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Darcy Forchheimer flow of chemically reactive magnetized ZnO-SAE50 nanolubricant over Riga plate with thermophoretic particle deposition: a numerical approach

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Abstract

Nanolubricants fall among the newly evolved and emerged technologies used in lubrication and heat transfer systems due to their unique thermo-physical properties. They are crucial to the industry because they enhance surface performance, reduce maintenance and fuel costs and boost engine efficiency. They are also used in mechanical systems to efficiently minimize friction and surplus heat. The present investigation focuses to analyze Darcy–Forchheimer flow of magnetized ZnO-SAE50 nanolubricant across Riga plate. Riga plate is poised of an electromagnetic equator that consists of an everlasting magnet and a span-wise collection of irregular electrodes mounted over a planner surface and is utilized in achieving proficient flow. The flow takes place in the presence of viscous dissipation, heat source–sink and chemical reaction of higher order. Newtonian heating and thermophoretic particle deposition effects are also investigated in this study. The role of viscosity is quite important and dynamical in various engineering and industrial fields. The viscosity variation highly fluctuates the thermal systems. The present work also highlights the role of variable viscosity, owing to its importance. A novel micro-nano-convection model called the Patel model is invoked in perspective of the enhancement in thermal conductivity of nanolubricant. The use of ZnO-SAE50 nanolubricant (a brand-new form of nanolubricant) over Riga plate, variable viscosity effects and the application of Patel model are novel features of this study. The application of selected transformations causes the modeled PDEs to change into ODEs. The modeled problem is executed numerically with MATLAB bvp-4c solver. The alterations in the concerned profiles corresponding to various emerging parameters of interest are presented graphically in order to develop better understanding and make analysis. The outcomes reveal that larger modified Hartmann number significantly favors the velocity of nanolubricant ZnO-SAE50, while solid volume fraction, magnetic parameter and variable viscosity parameter halt it. The heat source–sink parameter, Eckert number and solid volume fraction are found to be helpful agents in improving temperature of nanolubricant ZnO-SAE50. In comparison with Newtonian heating (NH), common wall temperature condition (CWT) yields better thermal enhancement. The enhancing chemical reaction order ameliorates the concentration profile but it gets minified for chemical reaction parameter and thermophoresis parameter. The increasing values of magnetic parameter, variable viscosity parameter and inertial parameter tend to enhance the skin friction, while the modified Hartman number reduces it. The enhancing values of Eckert number, magnetic parameter and heat source–sink parameter increase the value of Nusselt number.

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Abbreviations

\(u, v\) :

Velocity components in various directions \(({\mathrm{ms}}^{-1})\)

\({\mu }_{\text{SAE50}}\) :

Dynamic viscosity base fluid (SAE50) \(({\mathrm{kgm}}^{-1}{\mathrm{s}}^{-1})\)

\({\mu }_{\text{ZnO-SAE50}}\) :

Effective dynamic viscosity of nanolubricant (ZnO-SAE50 \(({\mathrm{kgm}}^{-1}{\mathrm{s}}^{-1})\)

\(\sigma \) :

Electrical conductivity \(({\mathrm{sm}}^{-1})\)

\(T\) :

Fluid temperature \((\mathrm{k})\)

\({\rho }_{\text{ZnO-SAE50}}\) :

Effective density of nanolubricant (ZnO-SAE50) \(({\mathrm{kgm}}^{-3})\)

\({\rho }_{\text{SAE50}}\) :

Density of \(\mathrm{SAE}50\) \(({\mathrm{kgm}}^{-3})\)

\({k}_{\text{SAE50}}\) :

Thermal conductivity \(\mathrm{SAE}50\) \(({\mathrm{Wm}}^{-1}{\mathrm{k}}^{-1})\)

\({\rho }_{\text{ZnO}}\) :

Density of np \(\mathrm{ZnO}\) \(({\mathrm{kgm}}^{-3})\)

