MHD Jeffrey nanofluid past a stretching sheet with viscous dissipation effect

Zokri, Syazwani Mohd; Arifin, Norihan; Salleh, Mohd Zuki; Kasim, Abdul Rahman Mohd; Mohammad, Nurul Farahain; Yusoff, Wan Nur Syahidah Wan

doi:10.1088/1742-6596/890/1/012002

Cited by 9 publications

(5 citation statements)

References 16 publications

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“…Above assumptions lead to Equations (1)–(4), which are mathematical model describing the flow system (Ahmad et al, 11 Hayat et al, 14 Zokri et al, 34 Hayat et al 35 ):

\frac{\partial \overset{u}{true}}{\partial η_{1}} + \frac{\partial \overset{v}{true}}{\partial η_{2}} = 0,

\overset{u}{true} \frac{\partial \overset{u}{true}}{\partial η_{1}} + \overset{v}{true} \frac{\partial \overset{u}{true}}{\partial η_{2}} = \frac{ν}{1 + λ_{1}} ([], \frac{\partial^{2} \overset{u}{true}}{\partial {η_{2}}^{2}} + λ_{2} ((), \begin{array}{l} \overset{u}{true} \frac{\partial^{3} \overset{u}{true}}{\partial η_{1} \partial {η_{2}}^{2}} + \overset{v}{true} \frac{\partial^{3} \overset{u}{true}}{\partial {η_{2}}^{3}} \\ - \frac{\partial \overset{u}{true}}{\partial η_{1}} \frac{\partial^{2} \overset{u}{true}}{\partial {η_{2}}^{2}} + \frac{\partial \overset{u}{true}}{\partial η_{2}} \frac{\partial^{2} \overset{u}{true}}{\partial η_{1} \partial η_{2}} \end{array})) + \frac{π j_{0} M_{0}}{8 ρ_{f}} e x p ((), - \frac{π}{a} η_{2}),

\begin{matrix} trueleft \\ \tilde{u} \frac{\partial \tilde{T}}{\partial η_{1}} + \tilde{v} \frac{\partial \tilde{T}}{\partial η_{2}} = \frac{1}{ρ <...>} \end{matrix}

…”

Section: Mathematical Formulationmentioning

confidence: 99%

Jeffrey nanofluid flow near a Riga plate: Spectral quasilinearization approach

2020

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This article attempts to report the flow mechanism of Jeffrey nanofluid flow on a Riga plate integrating the influences of viscous dissipation, irregular heat source/ sink, Brownian motion, and thermophoretic force. Nondimensionalization of mathematical model describing the flow system is accomplished by a set of compatible transformations. An accurate solution of ordinary differential equations is achieved by practicing spectral quasilinearization method. The present method is capable of giving results with good accuracy in few iterations, which infers speedy convergence. Solutionbased error norm (a measure of difference of approximate solution in two consecutive iteration level) is presented to authenticate precision of obtained approximate solution. The similarity between present approximate results and previously reported results is noted to check correctness. Obtained numerical solutions were replicated in a diagrammatic form to visualize the impact of flow parameters. Ratio of relaxation to retardation time produces an enhancing influence on momentum and nanoparticle concentration and a declining effect on the fluid temperature. Riga plate strengthens the momentum, which intensifies the transport of heat energy from boundary layer region, resulting in a reduction in fluid temperature. K E Y W O R D S convective boundary condition, electromagnetohydrodynamic, irregular heat generation/absorption, Jeffrey nanofluid, Riga plate, variable thermal conductivity

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“…Above assumptions lead to Equations (1)–(4), which are mathematical model describing the flow system (Ahmad et al, 11 Hayat et al, 14 Zokri et al, 34 Hayat et al 35 ):

\frac{\partial \overset{u}{true}}{\partial η_{1}} + \frac{\partial \overset{v}{true}}{\partial η_{2}} = 0,

\overset{u}{true} \frac{\partial \overset{u}{true}}{\partial η_{1}} + \overset{v}{true} \frac{\partial \overset{u}{true}}{\partial η_{2}} = \frac{ν}{1 + λ_{1}} ([], \frac{\partial^{2} \overset{u}{true}}{\partial {η_{2}}^{2}} + λ_{2} ((), \begin{array}{l} \overset{u}{true} \frac{\partial^{3} \overset{u}{true}}{\partial η_{1} \partial {η_{2}}^{2}} + \overset{v}{true} \frac{\partial^{3} \overset{u}{true}}{\partial {η_{2}}^{3}} \\ - \frac{\partial \overset{u}{true}}{\partial η_{1}} \frac{\partial^{2} \overset{u}{true}}{\partial {η_{2}}^{2}} + \frac{\partial \overset{u}{true}}{\partial η_{2}} \frac{\partial^{2} \overset{u}{true}}{\partial η_{1} \partial η_{2}} \end{array})) + \frac{π j_{0} M_{0}}{8 ρ_{f}} e x p ((), - \frac{π}{a} η_{2}),

\begin{matrix} trueleft \\ \tilde{u} \frac{\partial \tilde{T}}{\partial η_{1}} + \tilde{v} \frac{\partial \tilde{T}}{\partial η_{2}} = \frac{1}{ρ <...>} \end{matrix}

