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Two-dimensional Maxwell hybrid nanofluid flow subject to heat source/sink and convective conditions across a stretching surface: an application of parametric continuation method

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Abstract

Hybrid nanofluids (HNFs) have several applications in various fields due to their unique properties, heat exchangers, refrigeration systems, cooling of electronic devices, solar thermal energy, geothermal energy, nuclear power plants, biomedical engineering, coatings, ceramics, environmental remediation, rocket propulsion, thermal management systems, heat shields, etc. Due to these applications, the existing problem is presented to study the flow of Maxwell HNF for the stretching sheet in a permeable medium comprising of magnesium oxide (MgO) as well as iron (I, II) oxide (Fe3O4) nanoparticles (Nps) for the improvement of heat transport. The magnetic field effects are considered on the flow behavior. Transport of heat as well as mass is computed by using the concepts of Brownian diffusivity, diffusivity due to thermophoresis, and chemical reaction under convective conditions. The flow dynamics have been designed in the form of PDEs (partial differential equations). By using the suitable variables of similarity, higher-order nonlinear PDEs have been converted into ODEs (ordinary differential equations). Simulation of these ODEs of higher order is performed by using the parametric continuation method (PCM). In this study, it is examined that the NF and HNF velocity is reduced due to greater magnetic field parameters and volume fraction of Nps. Further, the increasing role of the NF and HNF temperature is obtained for the parameters of Brownian and thermophoresis.

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References

  1. Wang Y, Kumar RN, Gouadria S, Helmi MM, Gowda RP, El-Zahar ER, Khan MI. A three-dimensional flow of an Oldroyd-B liquid with magnetic field and radiation effects: An application of thermophoretic particle deposition. Int Commun Heat Mass Trans. 2022;134:106007.

    Article  Google Scholar 

  2. Raja MA, Tabassum R, El-Zahar ER, Shoaib M, Khan MI, Malik MY, Khan SU, Qayyum S. Intelligent computing through neural networks for entropy generation in MHD third-grade nanofluid under chemical reaction and viscous dissipation. Waves Random Complex Media. 2022;5:1–25.

    Article  Google Scholar 

  3. Nagaraja B, Gireesha BJ, Soumya DO, Almeida F. Characterization of MHD convective flow of Jeffrey nanofluid driven by a curved stretching surface by employing Darcy-Forchheimer law of porosity. Waves in Random Complex Med. 2022;25:1–20.

    Google Scholar 

  4. Alshahrani S, Ahammad NA, Bilal M, Ghoneim ME, Ali A, Yassen MF, Tag-Eldin E. Numerical simulation of ternary nanofluid flow with multiple slip and thermal jump conditions. Frontiers Energy Res. 2022;10:967307.

    Article  Google Scholar 

  5. Waqas H, Imran M, Khan SA, Khan I, Pasha AA, Irshad K (2022). Cattaneo–Christov double diffusion and bioconvection in magnetohydrodynamic three-dimensional nanomaterials of non-Newtonian fluid containing microorganisms with variable thermal conductivity and thermal diffusivity. Waves in Random and Complex Media, 1–20.

  6. Li YM, Ullah I, Alam MM, Khan H, Aziz A (2022). Lorentz force and Darcy-Forchheimer effects on the convective flow of non-Newtonian fluid with chemical aspects. Waves in Random and Complex Media, 1–15.

  7. Rasheed HU, Islam S, Zeeshan, Abbas T, Khan J (2022). Analytical treatment of MHD flow and chemically reactive Casson fluid with Joule heating and variable viscosity effect. Waves in Random and Complex Media, 1–17.

  8. Khalil KM, Soleiman A, Megahed AM, Abbas W. Impact of variable fluid properties and double diffusive Cattaneo-Christov model on dissipative non-Newtonian fluid flow due to a stretching sheet. Mathematics. 2022;10(7):1179.

    Article  Google Scholar 

  9. Alzahrani F, Khan MI. Entropy generation and Joule heating applications for Darcy Forchheimer flow of Ree-Eyring nanofluid due to double rotating disks with artificial neural network. Alex Eng J. 2022;61(5):3679–89.

    Article  Google Scholar 

  10. Waqas H, Wakif A, Al-Mdallal Q, Zaydan M, Farooq U, Hussain M. Significance of magnetic field and activation energy on the features of stratified mixed radiative-convective couple-stress nanofluid flows with motile microorganisms. Alex Eng J. 2022;61(2):1425–36.

    Article  Google Scholar 

  11. Muhammad T, Waqas H, Manzoor U, Farooq U, Rizvi ZF. On doubly stratified bioconvective transport of Jeffrey nanofluid with gyrotactic motile microorganisms. Alex Eng J. 2022;61(2):1571–83.

