Numerical solutions for magneto-convective boundary layer slip flow from a nonlinear stretching sheet with wall transpiration and thermal radiation effects

References

• Z. Tadmor and I. Klein, Engineering Principles of Plasticating Extrusion, Polymer Science and Engineering Series. New York: Van Nostrand Reinhold, 1970.
   Google Scholar
• L. Crane, “Flow past a stretching plate,” J. Appl. Math. Phys. (ZAMP), vol. 21, no. 4, pp. 645–647, 1970. DOI: 10.1007/BF01587695.
   Web of Science ®Google Scholar
• K. Vajravelu and J. R. Cannon, “Fluid flow over a nonlinearly stretching sheet,” Appl. Math. Comput., vol. 181, no. 1, pp. 609–618, 2006. DOI: 10.1016/j.amc.2005.08.051.
   Web of Science ®Google Scholar
• R. Cortell, “Viscous flow and heat transfer over a nonlinearly stretching sheet,” Appl. Math. Comput., vol. 184, no. 2, pp. 864–873, 2007. DOI: 10.1016/j.amc.2006.06.077.
   Web of Science ®Google Scholar
• C. Y. Wang, “Review of similarity stretching exact solutions of the Navier-Stokes equations,” Eur. J. Mech. B/Fluids., vol. 30, no. 5, pp. 475–479, 2011. DOI: 10.1016/j.euromechflu.2011.05.006.
   Web of Science ®Google Scholar
• R. Cortell, “Heat and fluid flow due to non-linearly stretching surfaces,” Appl. Math. Comput., vol. 217, no. 19, pp. 7564–7572, 2011. DOI: 10.1016/j.amc.2011.02.029.
   Web of Science ®Google Scholar
• W. F. Hughes and F. J. Young, The Electromagnetodynamics of Fluids. New York, USA: John Wiley, 1966.
   Google Scholar
• M. S. Abel, E. Sanjayanand and M. M. Nandeppanavar, “Viscoelastic MHD flow and heat transfer over a stretching sheet with viscous and Ohmic dissipations,” Commu. Nonlinear Sci. Numer. Simulat., vol. 13, no. 9, pp. 1808–1821, 2008. DOI: 10.1016/j.cnsns.2007.04.007.
   Web of Science ®Google Scholar
• P. Rana, R. Bhargava and O. A. Beg, “Finite element simulation of unsteady MHD transport phenomena on a stretching sheet in a rotating nanofluid,” Proc. IMECHE – Part N; J. Nanoeng. Nanosyst., vol. 227, no. 2, pp. 77–99, 2013. DOI: 10.1177/1740349912463312.
   Google Scholar
• A. Pantokratoras, “Study of MHD Boundary layer flow over a heated stretching sheet with variable viscosity: a numerical investigation,” Int. J. Heat Mass Transf., vol. 51, no. 1–2, pp. 104–110, 2008. DOI: 10.1016/j.ijheatmasstransfer.2007.04.007.
   Web of Science ®Google Scholar
• A. Raptis and C. Perdikis, “Viscous flow over a non-linearly stretching sheet in the presence of a chemical reaction and magnetic field,” Int. J. Non-Lin. Mech., vol. 41, no. 4, pp. 527–529, 2006. DOI: 10.1016/j.ijnonlinmec.2005.12.003.
   Web of Science ®Google Scholar
• O. A. Bég, A. Y. Bakier and V. R. Prasad, “Numerical study of free convection magnetohydrodynamic heat and mass transfer from a stretching surface to a saturated porous medium with Soret and Dufour effects,” Computat. Mater. Sci., vol. 46, no. 1, pp. 57–65, 2009. DOI: 10.1016/j.commatsci.2009.02.004.
   Web of Science ®Google Scholar
• C. Chen, “Combined effects of Joule heating and viscous dissipation on magnetohydrodynamic flow past a permeable, stretching surface with free convection and radiative heat transfer,” ASME J. Heat Transf., vol. 132, no. 6, pp. 064503–064501, 2010. DOI: 10.1115/1.4000946.
   Web of Science ®Google Scholar
• T. Javed, Z. Abbas, M. Sajid and N. Ali, “Heat transfer analysis for a hydromagnetic viscous fluid over a non-linear shrinking sheet,” Int. J. Heat Mass Transf., vol. 54, no. 9–10, pp. 2034–2042, 2011. DOI: 10.1016/j.ijheatmasstransfer.2010.12.025.
