H, Bilal M, Usman M, Shuaib M. Motile microorganisms hybrid nanoliquid flow with the influence of activation energy and heat source over a rotating disc. Nanotechnology. 2023. https://doi.org/10.1088/1361-6528/ace912.

    Article  PubMed  Google Scholar 

  28. Mishra NK, Anwar S, Kumam P, Seangwattana T, Bilal M, Saeed A. Numerical investigation of chemically reacting jet flow of hybrid nanofluid under the significances of bio-active mixers and chemical reaction. Heliyon. 2023;9:e17678.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Raizah Z, Saeed A, Bilal M, Galal AM, Bonyah E. Parametric simulation of stagnation point flow of motile microorganism hybrid nanofluid across a circular cylinder with sinusoidal radius. Open Phys. 2023;21(1):20220205.

    Article  CAS  Google Scholar 

  30. Yanala DR, Mella AK, Vempati SR, Goud BS. Influence of slip condition on transient laminar flow over an infinite vertical plate with ramped temperature in the presence of chemical reaction and thermal radiation. Heat Transf. 2021;50(8):7654–71.

    Article  Google Scholar 

  31. Algehyne EA, Alhusayni YY, Tassaddiq A, Saeed A, Bilal M. The study of nanofluid flow with motile microorganism and thermal slip condition across a vertical permeable surface. Waves Random Complex Media. 2022. https://doi.org/10.1080/17455030.2022.2071501.

    Article  Google Scholar 

  32. 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. Sci Rep. 2022;12(1):1–12.

    Google Scholar 

  33. Swain K, Mahanthesh B. Thermal enhancement of radiating magneto-nanoliquid with nanoparticles aggregation and joule heating: a three-dimensional flow. Arab J Sci Eng. 2021;46:5865–73.

    Article  CAS  Google Scholar 

  34. Kwak D-H, Ramasamy P, Lee Y-S, Jeong M-H, Lee J-S. High-performance hybrid InP QDs/black phosphorus photodetector. ACS Appl Mater Interfaces. 2019;11(32):29041–6.

    Article  CAS  PubMed  Google Scholar 

  35. Bilal M, Ullah I, Alam MM, Shah SI, Eldin SM. Energy transfer in Carreau Yasuda liquid influenced by engine oil with Magnetic dipole using tri-hybrid nanoparticles. Sci Rep. 2023;13(1):5432.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Murtaza S, Kumam P, Ahmad Z, Ramzan M, Ali I, Saeed A. Computational simulation of unsteady squeezing hybrid nanofluid flow through a horizontal channel comprised of metallic nanoparticles. J Nanofluids. 2023;12(5):1327–34.

    Article  Google Scholar 

  37. Alqahtani AM, Bilal M, Elsebaee FAA, Eldin SM, Alsenani TR, Ali A. Energy transmission through carreau yasuda fluid influenced by ethylene glycol with activation energy and ternary hybrid nanocomposites by using a mathematical model. Heliyon. 2023. https://doi.org/10.1016/j.heliyon.2023.e14740.

    Article  PubMed  PubMed Central  Google Scholar 

  38. Goud BS, Kumar PP, Malga BS. Effect of heat source on an unsteady MHD free convection flow of Casson fluid past a vertical oscillating plate in porous medium using finite element analysis. Partial Differ Equ Appl Math. 2020;2:100015.

    Article  Google Scholar 

  39. Hussain SM, Goud BS, Madheshwaran P, Jamshed W, Pasha AA, Safdar R, et al. Effectiveness of nonuniform heat generation (sink) and thermal characterization of a carreau fluid flowing across a nonlinear elongating cylinder: A numerical study. ACS Omega. 2022;7(29):25309–20.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Allehiany F, Alqahtani AM, Bilal M, Ali A, Eldin SM. Fractional study of radiative Brinkman-type nanofluid flow across a vertical plate with the effect of Lorentz force and Newtonian heating. AIP Adv. 2023. https://doi.org/10.1063/5.0151572.

    Article  Google Scholar 

  41. Hillesdon A, Pedley T. Bioconvection in suspensions of oxytactic bacteria: linear theory. J Fluid Mech. 1996;324:223–59.

    Article  Google Scholar 

  42. Wakif A. A novel numerical procedure for simulating steady MHD convective flows of radiative Casson fluids over a horizontal stretching sheet with irregular geometry under the combined influence of temperature-dependent viscosity and thermal conductivity. Math Probl Eng. 2020. https://doi.org/10.1155/2020/1675350.

    Article  Google Scholar 

  43. Ferdows M, Zaimi K, Rashad AM, Nabwey HA. MHD bioconvection flow and heat transfer of nanofluid through an exponentially stretchable sheet. Symmetry. 2020;12(5):692.

    Article  CAS  Google Scholar 

  44. Khan M, Hussain A, Malik M, Salahuddin T, Khan F. Boundary layer flow of MHD tangent hyperbolic nanofluid over a stretching sheet: a numerical investigation. Results Phys. 2017;7:2837–44.

    Article  Google Scholar 

  45. Fang T, Zhang J, Zhong Y. Boundary layer flow over a stretching sheet with variable thickness. Appl Math Comput. 2012;218(13):7241–52.

    Google Scholar 

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  1. Building and Construction Department, Shaqlawa Technical College, Erbil Polytechnic University, Erbil, Iraq

    Najiba Hasan Hamad

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Hamad, N.H. Numerical investigation of MHD tangent hyperbolic nanofluid flow across a vertical stretching surface subject to activation energy. J Therm Anal Calorim 148, 12687–12697 (2023). https://doi.org/10.1007/s10973-023-12548-9

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