    Article  Google Scholar 

  12. Varun Kumar RS, Gunderi Dhananjaya P, Naveen Kumar R, Punith Gowda RJ, Prasannakumara BC. Modeling and theoretical investigation on Casson nanofluid flow over a curved stretching surface with the influence of magnetic field and chemical reaction. Int J Comput Methods Eng Sci Mech. 2022;23(1):12–9.

    Article  CAS  Google Scholar 

  13. Bayones FS, Abd-Alla AM, Thabet EN (2022). Magnetized dissipative Soret effect on nonlinear radiative Maxwell nanofluid flow with porosity, chemical reaction and Joule heating. Waves in Random and Complex Media, 1–19.

  14. Alzahrani HA, Alsaiari A, Madhukesh JK, Naveen Kumar R, Prasanna BM (2022). Effect of thermal radiation on heat transfer in plane wall jet flow of Casson nanofluid with suction subject to a slip boundary condition. Waves in Random and Complex Media, 1–18.

  15. Nazeer M, Saleem S, Hussain F, Rafiq MU. Numerical solution of gyrotactic microorganism flow of nanofluid over a Riga plate with the characteristic of chemical reaction and convective condition. Waves Random Complex Med. 2022. https://doi.org/10.1080/17455030.2022.2061746.

    Article  Google Scholar 

  16. Ashraf W, Khan I, Shemseldin MA, Mousa AAA. Numerical energy storage efficiency of MWCNTs-propylene glycol by inducing thermal radiations and combined convection effects in the constitutive model. Front Chem. 2022;10: 879276.

    Article  PubMed  PubMed Central  Google Scholar 

  17. AlBaidani MM, Mishra NK, Ahmad Z, Eldin SM, Haq EU. Numerical study of thermal enhancement in ZnO-SAE50 nanolubricant over a spherical magnetized surface influenced by Newtonian heating and thermal radiation. Case Stud Therm Eng. 2023;45: 102917.

    Article  Google Scholar 

  18. Ali B, Jubair S, Fathima D, Akhter A, Rafique K, Mahmood Z. MHD flow of nanofluid over moving slender needle with nanoparticles aggregation and viscous dissipation effects. Sci Prog. 2023;106(2):00368504231176151.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Algehyne EA, Saeed A, Arif M, Bilal M, Kumam P, Galal AM. Gyrotactic microorganism hybrid nanofluid over a Riga plate subject to activation energy and heat source: numerical approach. Sci Rep. 2023;13(1):13675.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Alqarni MM, Bilal M, Allogmany R, Tag-Eldin E, Ghoneim ME, Yassen MF. Mathematical analysis of casson fluid flow with energy and mass transfer under the influence of activation energy from a non-coaxially spinning disc. Frontiers Energy Res. 2022;10:986284.

    Article  Google Scholar 

  21. Elattar S, Helmi MM, Elkotb MA, El-Shorbagy MA, Abdelrahman A, Bilal M, Ali A. Computational assessment of hybrid nanofluid flow with the influence of hall current and chemical reaction over a slender stretching surface. Alex Eng J. 2022;61(12):10319–31.

    Article  Google Scholar 

  22. Khan U, Zaib A, Ishak A, Sherif ESM, Waini I, Chu YM, Pop I. Radiative mixed convective flow induced by hybrid nanofluid over a porous vertical cylinder in a porous media with irregular heat sink/source. Case Stud Therm Eng. 2022;30: 101711.

    Article  Google Scholar 

  23. Hussain Z, Alshomrani AS, Muhammad T, Anwar MS. Entropy analysis in mixed convective flow of hybrid nanofluid subject to melting heat and chemical reactions. Case Stud Therm Eng. 2022;34: 101972.

    Article  Google Scholar 

  24. Khashi’ie NS, Arifin NM, Pop I. Magnetohydrodynamics (MHD) boundary layer flow of hybrid nanofluid over a moving plate with Joule heating. Alex Eng J. 2022;61(3):1938–45.

    Article  Google Scholar 

  25. Abdel-Nour Z, Aissa A, Mebarek-Oudina F, Rashad AM, Ali HM, Sahnoun M, El Ganaoui M. Magnetohydrodynamic natural convection of hybrid nanofluid in a porous enclosure: numerical analysis of the entropy generation. J Therm Anal Calorim. 2020;141(5):1981–92.

    Article  CAS  Google Scholar 

  26. Venkateswarlu A, Suneetha S, Babu MJ, Kumar JG, Raju CSK, Al-Mdallal Q. Significance of magnetic field and chemical reaction on the natural convective flow of hybrid nanofluid by a sphere with viscous dissipation: a statistical approach. Nonlinear Eng. 2021;10(1):563–73.

