Soret and Dufour effects on three dimensional Oldroyd-B fluid

Farooq, Aamir; Ali, Ramzan; Benim, Ali Cemal

doi:10.1016/j.physa.2018.02.204

Cited by 76 publications

(31 citation statements)

References 27 publications

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“…Invoking the above‐mentioned assumptions, the appropriate boundary layer equations are

\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0,

italicu \frac{normal∂ u}{normal∂ italicx} + v \frac{normal∂ u}{normal∂ y} = u_{\infty} \frac{normald u_{\infty}}{normald x} + \frac{{italicη}_{0}}{{italicρ}_{italicf}} (\frac{{normal∂}^{2} u}{\partial y^{2}}) - \frac{k_{0}}{ρ_{f}} [u \frac{\partial^{3} u}{normal∂ x normal∂ y^{2}} + v \frac{\partial^{3} u}{normal∂ y^{3}} + \frac{normal∂ u}{normal∂ x} \frac{\partial^{2} u}{normal∂ y^{2}} - \frac{normal∂ u}{normal∂ y} \frac{\partial^{2} u}{normal∂ x normal∂ y}] + \frac{π j_{0} M_{0}}{8 ρ_{f}} e^{- (π / normalΛ) y},

u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} + {normalΓ}_{T} {normalΛ}_{T} = {\frac{k_{f}}{true(ρ C_{p} true)}}_{f} \frac{{normal∂}^{2} T}{\partial y^{2}} + τ true[D_{B} \frac{\partial C}{\partial y} \frac{\partial T}{\partial y}

…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Invoking the above-mentioned assumptions, the appropriate boundary layer equations are 7,11,12,17,23…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Walters' B fluid provides the first order approximation to elasticity, and its low order elasticity reduces the flow instability. The Walters' B fluid model characterizes the polymeric liquids in biotechnology and chemical engineering …”

Section: Introductionmentioning

confidence: 99%

“…The Walters' B fluid model characterizes the polymeric liquids in biotechnology and chemical engineering. [6][7][8][9][10][11][12][13][14] The consideration of electromagnetic sheets has great relevance today. An electromagnetic sheet is unique in its feature in that it is an arrangement of a spanwise aligned array of alternating electrodes and permanent magnets placed on a plane surface.…”

Section: Introductionmentioning

confidence: 99%

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Impact of the Cattaneo‐Christov thermal and solutal diffusion models on the stagnation point slip flow of Walters' B nanofluid past an electromagnetic sheet

Nayak

Oyelakin

Mondal

et al. 2018

Heat Trans. Asian Res.

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The present study investigates the effect of Cattaneo‐Christov thermal and solutal diffusion on the stagnation point flow of Walters' B nanofluid past an electromagnetic sheet subject to velocity, thermal, and solutal slips. The study analyzed the role of electromagnetic fields. In addition, the authors introduced the heat transfer aspect due to Brownian motion and thermophoretic force. The numerical solution of the transformed governing equations employed the spectral local linearization method. Comparisons showed an excellent agreement with the numerical data presented in previous notable works. The study reveals that the developed electromagnetic field due to the arrangement of the sheet causes accelerated fluid motion, and diminution of nondimensional temperature and concentration. In addition, augmented velocity, thermal, and solutal slips develop the corresponding descending boundary layers. The augmented short memory coefficient enhances the skin friction coefficient. The Cattaneo‐Christov thermal and solutal diffusion upsurge the heat and mass transfer rates from the electromagnetic sheet, respectively.

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“…Invoking the above‐mentioned assumptions, the appropriate boundary layer equations are

\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0,

italicu \frac{normal∂ u}{normal∂ italicx} + v \frac{normal∂ u}{normal∂ y} = u_{\infty} \frac{normald u_{\infty}}{normald x} + \frac{{italicη}_{0}}{{italicρ}_{italicf}} (\frac{{normal∂}^{2} u}{\partial y^{2}}) - \frac{k_{0}}{ρ_{f}} [u \frac{\partial^{3} u}{normal∂ x normal∂ y^{2}} + v \frac{\partial^{3} u}{normal∂ y^{3}} + \frac{normal∂ u}{normal∂ x} \frac{\partial^{2} u}{normal∂ y^{2}} - \frac{normal∂ u}{normal∂ y} \frac{\partial^{2} u}{normal∂ x normal∂ y}] + \frac{π j_{0} M_{0}}{8 ρ_{f}} e^{- (π / normalΛ) y},

u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} + {normalΓ}_{T} {normalΛ}_{T} = {\frac{k_{f}}{true(ρ C_{p} true)}}_{f} \frac{{normal∂}^{2} T}{\partial y^{2}} + τ true[D_{B} \frac{\partial C}{\partial y} \frac{\partial T}{\partial y}