\({U}_{\text w}\) :

External free stream velocity \(({\mathrm{ms}}^{-1})\)

\(c\) :

Constant

\({u}_{\text{ZnO}}\) :

Brownian motion velocity of ZnO nps (ms−1)

\(Pe\) :

Peclet number

\({d}_{\text{SAE50}}\) :

Molecule size of \(\mathrm{SAE}50\) \((\mathrm{nm})\)

\({d}_{\text{ZnO}}\) :

Diameter of \(\mathrm{ZnO}\) particle \((\mathrm{nm})\)

\({\alpha }_{\text{SAE50}}\) :

Thermal diffusivity of \(\mathrm{SAE}50\) \(({\mathrm{m}}^{2}{\mathrm{s}}^{-1})\)

\(\in \) :

Variable viscosity parameter

\(\beta \) :

Width parameter

\(\tau \) :

Thermophoretic parameter

\(n\) :

Chemical reaction’s order

\(Rc\) :

Chemical reaction parameter

\(\lambda \) :

Porosity parameter

\(Q\) :

Modified Hartman number

\(M\) :

Magnetic parameter

\(Fr\) :

Inertial parameter

\(S\) :

Heat source parameter

\(Sc\) :

Schmidt number

\(Pr\) :

Prandtl number

\(Rd\) :

Radiation parameter

\(Ec\) :

Eckert number

\(\eta \) :

Dimensionless variable

References

  1. Shah Z, Dawar A, Khan I, Islam S, Ching DL, Khan AZ. Cattaneo-Christov model for electrical magnetite micropoler Casson ferrofluid over a stretching/shrinking sheet using effective thermal conductivity model. Case Stud Therm Eng. 2019;13: 100352.

    Google Scholar 

  2. Soltanimehr M, Afrand M. Thermal conductivity enhancement of COOH-functionalized MWCNTs/ethylene glycol–water nanofluid for application in heating and cooling systems. Appl Therm Eng. 2016;105:716–23.

    CAS  Google Scholar 

  3. HemmatEsfe M, Saedodin S, Yan WM, Afrand M, Sina N. Study on thermal conductivity of water-based nanofluids with hybrid suspensions of CNTs/Al2O3 nanoparticles. J Therm Anal Calorim. 2016;124:455–60.

    CAS  Google Scholar 

  4. Riaz M, Khan N. A numerical approach to the modeling of Thompson and Troian slip on magnetized flow of Al2O3–PAO nanolubricant over an inclined rotating disk. Adv Mech Eng. 2023;15(6):16878132231183926.

    CAS  Google Scholar 

  5. Uflyand IE, Zhinzhilo VA, Burlakova VE. Metal-containing nanomaterials as lubricant additives: state-of-the-art and future development. Friction. 2019;7:93–116.

    Google Scholar 

  6. Toghraie D, Chaharsoghi VA, Afrand M. Measurement of thermal conductivity of ZnO–TiO2/EG hybrid nanofluid: effects of temperature and nanoparticles concentration. J Therm Anal Calorim. 2016;125:527–35.

    CAS  Google Scholar 

  7. Sepyani K, Afrand M, Esfe MH. An experimental evaluation of the effect of ZnO nanoparticles on the rheological behavior of engine oil. J Mol Liq. 2017;236:198–204.

    CAS  Google Scholar 

  8. Gailitis AK, Lielausis OA. On the possibility of drag reduction of a flat plate in an electrolyte. Appl Magnetohydrodyn Trudy Inst Fisiky AN Latvia SSR. 1961;12:143.

    Google Scholar 

  9. Madhukesh JK, Ramesh GK, Aly EH, Chamkha AJ. Dynamics of water conveying SWCNT nanoparticles and swimming microorganisms over a Riga plate subject to heat source/sink. Alex Eng J. 2022;61(3):2418–29.

