MHD mixed convection stagnation-point flow of a nanofluid over a vertical permeable surface: a comprehensive report of dual solutions

Tamim, Hossein; Dinarvand, Saeed; Hosseini, Reza; Pop, Ioan

doi:10.1007/s00231-013-1264-2

Cited by 37 publications

(26 citation statements)

References 24 publications

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“…Indeed, it should be stated at this point, that the solutions f 0 (η) and θ 0 (η) were determined from the problem depicted in Equations (10)- (12). Upon obtaining the results, f 0 (η) and θ 0 (η) were again applied to Equations (28) and 29, and the linear eigenvalue problem (28)-(30) were solved. Harris et al [55] proposed to relax a suitable boundary condition on F 0 (∞) = 0 or G 0 (∞) = 0 to determine a better range of γ.…”

Section: Stability Analysismentioning

confidence: 99%

Mixed Convection Stagnation-Point Flow of a Nanofluid Past a Permeable Stretching/Shrinking Sheet in the Presence of Thermal Radiation and Heat Source/Sink

Jamaludin

Pop

2019

Energies

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In this study we numerically examine the mixed convection stagnation-point flow of a nanofluid over a vertical stretching/shrinking sheet in the presence of suction, thermal radiation and a heat source/sink. Three distinct types of nanoparticles, copper (Cu), alumina (Al2O3) and titania (TiO2), were investigated with water as the base fluid. The governing partial differential equations were converted into ordinary differential equations with the aid of similarity transformations and solved numerically by utilizing the bvp4c programme in MATLAB. Dual (upper and lower branch) solutions were determined within a particular range of the mixed convection parameters in both the opposing and assisting flow regions and a stability analysis was carried out to identify which solutions were stable. Accordingly, solutions were gained for the reduced skin friction coefficients, the reduced local Nusselt number, along with the velocity and temperature profiles for several values of the parameters, which consists of the mixed convection parameter, the solid volume fraction of nanoparticles, the thermal radiation parameter, the heat source/sink parameter, the suction parameter and the stretching/shrinking parameter. Furthermore, the solutions were presented in graphs and discussed in detail.

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Section: Stability Analysismentioning

confidence: 99%

Mixed Convection Stagnation-Point Flow of a Nanofluid Past a Permeable Stretching/Shrinking Sheet in the Presence of Thermal Radiation and Heat Source/Sink

Jamaludin

Pop

2019

Energies

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“…Meanwhile, Mahdy [4] discovered the effects of the unsteadiness parameter, mixed convection parameter, Prandtl number, and solid volume fraction of nanoparticles upon unsteady boundary layer flow past an elongating surface in nanofluids. Other than that, Tamim et al [5] scrutinized the consequences of the mass flux, magnetic field, as well as solid volume fraction of nanoparticles at the moving sheet upon mixed convection stagnation-point flow of a nanofluid. The valuable work of [5] was then extended by Mustafa et al [6] by incorporating the effects of magnetohydrodynamics and viscous dissipations and concluded that the combination of these effects depreciate the rate of heat transfer.…”

Section: Introductionmentioning

confidence: 99%

“…Other than that, Tamim et al [5] scrutinized the consequences of the mass flux, magnetic field, as well as solid volume fraction of nanoparticles at the moving sheet upon mixed convection stagnation-point flow of a nanofluid. The valuable work of [5] was then extended by Mustafa et al [6] by incorporating the effects of magnetohydrodynamics and viscous dissipations and concluded that the combination of these effects depreciate the rate of heat transfer. The initiative of Subhashini et al [7] to solve the problem of mixed convection flow of a nanofluid over an exponentially moving surface is also an excellent effort to fill the research gap within the scope of mixed convection nanofluid flow.…”

Section: Introductionmentioning

confidence: 99%

Thermal Radiation and MHD Effects in the Mixed Convection Flow of Fe3O4–Water Ferrofluid towards a Nonlinearly Moving Surface

2020

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This paper investigated the magnetohydrodynamic (MHD) mixed convection flow of Fe3O4-water ferrofluid over a nonlinearly moving surface. The present work focused on how the state of suction on the surface of the moving sheet and the effects of thermal radiation influence the fluid flow and heat transfer characteristics within the stagnation region. As such, a similarity solution is engaged to transform the governing partial differential equations to the ordinary differential equations. A collocation method, namely the bvp4c function in the MATLAB software solves the reduced system, numerically. Two different numerical solutions were identified for the cases of assisting and opposing flows. The stability analysis was conducted to test the stability of the non-uniqueness solutions. The increment of the thermal radiation effect affects the rate of heat transfer to decrease. The stability analysis conveyed that the upper branch solution is stable and vice versa for the other solution.

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“…Devi et al [13] computed Nuxand Rex1/2Cfwith variation of Pr for mixed convective boundarylayer flow on vertical flat surface and Ishak et al [14] showed same parameters with magnetohydrodynamic (MHD) effect on vertical surface flow with different Prandtl number. Later on, the same rheological problem studied for convective surface under the effect of magnetic field [15][16].…”

Section: Introductionmentioning

confidence: 99%

Analytical solution for mixed convection and MHD flow of electrically conducting non-Newtonian nanofluid with different nanoparticles: A comparative study

Sharma¹,

Kumar²,

Paswan³

2018

IJHT

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A rigorous analysis of unsteady electrically conducting nanofluid with MHD effect is presented. First, the governing partial differential equations for momentum and energy conservation are converted to couple nonlinear ordinary differential equations by means of exact similarity transformation. The Tiwari-Das nanofluid model is employed to obtain the analytical approximations for flow velocity and temperature distributions of alumina-sodium alginate nanofluid using HAM. The solution is found to be dependent on some parameters including the nanoparticle volume fraction, unsteadiness parameter, magnetic parameter, mixed convection parameter and the generalized Prandtl number. A systematic study is carried out to illustrate the effects of these parameters on the velocity and temperature distributions. Also, the value of skin friction coefficient and local Nusselt number are evaluated with variation of Prandtl number and compared with different nanoparticles.

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MHD mixed convection stagnation-point flow of a nanofluid over a vertical permeable surface: a comprehensive report of dual solutions

Cited by 37 publications

References 24 publications

Mixed Convection Stagnation-Point Flow of a Nanofluid Past a Permeable Stretching/Shrinking Sheet in the Presence of Thermal Radiation and Heat Source/Sink

Mixed Convection Stagnation-Point Flow of a Nanofluid Past a Permeable Stretching/Shrinking Sheet in the Presence of Thermal Radiation and Heat Source/Sink

Thermal Radiation and MHD Effects in the Mixed Convection Flow of Fe3O4–Water Ferrofluid towards a Nonlinearly Moving Surface

Analytical solution for mixed convection and MHD flow of electrically conducting non-Newtonian nanofluid with different nanoparticles: A comparative study

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