…”

Section: Mathematical Formulationmentioning

confidence: 99%

Jeffrey nanofluid flow near a Riga plate: Spectral quasilinearization approach

2020

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“…Here, *  and * k are the Stefan-Boltzmann value and absorption coefficient, respectively. Solving the function 4 T under Taylor's series which then can be simplified as…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…A great variety of these fluids are attributing to the development of many constitutive equations which are used to represent their rheological behaviour in order to find the best approximate model to cater their distinct properties. Among non-Newtonian fluids, the Jeffrey fluid model is frequently studied by researchers to examine the properties of fluid having viscose and elastic characteristic of polymer solutions by measuring the ratio of relaxation to retardation times and Deborah number [1][2][3][4][5]. Several studies are devoted to the investigational of Jeffrey fluid over a stretching sheet by considering different elements on the aspect of geometrical as well as the effects that acting on the fluid flow such as magnetohydrodynamic, heat source/sink and slip velocity [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

The Investigation of a Fluid-Solid Interaction Mathematical Model under Combined Convective Jeffrey Flow and Radiation Effect Embedded Newtonian Heating as the Thermal Boundary Condition over a Vertical Stretching Sheet

Kasim

Arifin

Zokri

et al. 2020

DDF

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The investigation on the interaction between solid and fluid under combined convective flow has been carried out mathematically. The Jeffrey fluid model is taken as the fluid phase and the model is being embedded with the dust particles (solid phase). This two-phase model is constructed by introducing the fluid-particles interaction forces in the momentum equations of the fluid and dust phases, respectively. The natural and forced convections together with the aligned magnetic field are considered on the fluid flow. Also, the Newtonian heating as thermal boundary condition is induced on the vertical stretching sheet. In order to reduce the complexity of the model, the governing equations are transformed from partial differential equation into ordinary differential equation via suitable similarity transformation. The solutions are obtained in terms of velocity and temperature profiles for the fluid and particles phases respectively whereby the Keller-box method is utilized to obtain the desired outcomes. The influences of several significant physical parameters are visualized graphically to clarify the flow and heat transfer characteristic for both phases. The investigation found that the fluid’s velocity is affected by the presence of the dust particles which led to decelerate the fluid transference. The present flow model is able to be compared with the single-phase fluid cases if the fluid-particle interaction parameter is ignored.

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“… (i.e−k∂T∂y=hffalse(Tf−Tfalse), DTT∞∂T∂y+DB∂C∂y=0) Chemically reacted species model (which elaborates the activation energy impact) is taken at the stretchable surface. The aforesaid considerations lead to the following flow expressions (Zokri et al , 2017): where Cauchy stress tensor τ˜ is: …”

Section: Mathematical Descriptionmentioning

confidence: 99%

Irreversibility in two-dimensional magneto-nanomaterial flow of Jeffrey fluid with Arrhenius activation energy

Ahmad

Khan

Hayat

et al. 2019

HFF

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Purpose The purpose of this paper is to study entropy generation in magneto-Jeffrey nanomaterial flow by impermeable moving boundary. Adopted nanomaterial model accounts Brownian and thermophoretic diffusions. Modeling is arranged for thermal radiation, nonlinear convection and viscous dissipation. In addition, the concept of Arrhenius activation energy associated with chemical reaction are introduced for description of mass transportation. Design/methodology/approach Homotopy algorithms are used to compute the system of ordinary differential equations. Findings The afore-stated analysis clearly notes that simultaneous aspects of activation energy and entropy generation are not yet investigated. Therefore, the intention here is to consider such effects to formulate and investigate the magneto-Jeffrey nanoliquid flow by impermeable moving surface. Originality/value As per the authors’ knowledge, no such work has yet been published in the literature.

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MHD Jeffrey nanofluid past a stretching sheet with viscous dissipation effect

Cited by 9 publications

References 16 publications

Jeffrey nanofluid flow near a Riga plate: Spectral quasilinearization approach

Jeffrey nanofluid flow near a Riga plate: Spectral quasilinearization approach

The Investigation of a Fluid-Solid Interaction Mathematical Model under Combined Convective Jeffrey Flow and Radiation Effect Embedded Newtonian Heating as the Thermal Boundary Condition over a Vertical Stretching Sheet

Irreversibility in two-dimensional magneto-nanomaterial flow of Jeffrey fluid with Arrhenius activation energy

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