OpenLB
Open Library of Bioscience
Advanced Search
Scientific reports
Jul 26, 2022;12 (1): 12727.

Williamson magneto nanofluid flow over partially slip and convective cylinder with thermal radiation and variable conductivity.

M Bilal, Imran Siddique, Andrzej Borawski, A Raza, M Nadeem, Mohammed Sallah
Author Information
  1. M Bilal: Department of Mathematics, University of Chenab, Gujrat, 50700, Pakistan. m.bilal@math.uol.edu.pk.
  2. Imran Siddique: Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan.
  3. Andrzej Borawski: Faculty of Mechanical Engineering, Bialystok University of Technology, 45C Wiejska Str., 15-351, Bialystok, Poland.
  4. A Raza: Department of Mathematics, University of Chenab, Gujrat, 50700, Pakistan.
  5. M Nadeem: Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan.
  6. Mohammed Sallah: Applied Mathematical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt.
PMID: 35882915 DOI: 10.1038/s41598-022-16268-2

Abstract

This article is concerned with the study of MHD non-Newtonian nanofluid flow over a stretching/shrinking cylinder along with thermal radiation effects. Two-component slip mechanism models, namely Brownian motion and thermophoresis of nanofluid for the mass and energy transportation, developed by Buongiorno, are used. Convective heat transfer and nonuniform magnetic field are retained for the expanding/contracting cylinder. Variable thermal conductivity and heat generation effects along with slip boundary conditions are utilized over the cylinder surface. By utilizing the similarity transformation, these governing partial differential equations are converted into nonlinear ordinary differential equations (ODEs). To obtain numerical results, these ODE'S are solved by the shooting method using MATLAB software. The impact of different parameters like variable thermal conductivity, radiation parameter, magnetic parameter, Prandtl number, Brownian motion parameter, the magnetic parameter, Weissenberg number, the viscosity ratio parameter and mass transfer parameter, on the velocity, temperature and concentration is discussed graphically. Further, the Sherwood number, Nusselt number, the skin friction coefficient are also discussed through figures. It is noted through analysis that the speed of the nanofluid reduces for the higher Weissenberg number and expanding cylinder. For the contracting cylinder, i.e., for the negative unsteadiness parameter, the velocity increases.

