Effect of suction and MHD induced Navier slip flow due to a non-linear stretching/shrinking sheet

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dc.citation.epage91
dc.citation.issue1
dc.citation.spage83
dc.contributor.affiliationУніверситет Путра Малайзія
dc.contributor.affiliationUniversiti Putra Malaysia
dc.contributor.authorАліас, Н. С.
dc.contributor.authorХафідзуддін, М. Е. Н.
dc.contributor.authorAlias, N. S.
dc.contributor.authorHafidzuddin, M. E. H.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2023-12-13T09:10:54Z
dc.date.available2023-12-13T09:10:54Z
dc.date.created2021-03-01
dc.date.issued2021-03-01
dc.description.abstractУ цьому дослідженні розглянуто проблему магнітогідродинамічного (МГД) індукованого потоку, враховуючи всмоктування та ковзання Нав’є, на шарі, який може нелінійно розтягуватися або стискатися. Перетворення подібності використано для перетворення головних нелінійних диференціальних рівнянь у частинних похідних до системи нелінійних звичайних рівнянь. Після цього, перетворені звичайні диференціальні рівняння розв’язуються за допомогою методу стрільби в Maple Software. Подвійні розв’язки отримані для певних керуючих параметрів. Отримані результати показують, що всмоктування покращує поверхневе тертя, тоді як параметр ковзання зменшує напруження зсуву стінки. Крім того, виявлено, що область подвійного розв’язку у випадку шару, який розтягується, є меншою у порівнянні зі шаром, який стискається.
dc.description.abstractIn this study, a problem of a magnetohydrodynamic (MHD) induced Navier slip flow over a non-linear stretching and shrinking sheet with the existence of suction is considered. Similarity transformation is used to transform the governing nonlinear partial differential equations into a system of nonlinear ordinary equations. The transformed ordinary differential equations are then solved by using the Shooting Method in Maple software. Dual solutions are obtained for certain governing parameters. The results obtained show that suction improves skin friction, while the slip parameter reduces shear wall stress. Moreover, it is established that the range of dual solutions for stretching sheet is smaller compared to the shrinking case.
dc.format.extent83-91
dc.format.pages9
dc.identifier.citationAlias N. S. Effect of suction and MHD induced Navier slip flow due to a non-linear stretching/shrinking sheet / N. S. Alias, M. E. H. Hafidzuddin // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 1. — P. 83–91.
dc.identifier.citationenAlias N. S. Effect of suction and MHD induced Navier slip flow due to a non-linear stretching/shrinking sheet / N. S. Alias, M. E. H. Hafidzuddin // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 1. — P. 83–91.
dc.identifier.doi10.23939/mmc2022.01.083
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/60538
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 1 (9), 2022
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dc.relation.references[2] Gupta P. S., Gupta A. S. Heat and mass transfer on a stretching sheet with suction or blowing. The Canadian Journal of Chemical Engineering. 55 (6), 744–746 (1977).
dc.relation.references[3] Rajagopal K. R., Na T. Y., Gupta A. S. Flow of a viscoelastic fluid over a stretching sheet. Rheologica Acta. 23 (2), 213–215 (1984).
dc.relation.references[4] Vajravelu K. Viscous flow over a nonlinearly stretching sheet. Applied Mathematics and Computation. 124 (3), 281–288 (2001).
dc.relation.references[5] Partha M. K., Murthy P. V. S. N., Rajasekhar G. P. Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface. Heat and Mass Transfer. 41 (4), 360–366 (2005).
dc.relation.references[6] Sajid M., Hayat T. Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet. International Communications in Heat and Mass Transfer. 35 (3), 347–356 (2008).
dc.relation.references[7] Bidin B., Nazar R. Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation. European journal of scientific research. 33 (4), 710–717 (2009).
dc.relation.references[8] Khan W. A., Pop I. Boundary-layer flow of a nanofluid past a stretching sheet. International Journal of Heat and Mass Transfer. 53 (11–12), 2477–2483 (2010).
dc.relation.references[9] Rana P., Bhargava R. Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: a numerical study. Communications in Nonlinear Science and Numerical Simulation. 17 (1), 212–226 (2012).
dc.relation.references[10] Hsiao K. L. Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet. Applied Thermal Engineering. 98, 850–861 (2016).
dc.relation.references[11] Daniel Y. S., Aziz Z. A., Ismail Z., Bahar A., Salah F. Slip role for unsteady MHD mixed convection of nanofluid over stretching sheet with thermal radiation and electric field. Indian Journal of Physics. 94 (2), 195–207 (2020).
dc.relation.references[12] Wang C. Y. Liquid film on an unsteady stretching surface. Quarterly of Applied Mathematics. 48 (4), 601–610 (1990).