    Article  Google Scholar 

  27. Naveed Khan M, Ahmad S, Ahammad NA, Alqahtani T, Algarni S. Numerical investigation of hybrid nanofluid with gyrotactic microorganism and multiple slip conditions through a porous rotating disk. Waves Random Complex Med. 2022. https://doi.org/10.1080/17455030.2022.2055205.

    Article  Google Scholar 

  28. Abderrahmane A, Qasem NA, Younis O, Marzouki R, Mourad A, Shah NA, Chung JD. MHD hybrid nanofluid mixed convection heat transfer and entropy generation in a 3-D triangular porous cavity with zigzag wall and rotating cylinder. Mathematics. 2022;10(5):769.

    Article  Google Scholar 

  29. Ali B, Jubair S, Duraihem FZ. Numerical analysis of viscous dissipative unsteady darcy forchhemier hybrid nanofluid flow subject to magnetic effect across a stretching cylinder. Mater Today Commun. 2023;36:106532.

    Article  CAS  Google Scholar 

  30. Abbas W, Bani-Fwaz MZ, Asogwa KK. Thermal efficiency of radiated tetra-hybrid nanofluid [(Al2O3-CuO-TiO2-Ag)/water] tetra under permeability effects over vertically aligned cylinder subject to magnetic field and combined convection. Sci Prog. 2023;106(1):00368504221149797.

    Article  PubMed  PubMed Central  Google Scholar 

  31. Ali B, Jubair S. Motile microorganism-based ternary nanofluid flow with the significance of slip condition and magnetic effect over a Riga plate. J Therm Anal Calorim. 2023. https://doi.org/10.1007/s10973-023-12397-6.

    Article  Google Scholar 

  32. Bilal M, Ali A, Mahmoud SR, Tag-Eldin E, Balubaid M. Fractional analysis of unsteady radiative brinkman-type nanofluid flow comprised of CoFe2O3 nanoparticles across a vertical plate. J Therm Anal Calorimet. 2023;148(24):13869–82.

    Article  CAS  Google Scholar 

  33. Bilal M, Waqas M, Shafi J, Eldin SM, Alaoui MK. Energy transmission through radiative ternary nanofluid flow with exponential heat source/sink across an inclined permeable cylinder/plate: numerical computing. Sci Rep. 2023;13(1):1–15.

    Article  Google Scholar 

  34. Aich W, Sarfraz G, Said NM, Bilal M, Elhag AFA, Hassan AM. Significance of radiated ternary nanofluid for thermal transport in stagnation point flow using thermal slip and dissipation function. Case Stud Therm Eng. 2023;51: 103631.

    Article  Google Scholar 

  35. Mishra NK, Anwar S, Kumam P, Seangwattana T, 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(7):e17678.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Elsebaee FAA, Mahmoud SR, Balubaid M, Shuaib M, Asamoah JK, Ali A. Motile micro-organism based trihybrid nanofluid flow with an application of magnetic effect across a slender stretching sheet: numerical approach. AIP Adv. 2023;13(3): 035237.

    Article  CAS  Google Scholar 

  37. Pattnaik PK, Bhatti MM, Mishra SR, Abbas MA, Bég OA. Mixed convective-radiative dissipative magnetized micropolar nanofluid flow over a stretching surface in porous media with double stratification and chemical reaction effects: ADM-Padé computation. J Math. 2022;2022:1–19.

    Google Scholar 

  38. Li YX, Mishra SR, Pattnaik PK, Baag S, Li YM, Khan MI, Khan SU. Numerical treatment of time dependent magnetohydrodynamic nanofluid flow of mass and heat transport subject to chemical reaction and heat source. Alexandria Eng J. 2022;61(3):2484–91.

    Article  Google Scholar 

  39. Ahmad I, Faisal M, Loganathan K, Kiyani MZ, Namgyel N. Nonlinear mixed convective bidirectional dynamics of double stratified radiative Oldroyd-B nanofluid flow with heat source/sink and higher-order chemical reaction. Math Prob Eng. 2022;2022:1–16.

    Google Scholar 

  40. Ibrahim M, Abdallah N, Abouzeid M. Activation energy and chemical reaction effects on MHD Bingham nanofluid flow through a non-Darcy porous media. Egypt J Chem. 2022;65(13):137–44.

    Google Scholar 

  41. Shah SL, Ayub A, Dehraj S, Wahab HA, Sagayam KM, Ali MR, Sabir Z. Magnetic dipole aspect of binary chemical reactive Cross nanofluid and heat transport over composite cylindrical panels. Waves Random Complex Med. 2022. https://doi.org/10.1080/17455030.2021.2020373.

