Multiple solutions in MHD flow and heat transfer of Sisko fluid containing nanoparticles migration with a convective boundary condition: Critical points

Dhanai, Ruchika; Rana, Puneet; Kumar, Lalit

doi:10.1140/epjp/i2016-16142-3

Cited by 21 publications

(5 citation statements)

References 41 publications

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“…To test the stability of the steady-flow solution, f (η) = f 0 (η), h(η) = h 0 (η), θ(η) = θ 0 (η), and φ(η) = φ 0 (η), satisfying the boundary value problem (15)-(18), we write as follows [26,27,47]:…”

Section: Subject To the Boundary Conditionsmentioning

confidence: 99%

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Slip effects on MHD Hiemenz stagnation point nanofluid flow and heat transfer along a nonlinearly shrinking sheet with induced magnetic field: multiple solutions

Rana

Uddin

Gupta

et al. 2017

J Braz. Soc. Mech. Sci. Eng.

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Nowadays, nanofluid (colloidal suspension) gains a lot of interest among various scientists and researchers in different countries due to its vast applications as heat transfer fluid [1], transportation [2, 3], bio-fluid [4], micro-heat sinks [5], micro-transformer [6], etc. Many experiments had been conducted to explore the tremendous heat transfer efficiency of nanofluid (metal and nonmetal nanoparticles) at Argonne National Laboratory, Chicago. The Argonne scientist team revealed that silicon carbide nanoparticles in ethylene glycol/ water carry heat away approximately 15 times more than conventional fluid. The development of nanofluids was focused on the basis of working of whole nanofluid system rather than individual properties (size, shape, conductivity, etc.) of the nanoparticles. Thus, the concentration and particle size were key to designing such systems. In 2006, Buongiorno [7] discussed the twocomponent modeling of nanofluid flow based on seven slip mechanism. He concluded that Brownian motion and thermophoresis are mainly responsible for anomalous heat transfer in nanofluids. Later, the extension of the Buongiorno's model was reported in vertical plate problem [8], Cheng-Minkowycz problem [9], linear and nonlinearly stretching sheet problem [10, 11], Hiemenz flow problem [12], Falkner-Skan problem [13], nonequilibrium model [14], double-diffusive problem [15, 16], non-Newtonian problem [17], and others. Recently, Kuznetsov and Nield [18, 19] revised their earlier published with new no-flux boundary conditions. Due to these boundary conditions, the impact of Brownian motion on heat transfer is now insignificant. Thenafter, many researchers tried to implement such boundary conditions in different flow regimes [20-27].

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Section: Subject To the Boundary Conditionsmentioning

confidence: 99%

“…The appropriate similarity transformations are developed by the Lie Group method [48,49]. The multiple solutions for the present governing equations are reported successfully with the help of the Runge-Kutta-Fehlberg method [22,[25][26][27]. The temporal stability analysis has also been performed.…”

mentioning

confidence: 99%

Slip effects on MHD Hiemenz stagnation point nanofluid flow and heat transfer along a nonlinearly shrinking sheet with induced magnetic field: multiple solutions

Rana

Uddin

Gupta

et al. 2017

J Braz. Soc. Mech. Sci. Eng.

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“…Turkyilmazoglu [26] discovered different solutions for two types of viscoelastic fluid using MHD slip flow across the stretching surface. Dhanai et al [27] investigated Sisko nanofluid and applied variable MHD flow and energy transfer solutions combined with convective boundary conditions. Ellahi et al [28] examine Hall's current MHD Jeffrey fluid flow effect.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer

et al. 2022

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The recent study was concerned with employing the finite element method for heat and mass transfer of MHD Maxwell nanofluid flow over the stretching sheet under the effects of radiations and chemical reactions. Moreover, the effects of viscous dissipation and porous plate were considered. The mathematical model of the flow was described in the form of a set of partial differential equations (PDEs). Further, these PDEs were transformed into a set of nonlinear ordinary differential equations (ODEs) using similarity transformations. Rather than analytical integrations, numerical integration was used to compute integrals obtained by applying the finite element method. The mesh-free analysis and comparison of the finite element method with the finite difference method are also provided to justify the calculated results. The effect of different parameters on velocity, temperature and concentration profile is shown in graphs, and numerical values for physical quantities of interest are also given in a tabular form. In addition, simulations were carried out by employing software that applies the finite element method for solving PDEs. The calculated results are also portrayed in graphs with varying sheet velocities. The results show that the second-order finite difference method is more accurate than the finite element method with linear interpolation polynomial. However, the finite element method requires less number of iterations than the finite difference method in a considered particular case. We had high hopes that this work would act as a roadmap for future researchers entrusted with resolving outstanding challenges in the realm of enclosures utilized in industry and engineering.

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“…Turkyilmazoglu 10 considered a stretching surface, to find multiple solutions of MHD slip flow for two types of viscoelastic fluid. Dhanai et al 11 addressed the multiple solutions of MHD flow and heat transfer of Sisko nanofluid with convective boundary conditions. Ellahi et al 12 considered a non-uniform rectangular duct to examine the MHD Jeffrey fluid flow with Hall's current effect.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of heat and mass transfer in a Maxwell fluid

Khan

Nadeem

Ahmad

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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The objective of current research is to analyze the MHD flow of a Maxwell fluid towards a stretching sheet with thermophoretic and stratification effects. The analysis of heat and mass transfer is presented in the presence of variable thermal conductivity and the Cattaneo-Christov theory. The Cattaneo-Christov theory is used instead of Fourier and Fick laws because Fourier and Fick's laws give parabolic equations, which propagate in the space with infinite speed. The under-consideration flow model is converted into a set of ordinary differential equations by using suitable transformation. The set of ODEs is numerically solved by adopting the bvp4c Matlab technique. Influences of emerging parameters on velocity profile, temperature, and concentration are discussed with graphs. It is observed that larger values of Deborah number induce a resistance, that declining the velocity of a fluid. Further, it is noticed that thermal stratification parameter and concentration stratification parameter reduce the temperature and concentration distribution.

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Multiple solutions in MHD flow and heat transfer of Sisko fluid containing nanoparticles migration with a convective boundary condition: Critical points

Cited by 21 publications

References 41 publications

Slip effects on MHD Hiemenz stagnation point nanofluid flow and heat transfer along a nonlinearly shrinking sheet with induced magnetic field: multiple solutions

Slip effects on MHD Hiemenz stagnation point nanofluid flow and heat transfer along a nonlinearly shrinking sheet with induced magnetic field: multiple solutions

Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer

Mathematical analysis of heat and mass transfer in a Maxwell fluid

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