…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Invoking the above-mentioned assumptions, the appropriate boundary layer equations are 7,11,12,17,23…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Impact of the Cattaneo‐Christov thermal and solutal diffusion models on the stagnation point slip flow of Walters' B nanofluid past an electromagnetic sheet

Nayak

Oyelakin

Mondal

et al. 2018

Heat Trans. Asian Res.

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show abstract

“…The others related studies can be found in the literature. [36][37][38] Waqas et al, [39][40][41][42] Bhatti et al 43,44 recently studied non-Newton fluid using different models with different effects. Sulochana et al 45 studied Darcy-Forchheimer Williamson Nanofluid fluid with nonlinear radiation.…”

Section: Introductionmentioning

confidence: 99%

An optimal analysis for Darcy–Forchheimer three-dimensional Williamson nanofluid flow over a stretching surface with convective conditions

Dawar

Shah

Islam

et al. 2019

Advances in Mechanical Engineering

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The augmented thermal conductivity is significant in betterment of heat transfer behavior of fluids. A number of other physical quantities such as density, viscosity, and specific heat play the key role in fluid flow behavior. Investigators have shown that the nanofluids have not only superior heat conductivity but also have better convective heat transfer capability than the base fluids. In this article, the analysis of three-dimensional Williamson fluid has been carried out under investigation. The fluid flow is taken over a linear porous stretching sheet under the influence of thermal radiation. The transformed system of equations has been solved by homotopy analysis method. The impact of embedded parameters on the fluid flow has shown graphically. The velocity profile in x-direction is decreased with the augmented stretching, Williamson, coefficient of inertia, and porosity parameters. The velocity profile in y-direction is increased with the enlarged stretching parameter, while reduced with the augmented Williamson, coefficient of inertia, and porosity parameters. The temperature profile is increased with the enlarged stretching, radiation, thermophoresis, parameter and Brownian motion parameters, and Biot number while decreased with the increased Prandtl number. The concentration profile is increased with the increased thermophoresis parameter and Biot numbers, while decreased with the enlarged stretching and Brownian motion parameters.

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Dufour and Soret influence on MHD boundary layer flow of a Maxwell fluid over a stretching sheet with nanoparticles

2022

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An analysis has been carried out to examine the heat and mass transfer properties of a two-dimensional incompressible electrically conducting Maxwell fluid over a stretching sheet in the existence of Soret, Dufour, and nanoparticles. In many practical scenarios, such as the polymer extrusion process, the problem presented here is crucial. The flow is examined in terms of the impacts of magnetohydrodynamics and elasticity. Brownian motion and thermophoresis are incorporated into the transport equations. Using adequate similarity variables, the governing partial differential equations and related boundary conditions are non-dimensionalized. The fourth-fifth-order Runge-Kutta-Fehlberg procedure is utilized to solve the consequent transformed ordinary differential equations. The effects of various embedded thermo-physical parameters on the fluid velocity, temperature, concentration, Nusselt number, and Sherwood number have been determined and discussed quantitatively. A comparison of a special case of our results with the one previously reported in the literature shows a very good agreement. An increase in the values of Du and Sr leads to an increase in the temperature and concentration distribution. Nusselt number estimates decrease as Nb estimations increase. Furthermore, this study leads to the study of different flows of electrically conducting fluid

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Soret and Dufour effects on three dimensional Oldroyd-B fluid

Cited by 76 publications

References 27 publications

Impact of the Cattaneo‐Christov thermal and solutal diffusion models on the stagnation point slip flow of Walters' B nanofluid past an electromagnetic sheet

Impact of the Cattaneo‐Christov thermal and solutal diffusion models on the stagnation point slip flow of Walters' B nanofluid past an electromagnetic sheet

An optimal analysis for Darcy–Forchheimer three-dimensional Williamson nanofluid flow over a stretching surface with convective conditions

Dufour and Soret influence on MHD boundary layer flow of a Maxwell fluid over a stretching sheet with nanoparticles

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