Multiple solutions of heat and mass transfer of MHD slip flow for the viscoelastic fluid over a stretching sheet

In this paper we investigate the magnetohydrodynamic slip flow of an electrically conducting, viscoelastic fluid past a stretching surface. The main concern is to analytically investigate the structure of the solutions and determine the thresholds beyond which multiple solutions exist or the physica...

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Published in:	International journal of thermal sciences Vol. 50; no. 11; pp. 2264 - 2276
Main Author:	Turkyilmazoglu, M.
Format:	Journal Article
Language:	English
Published:	Kidlington Elsevier Masson SAS 01.11.2011 Elsevier
Subjects:	Applied sciences Computational fluid dynamics Energy Energy. Thermal use of fuels Exact sciences and technology Fluid dynamics Fluid flow Fundamental areas of phenomenology (including applications) Heat source/sink Heat transfer Magnetohydrodynamics Magnetohydrodynamics and electrohydrodynamics Mass transfer Mathematical analysis Multiple solution Non-newtonian fluid flows Non-Newtonian fluids Physics Skin friction Slip flow Stretching Stretching surface Theoretical studies. Data and constants. Metering Thermal radiation Viscoelastic fluids Viscoelasticity Slip flow Viscoelasticity Multiple solution Magnetohydrodynamics Thermal radiation Heat source/sink Non-Newtonian fluids Stretching surface Heat transfer Mass transfer Viscoelastic fluid Heat sources Slip Moving wall MHD flow Fluid injection Heat sinks Stretching Flat plate Aspiration Boundary conditions Porous wall Heat mass transfer Conducting fluid Boundary layers
ISSN:	1290-0729, 1778-4166
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Abstract	In this paper we investigate the magnetohydrodynamic slip flow of an electrically conducting, viscoelastic fluid past a stretching surface. The main concern is to analytically investigate the structure of the solutions and determine the thresholds beyond which multiple solutions exist or the physical pure exponential type solution ceases to exist. In the case of the presence of multiple solutions, closed-form formulae for the boundary layer equations of the flow are presented for two classes of viscoelastic fluid, namely, the second-grade and Walter’s liquid B fluids. Heat transfer analysis is also carried out for two general types of boundary heating processes, either by a prescribed quadratic power-law surface temperature or by a prescribed quadratic power-law surface heat flux. The flow field is affected by the presence of physical parameters, such as slip, viscoelasticity, magnetic and suction/injection parameters, whereas the temperature field is additionally affected by thermal radiation, heat source/sink, Prandtl and Eckert numbers. The regions of existence or non-existence of unique/multiple solutions sketched by the combination of these parameters are initially worked out by providing critical values and then velocity/temperature profiles and skin friction coefficient/Nusselt number are examined and discussed. ► Explicit expressions representing single/multiple solutions are obtained. ► In the presence of slip, velocity solutions become multiple. ► In all cases, one of the double solutions is found to decay faster. ► For both slip and no-slip, the shear stress for the first branch of solutions increases. ► Heat transfer in both PST/PHF cases takes place at a larger rate for the second branch of solutions.
AbstractList	In this paper we investigate the magnetohydrodynamic slip flow of an electrically conducting, viscoelastic fluid past a stretching surface. The main concern is to analytically investigate the structure of the solutions and determine the thresholds beyond which multiple solutions exist or the physical pure exponential type solution ceases to exist. In the case of the presence of multiple solutions, closed-form formulae for the boundary layer equations of the flow are presented for two classes of viscoelastic fluid, namely, the second-grade and Walter's liquid B fluids. Heat transfer analysis is also carried out for two general types of boundary heating processes, either by a prescribed quadratic power-law surface temperature or by a prescribed quadratic power-law surface heat flux. The flow field is affected by the presence of physical parameters, such as slip, viscoelasticity, magnetic and suction/injection parameters, whereas the temperature field is additionally affected by thermal radiation, heat source/sink, Prandtl and Eckert numbers. The regions of existence or non-existence of unique/multiple solutions sketched by the combination of these parameters are initially worked out by providing critical values and then velocity/temperature profiles and skin friction coefficient/Nusselt number are examined and discussed. In this paper we investigate the magnetohydrodynamic slip flow of an electrically conducting, viscoelastic fluid past a stretching surface. The main concern is to analytically investigate the structure of the solutions and determine the thresholds beyond which multiple solutions exist or the physical pure exponential type solution ceases to exist. In the case of the presence of multiple solutions, closed-form formulae for the boundary layer equations of the flow are presented for two classes of viscoelastic fluid, namely, the second-grade and Walter’s liquid B fluids. Heat transfer analysis is also carried out for two general types of boundary heating processes, either by a prescribed quadratic power-law surface temperature or by a prescribed quadratic power-law surface heat flux. The flow field is affected by the presence of physical parameters, such as slip, viscoelasticity, magnetic and suction/injection parameters, whereas the temperature field is additionally affected by thermal radiation, heat source/sink, Prandtl and Eckert numbers. The regions of existence or non-existence of unique/multiple solutions sketched by the combination of these parameters are initially worked out by providing critical values and then velocity/temperature profiles and skin friction coefficient/Nusselt number are examined and discussed. ► Explicit expressions representing single/multiple solutions are obtained. ► In the presence of slip, velocity solutions become multiple. ► In all cases, one of the double solutions is found to decay faster. ► For both slip and no-slip, the shear stress for the first branch of solutions increases. ► Heat transfer in both PST/PHF cases takes place at a larger rate for the second branch of solutions.
Author	Turkyilmazoglu, M.
Author_xml	– sequence: 1 givenname: M. surname: Turkyilmazoglu fullname: Turkyilmazoglu, M. email: turkyilm@hotmail.com organization: Mathematics Department, University of Hacettepe, 06532-Beytepe, Ankara, Turkey
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Keywords	Slip flow Viscoelasticity Multiple solution Magnetohydrodynamics Thermal radiation Heat source/sink Non-Newtonian fluids Stretching surface Heat transfer Mass transfer Viscoelastic fluid Heat sources Slip Moving wall MHD flow Fluid injection Heat sinks Stretching Flat plate Aspiration Boundary conditions Porous wall Heat mass transfer Conducting fluid Boundary layers
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Snippet	In this paper we investigate the magnetohydrodynamic slip flow of an electrically conducting, viscoelastic fluid past a stretching surface. The main concern is...
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SubjectTerms	Applied sciences Computational fluid dynamics Energy Energy. Thermal use of fuels Exact sciences and technology Fluid dynamics Fluid flow Fundamental areas of phenomenology (including applications) Heat source/sink Heat transfer Magnetohydrodynamics Magnetohydrodynamics and electrohydrodynamics Mass transfer Mathematical analysis Multiple solution Non-newtonian fluid flows Non-Newtonian fluids Physics Skin friction Slip flow Stretching Stretching surface Theoretical studies. Data and constants. Metering Thermal radiation Viscoelastic fluids Viscoelasticity
Title	Multiple solutions of heat and mass transfer of MHD slip flow for the viscoelastic fluid over a stretching sheet
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