   Web of Science ®Google Scholar
• N. S. Akbar, D. Tripathi, Z. Khan and O. Anwar Bég, “A numerical study of magnetohydrodynamic transport of nanofluids from a vertical stretching sheet with exponential temperature-dependent viscosity and buoyancy effects,” Chem. Phys. Lett., vol. 661, pp. 20–30, 2016. DOI: 10.1016/j.cplett.2016.08.043.
   Web of Science ®Google Scholar
• T. Thumma, O. Anwar Bég and A. Kadir, “Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet,” J. Mol. Liq., vol. 232, pp. 159–173, 2017. DOI: 10.1016/j.molliq.2017.02.032.
   Web of Science ®Google Scholar
• H. I. Andersson, “Slip flow past a stretching surface,” Acta. Mech., vol. 158, no. 1–2, pp. 121–125, 2002. DOI: 10.1007/BF01463174.
   Web of Science ®Google Scholar
• B. Sahoo, “Effects of slip on sheet-driven flow and heat transfer of a non-Newtonian fluid past a stretching sheet,” Comp. Math. Appl., vol. 61, no. 5, pp. 1442–1456, 2011. DOI: 10.1016/j.camwa.2011.01.017.
   Web of Science ®Google Scholar
• A. S. Rao, V. R. Prasad, N. Nagendra, K. V. N. Murthy, N. B. Reddy and O. A. Beg, “Numerical modeling of non-similar mixed convection heat transfer over a stretching surface with slip conditions,” WJM., vol. 05, no. 06, pp. 117–128, 2015. DOI: 10.4236/wjm.2015.56013.
   Google Scholar
• M. Abd El-Aziz and A. A. Afify, “Influence of slip velocity and induced magnetic field on MHD stagnation-point flow and heat transfer of Casson fluid over a stretching sheet,” Math. Prob. Eng., vol. 2018, pp. 1–11, 2018. DOI: 10.1155/2018/9402836.
   Web of Science ®Google Scholar
• N. Shukla, P. Rana, O. A. Bég, B. Singh and A. Kadir, “Homotopy study of magnetohydrodynamic mixed convection nanofluid multiple slip flow and heat transfer from a vertical cylinder with entropy generation,” Propulsion Power Res., vol. 8, no. 2, pp. 147–162, 2019. DOI: 10.1016/j.jppr.2019.01.005.
   Web of Science ®Google Scholar
• T. Hayat, M. Qasim and S. Mesloub, “MHD flow and heat transfer over permeable stretching sheet with slip conditions,” Numer. Methods Fluids., vol. 66, no. 8, pp. 963–975, 2011. DOI: 10.1002/fld.2294.
   Web of Science ®Google Scholar
• M. H. Yazdi, S. Abdullah, I. Hashim and K. Sopian, “Slip MHD liquid flow and heat transfer over non-linear permeable stretching surface with chemical reaction,” Int. J. Heat Mass Transf., vol. 54, no. 15–16, pp. 3214–3225, 2011. DOI: 10.1016/j.ijheatmasstransfer.2011.04.009.
   Web of Science ®Google Scholar
• Y. D. Reddy, F. Mebarek-Oudina, B. S. Goud and A. I. Ismail, “Radiation, velocity and thermal slips effect toward MHD boundary layer flow through heat and mass transport of Williamson nanofluid with porous medium,” Arab J. Sci. Eng., vol. 47, no. 12, pp. 16355–16369, 2022. DOI: 10.1007/s13369-022-06825-2.
   Web of Science ®Google Scholar
• P. Mishra, D. Kumar, Y. Dharmendar Reddy and B. Shankar Goud, “Numerical investigation of MHD flow of Williamson nanofluid with variable viscosity pasting a wedge within porous media: a non‐Darcy model approach,” Heat Trans., vol. 51, no. 7, pp. 6071–6086, 2022. DOI: 10.1002/htj.22580.
   Google Scholar
• S. Goud Bejawada, Y. Dharmendar Reddy, W. Jamshed, K. S. Nisar, A. N. Alharbi and R. Chouikh, “Radiation effect on MHD Casson fluid flow over an inclined non-linear surface with chemical reaction in a Forchheimer porous medium,” Alexandria Eng. J., vol. 61, no. 10, pp. 8207–8220, 2022. DOI: 10.1016/j.aej.2022.01.043.
