High-order numerical methods of fractional-order Stokes’ first problem for heated generalized second grade fluid

Ye, Chao; Luo, Xiaoyu; Wen, Liping

doi:10.1007/s10483-012-1534-8

Cited by 6 publications

(4 citation statements)

References 19 publications

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“…Reference [29] presented the numerical discretization for Stokes' first problem for the HGSGF described by a fractional operator. Reference [30] provided a discretization for Stokes' equation for the HGSGF that contains the Riemann-Liouville derivative. For further information about the HGSGF, one could see works in [1,[31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Approximate Solutions of the Model Describing Fluid Flow Using Generalized ρ-Laplace Transform Method and Heat Balance Integral Method

Yavuz

Sene

2020

Axioms

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This paper addresses the solution of the incompressible second-grade fluid models. Fundamental qualitative properties of the solution are primarily studied for proving the adequacy of the physical interpretations of the proposed model. We use the Liouville-Caputo fractional derivative with its generalized version that gives more comprehensive physical results in the analysis and investigations. In this work, both the ρ-Laplace homotopy transform method (ρ-LHTM) and the heat balance integral method (HBIM) are successfully combined to solve the fractional incompressible second-grade fluid differential equations. Numerical simulations and their physical interpretations of the mentioned incompressible second-grade fluid model are ensured to illustrate the main findings. It is also proposed that one can recognize the differences in physical analysis of diffusions such as ballistic diffusion, super diffusion, and subdiffusion cases by considering the impact of the orders ρ and φ.

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Section: Introductionmentioning

confidence: 99%

Approximate Solutions of the Model Describing Fluid Flow Using Generalized ρ-Laplace Transform Method and Heat Balance Integral Method

Yavuz

Sene

2020

Axioms

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“…Since no exact solution exists for FDE, most efforts have supplied numerical and analytical methods to solve these equations. Indeed, many powerful methods have been recently developed, such as the Adomian decomposition method, homotopy analysis method, homotopy perturbation method, collocation method, finite difference method and Tau method [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

A New Variational Iteration Method for a Class of Fractional Convection-Diffusion Equations in Large Domains

2017

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Abstract:In this paper, we introduced a new generalization method to solve fractional convection-diffusion equations based on the well-known variational iteration method (VIM) improved by an auxiliary parameter. The suggested method was highly effective in controlling the convergence region of the approximate solution. By solving some fractional convection-diffusion equations with a propounded method and comparing it with standard VIM, it was concluded that complete reliability, efficiency, and accuracy of this method are guaranteed. Additionally, we studied and investigated the convergence of the proposed method, namely the VIM with an auxiliary parameter. We also offered the optimal choice of the auxiliary parameter in the proposed method. It was noticed that the approach could be applied to other models of physics.

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“…C.Ye and X.N. Luo [6] have come out the high-order numerical methods for heated generalized second grade fluid. I.G.…”

Section: Introductionmentioning

confidence: 99%

Slip Effects on Heat and Mass Transfer of a Non-newtonian Fluid in the Micro-channel

Zhu¹,

Sui²

2017

Proceedings of the 2017 International Conference on Applied Mathematics, Modelling and Statistics Application (AMMSA 2017)

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Abstract-The effects of velocity-slip and temperature-jump boundary conditions on Non-Newtonian flow and heat transfer in the micro channel have been investigated in this paper. The governing boundary layer equations have been transformed into a system of nonlinear differential equations through the similarity transformation, and the analytical approximations of solutions are derived by homotopy analysis method. The reliability and efficiency of the HAM solutions are verified by the residual errors. Furthermore, the effects of physical factors on the flow and heat are studied and discussed graphically.

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High-order numerical methods of fractional-order Stokes’ first problem for heated generalized second grade fluid

Cited by 6 publications

References 19 publications

Approximate Solutions of the Model Describing Fluid Flow Using Generalized ρ-Laplace Transform Method and Heat Balance Integral Method

Approximate Solutions of the Model Describing Fluid Flow Using Generalized ρ-Laplace Transform Method and Heat Balance Integral Method

A New Variational Iteration Method for a Class of Fractional Convection-Diffusion Equations in Large Domains

Slip Effects on Heat and Mass Transfer of a Non-newtonian Fluid in the Micro-channel

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