dc.relation.references[13] Miklavˇciˇc M., Wang C. Viscous flow due to a shrinking sheet. Quarterly of Applied Mathematics. 64 (2), 283–290 (2006).
dc.relation.references[14] Fang T., Zhang J. Closed-form exact solutions of MHD viscous flow over a shrinking sheet. Communications in Nonlinear Science and Numerical Simulation. 14 (7), 2853–2857 (2009).
dc.relation.references[15] Fang T., Zhang J., Yao S. Slip MHD viscous flow over a stretching sheet – an exact solution. Communications in Nonlinear Science and Numerical Simulation. 14 (11), 3731–3737 (2009).
dc.relation.references[16] Fang T., Yao S., Zhang J., Aziz A. Viscous flow over a shrinking sheet with a second order slip flow model. Communications in Nonlinear Science and Numerical Simulation. 15 (7), 1831–1842 (2010).
dc.relation.references[17] Sarpkaya T. Flow of non-Newtonian fluids in a magnetic field. AIChE Journal. 7 (2), 324–328 (1961).
dc.relation.references[18] Pavlov K. Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface. Magnitnaya Gidrodinamika. 4 (1), 146–147 (1974).
dc.relation.references[19] Mahabaleshwar U. S., Nagaraju K. R., Sheremet M. A., Vinay Kumar P. N., Lorenzini G. Effect of Mass Transfer and MHD Induced Navier’s Slip Flow Due to a non Linear Stretching Sheet. Journal of Engineering Thermophysics. 28 (4), 578–590 (2019).
dc.relation.references[20] Abdal S., Ali B., Younas S., Ali L., Mariam A. Thermo-Diffusion and Multislip Effects on MHD Mixed Convection Unsteady Flow of Micropolar Nanofluid over a Shrinking/Stretching Sheet with Radiation in the Presence of Heat Source. Symmetry. 12 (1), 49 (2020).
dc.relation.references[21] Navier C. M´emoire sur les lois du mouvement des fluides. M´emoires de l’Acad´emie Royale des Sciences de l’Institut de France. 6 (1823), 389–440 (1823).
dc.relation.references[22] Masmoudi N., Saint-Raymond L. From the Boltzmann equation to the Stokes–Fourier system in a bounded domain. Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences. 56 (9), 1263–1293 (2003).
dc.relation.references[23] Iftimie D., Sueur F. Viscous boundary layers for the Navier–Stokes equations with the Navier slip conditions. Archive for Rational Mechanics and Analysis. 199 (1), 145–175 (2011).
dc.relation.references[24] Das S., Jana R. N. Entropy generation due to MHD flow in a porous channel with Navier slip. Ain Shams Engineering Journal. 5 (2), 575–584 (2014).
dc.relation.references[25] Matin M. H., Khan W. A. Electrokinetic effects on pressure driven flow of viscoelastic fluids in nanofluidic channels with Navier slip condition. Journal of Molecular Liquids. 215, 472–480 (2016).
dc.relation.references[26] Tlili I., Hamadneh N. N., Khan W. A. Thermodynamic analysis of MHD heat and mass transfer of nanofluids past a static wedge with Navier slip and convective boundary conditions. Arabian Journal for Science and Engineering. 44 (2), 1255–1267 (2019).
dc.relation.referencesen[1] Crane L. J. Flow past a stretching plate. Zeitschrift f¨ur angewandte Mathematik und Physik ZAMP. 21 (4), 645–647 (1970).
dc.relation.referencesen[2] Gupta P. S., Gupta A. S. Heat and mass transfer on a stretching sheet with suction or blowing. The Canadian Journal of Chemical Engineering. 55 (6), 744–746 (1977).
dc.relation.referencesen[3] Rajagopal K. R., Na T. Y., Gupta A. S. Flow of a viscoelastic fluid over a stretching sheet. Rheologica Acta. 23 (2), 213–215 (1984).
dc.relation.referencesen[4] Vajravelu K. Viscous flow over a nonlinearly stretching sheet. Applied Mathematics and Computation. 124 (3), 281–288 (2001).
dc.relation.referencesen[5] Partha M. K., Murthy P. V. S. N., Rajasekhar G. P. Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface. Heat and Mass Transfer. 41 (4), 360–366 (2005).
dc.relation.referencesen[6] Sajid M., Hayat T. Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet. International Communications in Heat and Mass Transfer. 35 (3), 347–356 (2008).
dc.relation.referencesen[7] Bidin B., Nazar R. Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation. European journal of scientific research. 33 (4), 710–717 (2009).
dc.relation.referencesen[8] Khan W. A., Pop I. Boundary-layer flow of a nanofluid past a stretching sheet. International Journal of Heat and Mass Transfer. 53 (11–12), 2477–2483 (2010).
