Radiative nanofluid flow and heat transfer over a non-linear permeable sheet with slip conditions and variable magnetic field: Dual solutions

Rana, Puneet; Dhanai, Ruchika; Kumar, Lalit

doi:10.1016/j.asej.2015.08.016

Cited by 24 publications

(15 citation statements)

References 41 publications

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“…Equations (9)-(12) under the boundary conditions (13)- (14) have been solved numerically using the finite element method (FEM). The FEM has been applied to study different problems in computational fluid dynamic and extremely efficient method to solve different nonlinear problems [48][49][50].…”

Section: Finite Element Methods Solutionsmentioning

confidence: 99%

“…Swapna et al and Rana et al [52,53] described that variational finite element method solves boundary value problem very effectively, quickly, and accurately. We employe the finite element method to the solve nonlinear differential equations, Equations (9)- (12), with the boundary conditions (13)- (14), first we consider…”

Section: Finite Element Methods Solutionsmentioning

confidence: 99%

“…Ismail et al [13] examined the nonlinear radiation effects on nanofluid slip flow in porous media. The study of nonlinear radiation heat transfer plays an important role in industrial applications at high temperature [14]. Slip condition on stretching surfaces is important in several manufacturing processes.…”

Section: Introductionmentioning

confidence: 99%

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Finite Element Simulation of Multiple Slip Effects on MHD Unsteady Maxwell Nanofluid Flow over a Permeable Stretching Sheet with Radiation and Thermo-Diffusion in the Presence of Chemical Reaction

et al. 2019

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The aim of the present study is to investigate the multiple slip effects on magnetohydrodynamic unsteady Maxwell nanofluid flow over a permeable stretching sheet with thermal radiation and thermo-diffusion in the presence of chemical reaction. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations with the aid of appropriate similarity variables, and the transformed equations are then solved numerically by using a variational finite element method. The effects of various physical parameters on the velocity, temperature, solutal concentration, and nanoparticle concentration profiles as well as on the skin friction coefficient, rate of heat transfer, and Sherwood number for solutal concentration are discussed by the aid of graphs and tables. An exact solution of flow velocity, skin friction coefficient, and Nusselt number is compared with the numerical solution obtained by FEM and also with numerical results available in the literature. A good agreement between the exact and numerical solution is observed. Also, to justify the convergence of the finite element numerical solution, the calculations are carried out by reducing the mesh size. The present investigation is relevant to high-temperature nanomaterial processing technology.

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Section: Finite Element Methods Solutionsmentioning

confidence: 99%

Section: Finite Element Methods Solutionsmentioning

confidence: 99%

See 1 more Smart Citation

Finite Element Simulation of Multiple Slip Effects on MHD Unsteady Maxwell Nanofluid Flow over a Permeable Stretching Sheet with Radiation and Thermo-Diffusion in the Presence of Chemical Reaction

et al. 2019

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“…Furthermore, MHD nanofluid boundary layer fluid flow over disparate geometries was studied by numerous researchers. [11][12][13][14][15][16][17][18] Rana et al 19 investigated the dual solutions for MHD nanofluid velocity, nanoparticle volume fraction, and temperature over non-linear permeable sheet by using shooting technique. Hamid et al 20 examined the stability and duality of thermal transportation in Casson liquid over the extending sheet, and their results demonstrate that positive eigenvalues estimate stable solution when contrasted with negative eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

Critical points and stability analysis in MHD radiative non‐Newtonian nanoliquid transport phenomena with artificial neural network prediction