References

  1. Sakiadis, B. C. Boundary layer behaviour on continuous moving solid surfaces. I. Boundary layer equations for two-dimensional and axisymmetric flow. II. Boundary layer on a continuous flat surface. iii. boundary layer on a continuous cylindrical surface. Am. Inst. Chem. Eng. J. 7, 26–28 (1961). [DOI: 10.1002/aic.690070108]
  2. Crane, L. J. Flow past a stretching sheet. Z. Appl. Math. Phys. 21, 645–647 (1970).
  3. Gupta, P. S. & Gupta, A. S. Heat and mass transfer on a stretching sheet with suction or blowing. Can. J. Chem. Eng. 55, 744–746 (1977). [DOI: 10.1002/cjce.5450550619]
  4. Elbashbeshy, E. M. A. Heat transfer over a stretching surface with variable surface a heat flux. J. Phy. D: Appl. Phys. 31, 1951–1954 (1998). [DOI: 10.1088/0022-3727/31/16/002]
  5. Abd El-Aziz, M. Radiation effect on the flow and heat transfer over an unsteady stretching sheet. Int. Commun. Heat Mass Transf. 36, 521–524 (2009). [DOI: 10.1016/j.icheatmasstransfer.2009.01.016]
  6. Mukhopadyay, S. Effect of thermal radiation on unsteady mixed convection flow and heat transfer over a porous stretching surface in porous medium. Int. Commun. Heat Mass Transf. 52, 3261–3265 (2009). [DOI: 10.1016/j.ijheatmasstransfer.2008.12.029]
  7. Shateyi, S. & Motsa, S. S. Thermal radiation effects on heat and mass transfer over an unsteady stretching surface. Math. Probl. Eng. 2009, 1–13 (2009). [DOI: 10.1155/2009/965603]
  8. Abd El-Aziz, M. Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer by hydromagnetic three-dimensional free convection over a permeable stretching surface with radiation. Phys. Lett. 372, 263–272 (2007). [DOI: 10.1016/j.physleta.2007.07.015]
  9. Hady, F. M., Ibrahim, F. S., Abdel-Gaied, S. M. & Eid, M. R. Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet. Nanoscale Res. Lett. 7(1), 229 (2012). [PMID: 22520273]
  10. Pavlov, K. B. Magnetohydromagnetic flow of an incompressible viscous fluid caused by deformation of a surface. Magnitnaya Gidrodinamika 4, 146–148 (1974).
  11. Bianco, V., Manca, O. & Nardini, S. Second law analysis of [Formula: see text] water nanofluid turbulent forced convection in a circular cross section tube with constant wall temperature. Adv. Mech. Engr. 203, 1–12 (2013).
  12. Nadeem amd, S., Haq, R. . U. & Noreen, S. . A. MHD three dimensional Casson fluid flow past a porous linearly stretching sheet. Alex. Engr. J. 52, 577–582 (2013). [DOI: 10.1016/j.aej.2013.08.005]
  13. Elbashbeshy, E. M. A. & Bazid, M. A. Heat transfer over an unsteady stretching surface with internal heat generation. Appl. Math. Comput. 138, 239–245 (2003).
  14. Akbar, N. S., Haq, R. U. & Nadeem, S. Study of Williamson nanofluid flow in an asymmetric channel. Res. Phys. 3, 161–166 (2013).
  15. Khan, I., Nasir, M., Khan, M. & Malik, M. Y. Theory of Williamson nanofluid over a cone and plate with chemically reactive species. J. Mol. Liq. 231, 580–588 (2017). [DOI: 10.1016/j.molliq.2017.02.031]
  16. Khan, M. I., Qayyum, S., Hayat, T., Khan, M. I., Alsaedi, A. Entropy optimization in flow of Williamson nanofluid in the presence of chemical reaction and Joule heating. Int. J. Heat Mass Trans. 133, 959–967 (2019).
  17. Khan, S. U., Shehzad, S. A. & Ali, N. Interaction of magneto-nanoparticles in Williamson fluid flow over convective oscillatory moving surface. J. Braz. Soc. Mech. Sci. Eng. 40, 195 (2018). [DOI: 10.1007/s40430-018-1126-4]
  18. Choi, S. U. S. Enhancing thermal conductivity of fluids with nanoparticles. ASME-Publ. Fed. 231, 99–106 (1995).
  19. Buongiorno, J. Convective transport in nanofluids. J. Heat Trans. 128, 240–250 (2006). [DOI: 10.1115/1.2150834]
  20. Leala, L. et al. An overview of heat transfer enhancement and new perspective: Focus on active method using electro active material. Int. J. Heat Mass Transf. 61, 505–524 (2013). [DOI: 10.1016/j.ijheatmasstransfer.2013.01.083]
  21. Kang, H. U., Kim, S. H. & Oh, J. M. Estimation of thermal conductivity of nanofluid using experimental effective particle volume. Heat Transf. 19, 181–191 (2006).
  22. Ganji, D. & Hatami, M. Squeezing Cu-water nanofluid flow analysis between parallel plates by DTM-Pade method. J. Mol. Liq. 193, 37–44 (2014). [DOI: 10.1016/j.molliq.2013.12.034]
  23. Volder, M. D. et al. Diverse 3D microarchitecture made by capillary forming of carbon nanotubes (CNT). Adv. Mater. 22, 4384–4389 (2010). [PMID: 20814919]
  24. Ghadikolaei, S. S., Hosseinadeh, Kh., Yassari, M., Sadeghi, H. & Ganji, D. D. Analytical and numerical solution of non-Newtonian second-grade fluid flow on stetching sheet. Therm. Sci. Eng. Prog. 5, 309–316 (2018). [DOI: 10.1016/j.tsep.2017.12.010]
  25. Akbar, N. S. & Nadeem, S. Endoscopic effect on peristaltic flow of nanofluids. Commun. Theor. Phys. 56, 761–768 (2011). [DOI: 10.1088/0253-6102/56/4/28]
  26. Landeghem, F., Huff, K. M. & Jordan, A. Postmortem studies in glioblastoma patients treated with thermotherapy using magnetic nanoparticles biomaterials. Biomaterials 30(1), 52–57 (2009). [PMID: 18848723]
  27. Song, Y. . Q. et al. Solar energy aspects of gyrotactic mixed bioconvection flow of nanofluid past a vertical thin moving needle influenced by variable Prandtl number. Chaos Solitons Fract. 151, 111244 (2021). [DOI: 10.1016/j.chaos.2021.111244]