    Google Scholar 

  10. Madhukesh JK, Alhadhrami A, Naveen Kumar R, Punith Gowda RJ, Prasannakumara BC, Varun Kumar RS. Physical insights into the heat and mass transfer in Casson hybrid nanofluid flow induced by a Riga plate with thermophoretic particle deposition. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering. 2021:09544089211039305.

  11. Xu YJ, Shah F, Khan MI, Naveen Kumar R, Punith Gowda RJ, Prasannakumara BC, Malik MY, Khan SU. New modeling and analytical solution of fourth grade (non-Newtonian) fluid by a stretchable magnetized Riga device. Int J Mod Phys C. 2022;33(01):2250013.

    CAS  Google Scholar 

  12. Riaz M, Khan N, Shehzad SA. Rheological behavior of magnetized ZnO–SAE 50 nanolubricant over Riga plate: a theoretical study. Adv Mech Eng. 2023;15(3):16878132231162304.

    CAS  Google Scholar 

  13. Riaz M, Khan N, Hashmi MS, Younis J. Heat and mass transfer analysis for magnetized flow of ZnO–SAE 50 nanolubricant with variable properties: an application of Cattaneo–Christov model. Sci Rep. 2023;13(1):8717.

    CAS  PubMed  PubMed Central  Google Scholar 

  14. Kumar RN, Gowda RP, Madhukesh JK, Prasannakumara BC, Ramesh GK. Impact of thermophoretic particle deposition on heat and mass transfer across the dynamics of Casson fluid flow over a moving thin needle. Phys Scr. 2021;96(7): 075210.

    Google Scholar 

  15. Chen SB, Shahmir N, Ramzan M, Sun YL, Aly AA, Malik MY. Thermophoretic particle deposition in the flow of dual stratified Casson fluid with magnetic dipole and generalized Fourier’s and Fick’s laws. Case Stud Therm Eng. 2021;26: 101186.

    Google Scholar 

  16. Alhadhrami A, Alzahrani HA, Kumar RN, Gowda RP, Sarada K, Prasanna BM, Madhukesh JK, Madhukeshwara N. Impact of thermophoretic particle deposition on Glauert wall jet slip flow of nanofluid. Case Stud Therm Eng. 2021;28: 101404.

    Google Scholar 

  17. Shehzad SA, Mabood F, Rauf A, Tlili I. Forced convective Maxwell fluid flow through rotating disk under the thermophoretic particles motion. Int Commun Heat Mass Transfer. 2020;116: 104693.

    Google Scholar 

  18. Punith Gowda RJ, Baskonus HM, Naveen Kumar R, Prakasha DG, Prasannakumara BC. Evaluation of heat and mass transfer in ferromagnetic fluid flow over a stretching sheet with combined effects of thermophoretic particle deposition and magnetic dipole. Waves Random Complex Media. 2021;1–9.

  19. Gowda RP, Kumar RN, Aldalbahi A, Issakhov A, Prasannakumara BC, Rahimi-Gorji M, Rahaman M. Thermophoretic particle deposition in time-dependent flow of hybrid nanofluid over rotating and vertically upward/downward moving disk. Surf Interfaces. 2021;22: 100864.

    Google Scholar 

  20. Naveen Kumar R, Punith Gowda RJ, Prasanna GD, Prasannakumara BC, Nisar KS, Jamshed W. Comprehensive study of thermophoretic diffusion deposition velocity effect on heat and mass transfer of ferromagnetic fluid flow along a stretching cylinder. Proc Inst Mech Eng, Part E: J Process Mech Eng. 2021;235(5):1479–89.

    CAS  Google Scholar 

  21. Shamshuddin MD, Satya Narayana PV. Combined effect of viscous dissipation and Joule heating on MHD flow past a Riga plate with Cattaneo–Christov heat flux. Indian J Phys. 2020;94(9):1385–94.