Rana

Bhardwaj

Makkar

et al. 2022

Math Methods in App Sciences

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In the present framework, flow and thermal transport behavior of non-Newtonian viscoelastic fluid induced by stretching/shrinking of the horizontal sheet under the influence of Lorentz force, volumetric heat source/sink, and radiation (assuming optically thick medium) has been investigated. Multiple solutions (Branches) have been predicted numerically using Lie symmetry transformation and Runge Kutta Dormand Prince (RKDP) algorithm-based Shooting method for the different controlling parameters, stretching/shrinking (𝛾 c < −1 < 𝛾 < ∞), and suction (𝛼 c < 𝛼 < ∞) with substantial impact with UCM parameter, 𝛽 > 0. Some of the results have also been compared with MATLAB built-in solvers to validate our in-house code. The deviations in critical (turning) points (𝛽 c , 𝛾 c ) have been noticed for different values of M and 𝛼. The temporal stability analysis is performed for these parameters (𝛽, 𝛾), and the upper (lower) branch is only physically feasible (infeasible). The combined effect on Nusselt number and skin-friction coefficient is also depicted in the form of contour plots. The outcomes from artificial neural network (ANN) using Levenberg-Marquardt algorithm give a preferred estimate for current numerical simulation. In ANN prediction, the optimal number of neurons in the hidden layer is used, having minimum value of RMSE and RMRE with maximum R 2 for different cases of non Newtonian stretching/shrinking sheet. Finally, the results conclude that the applied ANN model can accurately predict the output results.

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“…It was discovered that the momentum boundary layer thickness for the first solution reduces with slip and suction parameters, but rises with the power-law index of the decreasing velocity. The computational examination of steady, magnetohydrodynamic boundary-layer slip flow of a nanofluid across a permeable stretching/shrinking sheet with heat radiation, using RKF45 with a shot approach, was addressed in previous work [9]. According to the findings, the Nusselt number falls with the increasing of the thermophoresis parameter and the thermal slip parameter, but rises with the increasing of the thermal radiation and the Prandtl number.…”

Section: Introductionmentioning

confidence: 99%

Insights into Partial Slips and Temperature Jumps of a Nanofluid Flow over a Stretched or Shrinking Surface

Elazem

2021

Energies

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This paper elucidates the significance of partial slips and temperature jumps on the heat and mass transfer of a boundary layer nanofluid flowing through a stretched or shrinking surface. Considerable consideration is given to the dynamic properties of the nanofluid process, including Brownian motion and thermophoresis. A similarity transform is introduced to obtain a physical model of nonlinear ordinary differential equations, and the Chebyshev method of collocation is used to numerically analyze the influences of parameters of physical flow such as slip, temperature jump, Brownian motion, thermophoresis, suction (or injection) parameters, and Lewis and Prandtl numbers. The numerical results for temperature and concentration profiles, and heat and mass transfer rates, are graphically represented, and insights into the effects of slips and temperature jumps are revealed. In the case of a stretched sheet, the slip parameter enhances the temperature field and increases the thermal boundary layer thickness as well as the concentration function’s boundary layer thickness. When the slip parameter is raised in the case of the shrinking sheet, the dual solutions for temperature and concentration functions are reduced. For the first solution, both the temperature and concentration functions drop as the slip parameter increases, but for the second solution, both the temperature and concentration functions rise as the slip parameter increases. The discoveries have applications in a number of disciplines, including heat transfer in a solar energy collector. Glass blowing, annealing, and copper wire thinning are just a few of the technical and oilfield applications for the current problem. In high-temperature industrial applications, radiation heat transfer research is critical.

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Radiative nanofluid flow and heat transfer over a non-linear permeable sheet with slip conditions and variable magnetic field: Dual solutions

Cited by 24 publications

References 41 publications

Finite Element Simulation of Multiple Slip Effects on MHD Unsteady Maxwell Nanofluid Flow over a Permeable Stretching Sheet with Radiation and Thermo-Diffusion in the Presence of Chemical Reaction

Finite Element Simulation of Multiple Slip Effects on MHD Unsteady Maxwell Nanofluid Flow over a Permeable Stretching Sheet with Radiation and Thermo-Diffusion in the Presence of Chemical Reaction

Critical points and stability analysis in MHD radiative non‐Newtonian nanoliquid transport phenomena with artificial neural network prediction

Insights into Partial Slips and Temperature Jumps of a Nanofluid Flow over a Stretched or Shrinking Surface

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