  28. Kumar, R. . N. et al. Inspection of convective heat transfer and KKL correlation for simulation of nanofluid flow over a curved stretching sheet. Int. Commun. Heat Mass Transf. 126, 105445 (2021). [DOI: 10.1016/j.icheatmasstransfer.2021.105445]
  29. Prasannakumara, B. C. Assessment of the local thermal non-equilibrium condition for nanofluid flow through porous media: a comparative analysis. Indian J. Phys. https://doi.org/10.1007/s12648-021-02216-9 (2021). [DOI: 10.1007/s12648-021-02216-9]
  30. Li, Y. . X. et al. Dynamics of aluminum oxide and copper hybrid nanofluid in nonlinear mixed Marangoni convective flow with entropy generation: Applications to renewable energy. Chin. J. Phys. 73, 275–287 (2021). [DOI: 10.1016/j.cjph.2021.06.004]
  31. Zhou, S. . S. et al. Nonlinear mixed convective Williamson nanofluid flow with the suspension of gyrotactic microorganisms. Int. J. Modern Phys. 35(12), 2150145 (2021). [DOI: 10.1142/S0217979221501459]
  32. Song, Y. Q. et al. Physical impact of thermo-diffusion and diffusion-thermo on Marangoni convective flow of hybrid nanofluid ([Formula: see text]) with nonlinear heat. Modern Phys. Lett. B 35(22), 2141006 (2021). [DOI: 10.1142/S0217984921410062]
  33. Kumar, R. N. et al. Impact of magnetic dipole on ferromagnetic hybrid nanofluid flow over a stretching cylinder. Phy. Scripta 96, 045215 (2021). [DOI: 10.1088/1402-4896/abe324]
  34. Song, Y. Q. et al. Unsteady mixed convection flow of magneto-Williamson nanofluid due to stretched cylinder with significant non-uniform heat source/sink features. Alex. Eng. J. 61, 195–206 (2022). [DOI: 10.1016/j.aej.2021.04.089]
  35. Kumar, R. N. et al. Comprehensive study of thermophoretic diffusion deposition velocity effect on heat and mass transfer of ferromagnetic fluid flow along a stretching cylinder. J. Process Mech. Engr. Part E 235, 1479–1489 (2021). [DOI: 10.1177/09544089211005291]
  36. Punith Gowda, R. . J., Kumar, R. . N. . & Prasannakumara, B. . C. . Two-phase Darcy–Forchheimer flow of dusty hybrid nanofluid with viscous dissipation over a cylinder. Int. J. Appl. Comput. Math. 7, 95 (2021). [DOI: 10.1007/s40819-021-01033-2]
  37. Khan, S. A. et al. Magnetic dipole and thermal radiation impacts on stagnation point flow of micropolar based nanofluids over a vertically stretching sheet: Finite element approach. Processes 9, 1089 (2021). [DOI: 10.3390/pr9071089]
  38. Khan, S. A., Nie, Y. & Ali, B. Multiple slip effects on magnetohydrodynamic axisymmetric buoyant nanofluid flow above a stretching sheet with radiation and chemical reaction. Symmetry 11, 1171 (2019). [DOI: 10.3390/sym11091171]
  39. Ali, B., Hussain, D., Naqvi, R. A., Masood, B. & Hussain, S. Magnetic dipole and thermal radiation effects on hybrid base micropolar CNTs flow over a stretching sheet: Finite element method approach. Results Phys. 25, 104145 (2021). [DOI: 10.1016/j.rinp.2021.104145]
  40. Ali, B., Nie, Y., Khan, S. A., Sadiq, M. T. & Tariq, M. Finite element simulation of multiple slip effects on MHD unsteady Maxwell nanofluid flow over a permeable stretching sheet with radiation and thermo-diffusion in the presence of chemical reaction. Processes 7, 628 (2019). [DOI: 10.3390/pr7090628]
  41. Ali, B., Hussain, S., Nie, Y., Khan, S. A. & Naqvi, S. I. R. Finite element simulation of bioconvection Falkner–Skan flow of a Maxwell nanofluid fluid along with activation energy over a wedge. Phys. Scr. 95, 095214 (2020). [DOI: 10.1088/1402-4896/abb0aa]
  42. Ali, B., Khan, S. A., Hussein, A. K., Thumma, T. & Hussain, S. Hybrid nanofluids: Significance of gravity modulation, heat source/ sink, and magnetohydrodynamic on dynamics of micropolar fluid over an inclined surface via finite element simulation. Appl. Math. Comput. 419(15), 126878 (2022).
  43. Rice, C. L. & Whitehead, R. Electrokinetic flow in a narrow cylindrical capillary. J. Phys. Chem. 69, 4017–4024 (1965). [DOI: 10.1021/j100895a062]
  44. Sorensen, T. S. & Koefoed, J. Electrokinetic flow in cylindrical capillary. J. Chem. Soc. Faraday Trans. 2(70), 665–675 (1974).
  45. Dogonchi, A. S., Ganji, D. D. Investigation of MHD nanofluid flow and heat transfer in a stretching/shrinking convergent/divergent channel considering thermal radiation. J. Mol. Liq. 220, 592–603 (2016).
  46. Singh, Padam & Kumar, Manooj. Mass transfer in MHD flow of alumina water nanofluid over a flat plate under slip condition. Alex. Engr. J. 54, 383–387 (2015). [DOI: 10.1016/j.aej.2015.04.005]
  47. Hashim, A., Hamid, A. & Khan, M. Multiple solutions for MHD transient flow of Williamson nanofluids with convective heat transport. J. Taiwan Inst. Chem. Eng. 103, 126–137 (2019). [DOI: 10.1016/j.jtice.2019.07.001]
  48. Bilal, M., Inam, S., Kanwal, S. & Nazeer, M. Aspects of the aligned magnetic field past a stratified inclined sheet with nonlinear convection and variable thermal conductivity. Eng. Transf. 69(3), 271–292 (2021).
  49. Fang, T., Zhang, J., Zhong, Y. & Tao, H. Unsteady viscous flow over an expanding stretching cylinder. Chin. Phys. Lett. 12, 124707 (2011). [DOI: 10.1088/0256-307X/28/12/124707]

