On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Ahmad, Bashir

doi:10.1016/j.jmmm.2016.02.017

Cited by 87 publications

(32 citation statements)

References 44 publications

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“…In this section, we solve linear variants of the problems in Equations (1) and (2), and Equations (1) and (3). Lemma 1.…”

Section: Preliminary Resultsmentioning

confidence: 99%

“…In [2], the authors studied the existence of solutions for third-order nonlinear boundary value problems arising in nano-boundary layer fluid flows over stretching surfaces. In the study of magnetohydrodynamic flow of a second grade nanofluid over a nonlinear stretching sheet, the system of transformed governing equations involves a nonlinear third-order ordinary equation and is solved for local behavior of velocity distributions [3]. The investigation of the model of magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet is also based on a nonlinear third-order ordinary differential equation [4].…”

Section: Introductionmentioning

confidence: 99%

“…The Ulam type stability for the problem in Equations (1) and (2) is discussed in Section 4. In Section 5, we describe the outline for developing the existence theory for the problem in Equations (1) and (3). Section 2 contains the auxiliary lemmas related to the linear variants of the given problems, which lay the foundation for establishing the desired results.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Existence Theory for Nonlinear Third-Order Ordinary Differential Equations with Nonlocal Multi-Point and Multi-Strip Boundary Conditions

et al. 2019

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We investigate the solvability and Ulam stability for a nonlocal nonlinear third-order integro-multi-point boundary value problem on an arbitrary domain. The nonlinearity in the third-order ordinary differential equation involves the unknown function together with its first- and second-order derivatives. Our main results rely on the modern tools of functional analysis and are well illustrated with the aid of examples. An analogue problem involving non-separated integro-multi-point boundary conditions is also discussed.

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“…In this section, we solve linear variants of the problems in Equations (1) and (2), and Equations (1) and (3). Lemma 1.…”

Section: Preliminary Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Existence Theory for Nonlinear Third-Order Ordinary Differential Equations with Nonlocal Multi-Point and Multi-Strip Boundary Conditions

et al. 2019

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“…Further, MHD can be used in continuous casting of metal processing to suppress instabilities and control flow field. In this context, Hayat et al [1,2] explored the MHD flow through moving surfaces and concluded that enhancement in magnetic parameter shows increase in nanoparticles concentration and temperature profiles. Hayat et al [3,4] numerically studied heat transfer impact on MHD axisymmetric third grade liquid flow.…”

Section: Introductionmentioning

confidence: 99%

On the MHD Casson Axisymmetric Marangoni Forced Convective Flow of Nanofluids

et al. 2019

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The proposed investigation concerns the impact of inclined magnetohydrodynamics (MHD) in a Casson axisymmetric Marangoni forced convective flow of nanofluids. Axisymmetric Marangoni convective flow has been driven by concentration and temperature gradients due to an infinite disk. Brownian motion appears due to concentration of the nanosize metallic particles in a typical base fluid. Thermophoretic attribute and heat source are considered. The analysis of flow pattern is perceived in the presence of certain distinct fluid parameters. Using appropriate transformations, the system of Partial Differential Equations (PDEs) is reduced into non-linear Ordinary Differential Equations (ODEs). Numerical solution of this problem is achieved invoking Runge–Kutta fourth-order algorithm. To observe the effect of inclined MHD in axisymmetric Marangoni convective flow, some suitable boundary conditions are incorporated. To figure out the impact of heat/mass phenomena on flow behavior, different physical and flow parameters are addressed for velocity, concentration and temperature profiles with the aid of tables and graphs. The results indicate that Casson fluid parameter and angle of inclination of MHD are reducing factors for fluid movement; however, stronger Marangoni effect is sufficient to improve the velocity profile.

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“…Therefore, different types of non-Newtonian relations are given in the literature. Amongst these relations, the elastico-viscous and second grade materials [31–36] are the simplest subclasses of differential type non-Newtonian materials which describe the effects of normal stress. Moreover the analysis of liquid-liquid two-phase flows are widely involved in several industrial processes such as spray processes, lubrication, natural gas networks, nuclear reactor cooling etc.…”

Section: Introductionmentioning

confidence: 99%

Model and Comparative Study for Flow of Viscoelastic Nanofluids with Cattaneo-Christov Double Diffusion

et al. 2017

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Here two classes of viscoelastic fluids have been analyzed in the presence of Cattaneo-Christov double diffusion expressions of heat and mass transfer. A linearly stretched sheet has been used to create the flow. Thermal and concentration diffusions are characterized firstly by introducing Cattaneo-Christov fluxes. Novel features regarding Brownian motion and thermophoresis are retained. The conversion of nonlinear partial differential system to nonlinear ordinary differential system has been taken into place by using suitable transformations. The resulting nonlinear systems have been solved via convergent approach. Graphs have been sketched in order to investigate how the velocity, temperature and concentration profiles are affected by distinct physical flow parameters. Numerical values of skin friction coefficient and heat and mass transfer rates at the wall are also computed and discussed. Our observations demonstrate that the temperature and concentration fields are decreasing functions of thermal and concentration relaxation parameters.

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On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet

Cited by 87 publications

References 44 publications

Existence Theory for Nonlinear Third-Order Ordinary Differential Equations with Nonlocal Multi-Point and Multi-Strip Boundary Conditions

Existence Theory for Nonlinear Third-Order Ordinary Differential Equations with Nonlocal Multi-Point and Multi-Strip Boundary Conditions

On the MHD Casson Axisymmetric Marangoni Forced Convective Flow of Nanofluids

Model and Comparative Study for Flow of Viscoelastic Nanofluids with Cattaneo-Christov Double Diffusion

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