   Web of Science ®Google Scholar
• Y. Reddy, B. Shankar Goud, M. R. Khan, M. AbdelghanyElkotb and A. M. Galal, “Transport properties of a hydromagneticradiative stagnation point flow of a nanofluid across a stretching surface,” Case Stud. Therm. Eng, vol. 31, pp. 101839, 2022. DOI: 10.1016/j.csite.2022.101839.
   Web of Science ®Google Scholar
• Y. D. Reddy, B. S. Goud, A. J. Chamkha and M. A. Kumar, “Influence of radiation and viscous dissipation on MHD heat transfer Cassonnanofluid flow along a nonlinear stretching surface with chemical reaction,” Heat Trans., vol. 51, no. 4, pp. 3495–3511, 2022. DOI: 10.1002/htj.22460.
   Google Scholar
• B. Shankar Goud, Y. Dharmendar Reddy and S. Mishra, “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 J. Nanomater. Nanoeng. Nanosyst., vol. 237, no. 3-4, 2022. 23977914221100961.
   Google Scholar
• B. Vasu, R. S. R. Gorla, P. V. S. N. Murthy, V. R. Prasad, O. A. Bég and S. Siddiqa, “MHD free convection-radiation interaction in a porous medium – part II: Soret/Dufour effects,” Int. J. Appl. Mech. Eng., vol. 25, no. 2, pp. 157–175, 2020. DOI: 10.2478/ijame-2020-0013.
   Google Scholar
• S. Kuharat, O. Anwar Bég, A. Kadir and B. Vasu, “Computation of metallic nanofluid natural convection in a two-dimensional solar enclosure with radiative heat transfer, aspect ratio and volume fraction effects,” Arabian J. Sci. Eng., vol. 11, pp. 9075–9093, 2020. DOI: 10.1007/s13369-020-04678-1.
   Google Scholar
• T. Thumma, S. R. Mishra and O. A. Bég, “ADM solution for Cu/CuO–water viscoplastic nanofluid transient slip flow from a porous stretching sheet with entropy generation, convective wall temperature and radiative effects,” J. Appl. Comput. Mech., vol. 7, no. 3, pp. 1291–1305, 2021. DOI: 10.22055/jacm.2020.33137.2167.
   Web of Science ®Google Scholar
• A. G. Hansen, Similarity Analyses of Boundary Value Problems in Engineering. Englewood Cliffs, N.J.: Prentice Hall, 1964, pp. 86–91.
   Google Scholar
• T. Y. Na, Computational Methods in Engineering Boundary Value Problems. New York: Academic Press, 1979.
   Google Scholar
• R. Seshadri and T. Y. Na, Group Invariance in Engineering Boundary Value Problems. New York: Springer, 1985.
   Google Scholar
• G. W. Bluman and S. C. Anco, Symmetry and Integration Methods for Differential Equations. New York: Springer, 2009.
   Google Scholar
• A. A. Avramenko, S. G. Kobzar, I. V. Shevchuk, A. V. Kuznetsov and L. T. Iwanisov, “Symmetry of turbulent boundary-layer flows: investigation of different eddy viscosity models,” Acta Mech., vol. 151, no. 1–2, pp. 1–14, 2001. DOI: 10.1007/BF01272521.
   Web of Science ®Google Scholar
• M. G. Murtaza, E. E. Tzirtzilakis and M. Ferdows, “Biomagnetic fluid flow past a stretching/shrinking sheet with slip conditions using lie group analysis,” AIP Conference Proceedings 2121, pp. 050005, 2019. DOI: 10.1063/1.5115892.
   Google Scholar
• M. Ferdows, G. Murtaza, J. C. Misra, E. E. Tzirtzilakis and A. Alsenafi, “Dual solutions in biomagnetic fluid flow and heat transfer over a nonlinear stretching/shrinking sheet: application of lie group transformation method,” Math. Biosci. Eng., vol. 17, no. 5, pp. 4852–4874, 2020. DOI: 10.3934/mbe.2020264.
   PubMed Web of Science ®Google Scholar
• M. J. Uddin, N. H. M. Yusoff, O. A. Beg and A. I. Ismail, “Lie group analysis and numerical solutions for non-Newtonian nanofluid flow in a porous medium with internal heat generation,” Phys. Scr., vol. 87, no. 2, pp. 025401, 2013. DOI: 10.1088/0031-8949/87/02/025401.