    CAS  Google Scholar 

  22. Nadeem S, Ijaz M, Ayub M. Darcy–Forchheimer flow under rotating disk and entropy generation with thermal radiation and heat source/sink. J Therm Anal Calorim. 2021;143:2313–28.

    CAS  Google Scholar 

  23. Jyothi AM, Varun Kumar RS, Madhukesh JK, Prasannakumara BC, Ramesh GK. Squeezing flow of Casson hybrid nanofluid between parallel plates with a heat source or sink and thermophoretic particle deposition. Heat Transfer. 2021;50(7):7139–56.

    Google Scholar 

  24. Waqas H, Farooq U, Alqarni MS, Muhammad T, Khan MA. Bioconvection transport of magnetized micropolar nanofluid by a Riga plate with non-uniform heat sink/source. Waves Random Complex Media. 2021;1–20.

  25. Gowda RP, Naveenkumar R, Madhukesh JK, Prasannakumara BC, Gorla RS. Theoretical analysis of SWCNT-MWCNT/H2O hybrid flow over an upward/downward moving rotating disk. Proc Inst Mech Eng, Part N: J Nanomater, Nanoeng Nanosyst. 2021;235(3–4):97–106.

    CAS  Google Scholar 

  26. Merkin JH. Natural-convection boundary-layer flow on a vertical surface with Newtonian heating. Int J Heat Fluid Flow. 1994;15(5):392–8.

    Google Scholar 

  27. Wakif A, Sehaqui R. Generalized differential quadrature scrutinization of an advanced MHD stability problem concerned water-based nanofluids with metal/metal oxide nanomaterials: a proper application of the revised two-phase nanofluid model with convective heating and through-flow boundary conditions. Numer Methods Partial Differ Equ. 2022;38(3):608–35.

    Google Scholar 

  28. Kotha G, Munagala VS, Damerla VK, Gorla RS. Newtonian heating effect on laminar flow of Casson fluids: thermal analysis. Heat Transf. 2020;49(4):2390–405.

    Google Scholar 

  29. Anurag, Singh AK, Chandran P, Sacheti NC. Effect of Newtonian heating/cooling on free convection in an annular permeable region in the presence of heat source/sink. Heat Transf. 2021;50(1):712–32.

    Google Scholar 

  30. Shah NA, Wang S, Elnaqeeb T, Qi H. Soret and memory effects on unsteady MHD natural convection heat and mass transfer flow in a porous medium with Newtonian heating. J Porous Media. 2021;24(7):45–59.

    Google Scholar 

  31. Madhukesh JK, Kumar RN, Gowda RP, Prasannakumara BC, Ramesh GK, Khan MI, Khan SU, Chu YM. Numerical simulation of AA7072-AA7075/water-based hybrid nanofluid flow over a curved stretching sheet with Newtonian heating: a non-Fourier heat flux model approach. J Mol Liq. 2021;335: 116103.

    CAS  Google Scholar 

  32. Devi SA, Ganga B. Effects of viscous and Joules dissipation on MHD flow, heat and mass transfer past a stretching porous surface embedded in a porous medium. Nonlinear Anal: Model Control. 2009;14(3):303–14.

    CAS  Google Scholar 

  33. Shah S, Hussain S, Sagheer M. Thermal stratification effects on mixed convective Maxwell fluid flow with variable thermal conductivity and homogeneous/heterogeneous reactions. J Braz Soc Mech Sci Eng. 2018;40(9):452.

    Google Scholar 

  34. Majeed A, Zeeshan A, Ellahi R. Chemical reaction and heat transfer on boundary layer Maxwell Ferro-fluid flow under magnetic dipole with Soret and suction effects. Eng Sci Technol, Int J. 2017;20(3):1122–8.

    Google Scholar 

  35. Al-Odat MQ, Al-Azab TA. Influence of chemical reaction on transient MHD free convection over a moving vertical plate. Emir J Eng Res. 2007;12(3):15–21.