Grants

  1. WZ/WM-IIM/4/2020/Andrzej Borawski
  2. WZ/WM-IIM/4/2020/Andrzej Borawski
  3. WZ/WM-IIM/4/2020/Andrzej Borawski
  4. WZ/WM-IIM/4/2020/Andrzej Borawski
  5. WZ/WM-IIM/4/2020/Andrzej Borawski
  6. WZ/WM-IIM/4/2020/Andrzej Borawski
Journal Article

Word Cloud

Created with Highcharts 10.0.0parametercylindernumbernanofluidthermalradiationslipmagneticconductivityflowalongeffectsBrownianmotionmassheattransferdifferentialequationsvariableWeissenbergvelocitydiscussedarticleconcernedstudyMHDnon-Newtonianstretching/shrinkingTwo-componentmechanismmodelsnamelythermophoresisenergytransportationdevelopedBuongiornousedConvectivenonuniformfieldretainedexpanding/contractingVariablegenerationboundaryconditionsutilizedsurfaceutilizingsimilaritytransformationgoverningpartialconvertednonlinearordinaryODEsobtainnumericalresultsODE'SsolvedshootingmethodusingMATLABsoftwareimpactdifferentparameterslikePrandtlviscosityratiotemperatureconcentrationgraphicallySherwoodNusseltskinfrictioncoefficientalsofiguresnotedanalysisspeedreduceshigherexpandingcontractingienegativeunsteadinessincreasesWilliamsonmagnetopartiallyconvective

Similar Articles

Cited By