   Web of Science ®Google Scholar
• M. J. Uddin, W. A. Khan and A. I. M. Ismail, “Scaling group transformation for MHD boundary layer slip flow of a nanofluid over a convectively heated stretching sheet with heat generation,” Math. Prob. Eng., vol. 2012, pp. 1–20, 2012. DOI: 10.1155/2012/934964.
   Web of Science ®Google Scholar
• S. Mukhopadhyay and G. C. Layek, “Effects of variable fluid viscosity on flow past a heated stretching sheet embedded in a porous medium in presence of heat source/sink,” Meccanica., vol. 47, no. 4, pp. 863–876, 2012. DOI: 10.1007/s11012-011-9457-6.
   Web of Science ®Google Scholar
• O. A. Bég, M. J. Uddin, M. M. Rashidi and N. Kavyani, “Double-diffusive radiative magnetic mixed convective slip flow with Biot and Richardson number effects,” J. Eng. Thermophys., vol. 23, no. 2, pp. 79–97, 2014. DOI: 10.1134/S1810232814020015.
   Web of Science ®Google Scholar
• M. J. Uddin, O. A. Bég and N. S. Amin, “Hydromagnetic transport phenomena from a stretching or shrinking nonlinear nanomaterial sheet with Navier slip and convective heating: a model for bio-nano-materials processing,” J. Magnet. Mag. Mater., vol. 368, pp. 252–261, 2014. DOI: 10.1016/j.jmmm.2014.05.041.
   Web of Science ®Google Scholar
• O. Anwar Bég, W. A. Khan and M. J. Uddin, “Multiple slip effects on unsteady magnetohydrodynamic nanofluid transport with heat generation/absorption effects in temperature dependent porous media,” J. Por. Media, vol. 18, no. 9, pp. 907–922, 2015. DOI: 10.1615/JPorMedia.v18.i9.70.
   Web of Science ®Google Scholar
• M. J. Uddin, O. A. Bég and A. I. Ismail, “Radiative-convective nanofluid flow past a stretching/shrinking sheet with slip effects,” J. Thermophys. Heat Transf., vol. 29, no. 3, pp. 513–523, 2015. DOI: 10.2514/1.T4372.
   Web of Science ®Google Scholar
• N. A. Amirsom, M. F. M. Basir, M. J. Uddin, A. I. Ismail, O. A. Bég and A. Kadir, “Computation of melting dissipative magnetohydrodynamic nanofluid bioconvection with second order slip and variable thermophysical properties,” Appl. Sci. (Applied Biosciences and Bioengineering Section), vol. 9, no. 12, pp. 2493, 2019. DOI: 10.3390/app9122493.
   Google Scholar
• O. A. Bég, M. J. Uddin, T. A. Bég, A. Kadir, M. Shamshuddin and M. Babaie, “Numerical study of self-similar natural convection mass transfer from a rotating cone in anisotropic porous media with Stefan blowing and Navier slip,” Indian J. Phys., vol. 94, no. 6, pp. 863–877, 2020. DOI: 10.1007/s12648-019-01520-9.
   Web of Science ®Google Scholar
• M. J. Uddin, W. A. Khan, O. A. Bég and A. I. M. Ismail, “Non-similar solution of g-jitter induced unsteady magnetohydrodynamic radiative slip flow of nanofluid,” Appl. Sci., vol. 10, no. 4, pp. 1420, 2020. DOI: 10.3390/app10041420.
   Google Scholar
• W. A. Khan and A. Aziz, “Natural convection flow of nanofluid over a vertical plate with uniform surface heat flux,” Int. J. Therm. Sci., vol. 50, no. 7, pp. 1207–1214, 2011. DOI: 10.1016/j.ijthermalsci.2011.02.015.
   Web of Science ®Google Scholar
• O. D. Makinde and A. Aziz, “Boundary layer flow of a naofluid past a stretching sheet with convective boundary condition,” Int. J. Therm. Sci., vol. 50, no. 7, pp. 1326–1332, 2011. DOI: 10.1016/j.ijthermalsci.2011.02.019.
   Web of Science ®Google Scholar
• F. P. Incropera and D. DeWitt, Fundamentals of Heat and Mass Transfer. 6th ed. New York: John Wiley, 2007.
   Google Scholar
• G. W. Sutton and A. Sherman, Engineering Magnetohydrodynamics. New York, USA: McGraw-Hill Book Company, 1965.
   Google Scholar