    Google Scholar 

  36. Khan N, Riaz M, Hashmi MS, Khan SU, Tlili I, Khan MI, Nazeer M. Soret and Dufour features in peristaltic motion of chemically reactive fluid in a tapered asymmetric channel in the presence of Hall current. J Phys Commun. 2020;4(9): 095009.

    CAS  Google Scholar 

  37. Khan N, Riaz I, Hashmi MS, Musmar SA, Khan SU, Abdelmalek Z, Tlili I. Aspects of chemical entropy generation in flow of Casson nanofluid between radiative stretching disks. Entropy. 2020;22(5):495.

    CAS  PubMed  PubMed Central  Google Scholar 

  38. Khan N, Al-Khaled K, Khan A, Hashmi MS, Khan SU, Khan MI, Qayyum S. Aspects of constructive/destructive chemical reactions for viscous fluid flow between deformable wall channel with absorption and generation features. Int Commun Heat Mass Transf. 2021;120: 104956.

    CAS  Google Scholar 

  39. Khan N, Hashmi MS, Khan SU, Chaudhry F, Tlili I, Shadloo MS. Effects of homogeneous and heterogeneous chemical features on Oldroyd-B fluid flow between stretching disks with velocity and temperature boundary assumptions. Math Probl Eng. 2020;2020:1–3.

    Google Scholar 

  40. Ahmad I, Khan MN, Inc M, Ahmad H, Nisar KS. Numerical simulation of simulate an anomalous solute transport model via local meshless method. Alex Eng J. 2020;59(4):2827–38.

    Google Scholar 

  41. Ahmad H, Akgül A, Khan TA, Stanimirović PS, Chu YM. New perspective on the conventional solutions of the nonlinear time-fractional partial differential equations. Complexity. 2020;2020:1–10.

    Google Scholar 

  42. Ahmad H, Khan TA, Stanimirovic PS, Ahmad I. Modified variational iteration technique for the numerical solution of fifth order KdV-type equations. J Appl Comput Mech. 2020;6(Special Issue):1220–7.

    Google Scholar 

  43. Ahmad H, Seadawy AR, Khana TA. modified variational iteration algorithm to find approximate solutions of nonlinear Parabolic equation. Mathemat Comput Simul. 2020;177:13–23.

    Google Scholar 

  44. Ahmad I, Ahmad H, Inc M, Yao SW, Almohsen B. Application of local meshless method for the solution of two term time fractional-order multi-dimensional PDE arising in heat and mass transfer. Therm Sci. 2020;24(Suppl. 1):95–105.

    Google Scholar 

  45. Inc M, Khan MN, Ahmad I, Yao SW, Ahmad H, Thounthong P. Analysing time-fractional exotic options via efficient local meshless method. Results Phys. 2020;19: 103385.

    Google Scholar 

  46. Nawaz Khan M, Ahmad I, Ahmad H. A radial basis function collocation method for space-dependent inverse heat problems. J Appl Comput Mech. 2020.

  47. Shah NA, Ahmad I, Bazighifan O, Abouelregal AE, Ahmad H. Multistage optimal homotopy asymptotic method for the nonlinear Riccati ordinary differential equation in nonlinear physics. Appl Math. 2020;14(6):1009–16.

    Google Scholar 

  48. Wang F, Ali SN, Ahmad I, Ahmad H, Alam KM, Thounthong P. Solution of Burgers’ equation appears in fluid mechanics by multistage optimal homotopy asymptotic method. Therm Sci. 2022;26(1 Part B):815–21.

    Google Scholar 

  49. Liu X, Ahsan M, Ahmad M, Nisar M, Liu X, Ahmad I, Ahmad H. Applications of haar wavelet-finite difference hybrid method and its convergence for hyperbolic nonlinear schr ö dinger equation with energy and mass conversion. Energies. 2021;14(23):7831.