dc.relation.referencesen[9] Rana P., Bhargava R. Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: a numerical study. Communications in Nonlinear Science and Numerical Simulation. 17 (1), 212–226 (2012).
dc.relation.referencesen[10] Hsiao K. L. Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet. Applied Thermal Engineering. 98, 850–861 (2016).
dc.relation.referencesen[11] Daniel Y. S., Aziz Z. A., Ismail Z., Bahar A., Salah F. Slip role for unsteady MHD mixed convection of nanofluid over stretching sheet with thermal radiation and electric field. Indian Journal of Physics. 94 (2), 195–207 (2020).
dc.relation.referencesen[12] Wang C. Y. Liquid film on an unsteady stretching surface. Quarterly of Applied Mathematics. 48 (4), 601–610 (1990).
dc.relation.referencesen[13] Miklavˇciˇc M., Wang C. Viscous flow due to a shrinking sheet. Quarterly of Applied Mathematics. 64 (2), 283–290 (2006).
dc.relation.referencesen[14] Fang T., Zhang J. Closed-form exact solutions of MHD viscous flow over a shrinking sheet. Communications in Nonlinear Science and Numerical Simulation. 14 (7), 2853–2857 (2009).
dc.relation.referencesen[15] Fang T., Zhang J., Yao S. Slip MHD viscous flow over a stretching sheet – an exact solution. Communications in Nonlinear Science and Numerical Simulation. 14 (11), 3731–3737 (2009).
dc.relation.referencesen[16] Fang T., Yao S., Zhang J., Aziz A. Viscous flow over a shrinking sheet with a second order slip flow model. Communications in Nonlinear Science and Numerical Simulation. 15 (7), 1831–1842 (2010).
dc.relation.referencesen[17] Sarpkaya T. Flow of non-Newtonian fluids in a magnetic field. AIChE Journal. 7 (2), 324–328 (1961).
dc.relation.referencesen[18] Pavlov K. Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface. Magnitnaya Gidrodinamika. 4 (1), 146–147 (1974).
dc.relation.referencesen[19] Mahabaleshwar U. S., Nagaraju K. R., Sheremet M. A., Vinay Kumar P. N., Lorenzini G. Effect of Mass Transfer and MHD Induced Navier’s Slip Flow Due to a non Linear Stretching Sheet. Journal of Engineering Thermophysics. 28 (4), 578–590 (2019).
dc.relation.referencesen[20] Abdal S., Ali B., Younas S., Ali L., Mariam A. Thermo-Diffusion and Multislip Effects on MHD Mixed Convection Unsteady Flow of Micropolar Nanofluid over a Shrinking/Stretching Sheet with Radiation in the Presence of Heat Source. Symmetry. 12 (1), 49 (2020).
dc.relation.referencesen[21] Navier C. M´emoire sur les lois du mouvement des fluides. M´emoires de l’Acad´emie Royale des Sciences de l’Institut de France. 6 (1823), 389–440 (1823).
dc.relation.referencesen[22] Masmoudi N., Saint-Raymond L. From the Boltzmann equation to the Stokes–Fourier system in a bounded domain. Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences. 56 (9), 1263–1293 (2003).
dc.relation.referencesen[23] Iftimie D., Sueur F. Viscous boundary layers for the Navier–Stokes equations with the Navier slip conditions. Archive for Rational Mechanics and Analysis. 199 (1), 145–175 (2011).
dc.relation.referencesen[24] Das S., Jana R. N. Entropy generation due to MHD flow in a porous channel with Navier slip. Ain Shams Engineering Journal. 5 (2), 575–584 (2014).
dc.relation.referencesen[25] Matin M. H., Khan W. A. Electrokinetic effects on pressure driven flow of viscoelastic fluids in nanofluidic channels with Navier slip condition. Journal of Molecular Liquids. 215, 472–480 (2016).
dc.relation.referencesen[26] Tlili I., Hamadneh N. N., Khan W. A. Thermodynamic analysis of MHD heat and mass transfer of nanofluids past a static wedge with Navier slip and convective boundary conditions. Arabian Journal for Science and Engineering. 44 (2), 1255–1267 (2019).
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.subjectМГД
dc.subjectковзання Нав’є
dc.subjectрозтягування/стиснення шару
dc.subjectнелінійний
dc.subjectподвійний розв’язок
dc.subjectMHD
dc.subjectNavier slip
dc.subjectstretching/shrinking sheet
dc.subjectnon-linear
dc.subjectdual solution
dc.titleEffect of suction and MHD induced Navier slip flow due to a non-linear stretching/shrinking sheet
dc.title.alternativeМагнітогідродинамічний індукований потік ковзання Нав’є та вплив всмоктування внаслідок нелінійного розтягування/стиснення шару
dc.typeArticle

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Mathematical Modeling And Computing. – 2022. – Vol. 9, No. 1