    Article  Google Scholar 

  42. Alrihieli H, Areshi M, Alali E, Megahed AM. MHD dissipative Williamson nanofluid flow with chemical reaction due to a slippery elastic sheet which was contained within a porous medium. Micromachines. 2022;13(11):1879.

    Article  PubMed  PubMed Central  Google Scholar 

  43. Nandi S, Kumbhakar B. Viscous dissipation and chemical reaction effects on tangent hyperbolic nanofluid flow past a stretching wedge with convective heating and navier’s slip conditions. Iranian J Sci Technol, Trans Mech Eng. 2022;46(2):379–97.

    Article  Google Scholar 

  44. Basavarajappa M, Muhammad T, Lorenzini G, Swain K. Darcy-Forchheimer nanoliquid flow and radiative heat transport over convectively heated surface with chemical reaction. J Eng Thermophys. 2022;31(2):261–73.

    Article  CAS  Google Scholar 

  45. Alharbi KAM, Bilal M, Ali A, Eldin SM, Soliman AF, Rahman MU. Stagnation point flow of hybrid nanofluid flow passing over a rotating sphere subjected to thermophoretic diffusion and thermal radiation. Sci Rep. 2023;13(1):19093.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  46. Jayavel P, Ramzan M, Saleem S, Verma A, Ramesh K. Homotopy analysis on the bio-inspired radiative magnesium and iron oxides/blood nanofluid flow over an exponential stretching sheet. Comput Particle Mech. 2023;10(6):1955–75.

    Article  Google Scholar 

  47. Shuaib M, Shah RA. Variable thickness flow over a rotating disk under the influence of variable magnetic field: an application to parametric continuation method. Adv Mech Eng. 2020;12(6):1687814020936385.

    Article  CAS  Google Scholar 

  48. Alharbi KAM, Ahmed AES, Ould Sidi M, Ahammad NA, Mohamed A, El-Shorbagy MA, Marzouki R. Computational valuation of darcy ternary-hybrid nanofluid flow across an extending cylinder with induction effects. Micromachines. 2022;13(4):588.

    Article  PubMed  PubMed Central  Google Scholar 

  49. Ali B, Duraihem FZ, Jubair S, Alqahtani H, Yagoob B. Analysis of interparticle spacing and nanoparticle radius on the radiative alumina based nanofluid flow subject to irregular heat source/sink over a spinning disk. Mater Today Commun. 2023;36: 106729.

    Article  CAS  Google Scholar 

  50. Reddy Gorla RS, Sidawi I. Free convection on a vertical stretching surface with suction and blowing. Appl Sci Res. 1994;52:247–57.

    Article  Google Scholar 

  51. Hamad MAA. Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field. Int Commun Heat Mass Transfer. 2011;38(4):487–92.

    Article  CAS  Google Scholar 

  52. Dawar A, Islam S, Shah Z, Mahmuod SR, Lone SA. Dynamics of inter-particle spacing, nanoparticle radius, inclined magnetic field and nonlinear thermal radiation on the water-based copper nanofluid flow past a convectively heated stretching surface with mass flux condition: a strong suction case. Int Commun Heat Mass Transfer. 2022;137: 106286.

    Article  CAS  Google Scholar 

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Funding

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia, for funding this work through the Research Group Project under Grant Number (RGP.2/505/44).

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Authors and Affiliations

  1. Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, (Jeddah-M), Riyadh, 11673, Kingdom of Saudi Arabia

    Showkat Ahmad Lone

  2. College of Engineering, Al Ain University, Al Ain, United Arab Emirates

    Hussam Alrabaiah

  3. Mathematics Department, Tafila Technical University, Tafila, Jordan

    Hussam Alrabaiah

  4. Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia

    Zehba Raizah

  5. Department of Mathematics, University of Calcutta, 92 APC Road, Kolkata, India

    Ramashis Banerjee

  6. Department of Mathematics and Statistics, University of Swat, Swat, Khyber Pakhtunkhwa, Pakistan

    Amir Khan

  7. Department of Mathematics, Abdul Wali Khan University, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan

    Anwar Saeed

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  1. Showkat Ahmad Lone
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  2. Hussam Alrabaiah
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Correspondence to Anwar Saeed.

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Lone, S.A., Alrabaiah, H., Raizah, Z. et al. Two-dimensional Maxwell hybrid nanofluid flow subject to heat source/sink and convective conditions across a stretching surface: an application of parametric continuation method. J Therm Anal Calorim (2024). https://doi.org/10.1007/s10973-024-13040-8

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