    Google Scholar 

  50. Ahsan M, Lin S, Ahmad M, Nisar M, Ahmad I, Ahmed H, Liu X. A Haar wavelet-based scheme for finding the control parameter in nonlinear inverse heat conduction equation. Open Phys. 2021;19(1):722–34.

    Google Scholar 

  51. Kierzenka J, Shampine LF. A BVP solver based on residual control and the Maltab PSE. ACM Trans Math Softw (TOMS). 2001;27(3):299–316.

    Google Scholar 

  52. Wakif A, Chamkha A, Animasaun IL, Zaydan M, Waqas H, Sehaqui R. Novel physical insights into the thermodynamic irreversibilities within dissipative EMHD fluid flows past over a moving horizontal riga plate in the coexistence of wall suction and joule heating effects: a comprehensive numerical investigation. Arab J Sci Eng. 2020;45:9423–38.

    CAS  Google Scholar 

  53. Ramesh GK, Roopa GS, Gireesha BJ, Shehzad SA, Abbasi FM. An electro-magneto-hydrodynamic flow Maxwell nanoliquid past a Riga plate: a numerical study. J Braz Soc Mech Sci Eng. 2017;39:4547–54.

    CAS  Google Scholar 

  54. Epstein M, Hauser GM, Henry RE. Thermophoretic deposition of particles in natural convection flow from a vertical plate. J Heat Transfer. 1985;107:272–6.

    CAS  Google Scholar 

  55. Saeed M, Ahmad B, ul Hassan QM. Variable thermal effects of viscosity and radiation of ferrofluid submerged in porous medium. Ain Shams Eng J. 2022;13(4):101653.

    Google Scholar 

  56. Talbot LR, Cheng RK, Schefer RW, Willis DR. Thermophoresis of particles in a heated boundary layer. J Fluid Mech. 1980;101(4):737–58.

    Google Scholar 

  57. Ghasemi SE, Hatami M. Solar radiation effects on MHD stagnation point flow and heat transfer of a nanofluid over a stretching sheet. Case Stud Therm Eng. 2021;25: 100898.

    Google Scholar 

  58. Salleh MZ, Nazar R, Pop I. Boundary layer flow and heat transfer over a stretching sheet with Newtonian heating. J Taiwan Inst Chem Eng. 2010;41(6):651–5.

    CAS  Google Scholar 

  59. Pourmehran O, Rahimi-Gorji M, Ganji DD. Heat transfer and flow analysis of nanofluid flow induced by a stretching sheet in the presence of an external magnetic field. J Taiwan Inst Chem Eng. 2016;65:162–71.

    CAS  Google Scholar 

  60. Patel HE, Anoop KB, Sundararajan T, Das SK. A micro-convection model for thermal conductivity of nanofluids. In: International Heat Transfer Conference 13 2006. Begel House Inc..

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Acknowledgements

This research work was funded by Institutional Fund Projects under grant no. (IFPIP:1264-130-1443). The authors gratefully acknowledge technical and financialsupport provided by the Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

    Muhammad Riaz & Nargis Khan

  2. Department of Mathematics, The Government Sadiq College Women University, Bahawalpur, Pakistan

    M. S. Hashmi

  3. Department of Mathematics, King Abdulaziz University, P. O. Box 80203, 21589, Jeddah, Saudi Arabia

    Ali Saleh Alshomrani

  4. Department of Mathematics, Faculty of Science, Firat University, 23119, Elazig, Turkey

    Mustafa Inc

  5. Department of Medical Research, China Medical University, 40402, Taichung, Taiwan

    Mustafa Inc

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Riaz, M., Khan, N., Hashmi, M.S. et al. Darcy Forchheimer flow of chemically reactive magnetized ZnO-SAE50 nanolubricant over Riga plate with thermophoretic particle deposition: a numerical approach. J Therm Anal Calorim 148, 12285–12300 (2023). https://doi.org/10.1007/s10973-023-12468-8

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