Analysis of fractional multi-dimensional Navier–Stokes equation

Chu, Yu‐Ming; Shah, Nehad Ali; Agarwal, Praveen; Chung, Jae Dong

doi:10.1186/s13662-021-03250-x

Cited by 46 publications

(17 citation statements)

References 40 publications

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“…They have examined very big change in their heat conduction power after adding very small amount of nanoparticles as compared to common fluids. [14][15][16][17][18][19][20][21][22] MHD nanoparticles are playing significant role in numerous industrial processes. Such fluids have broad range applications in optical industry as gratings, fiber filters, modulator, and polymer processes.…”

Section: Introductionmentioning

confidence: 99%

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Thermo-convective Arrhenius reactive fluid flow between two parallel plates

Hussain

Shuaib

Ali

et al. 2022

Advances in Mechanical Engineering

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A nonlinear thermo-convective Arrhenius Casson fluid flow between two vertical parallel plates is modeled under the actions of exothermic chemical reaction, linear and nonlinear volumetric thermal and concentration expansions. The non dimensional coupled system of ordinary differential equations are solved numerically by using Parametric Continuation Method (PCM). The numerical results of (PCM) method are graphically justified with the solutions of [Formula: see text] package, which presented an excellent agreement with each other. For further validation of (PCM) method, the obtained results are also compared with previously published work and found an accuracy upto two decimal places. It has been found that Frank-Kameneskii’s parameter, depends on Arrhenius kinetics, has the tendency to enhanced the exothermic chemical reaction, which give rise in internal heat generation and heat transfer rate. The findings of the present study may be used for making energy source materials and in biological systems. Furthermore, the increasing values of [Formula: see text] are responsible to drop the exothermic reaction level within the flow system, due to which the mass transfer is reduced and make a reduction in concentration profile.

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Section: Introductionmentioning

confidence: 99%

“…They have examined very big change in their heat conduction power after adding very small amount of nanoparticles as compared to common fluids. 14–22…”

Section: Introductionmentioning

confidence: 99%

Thermo-convective Arrhenius reactive fluid flow between two parallel plates

Hussain

Shuaib

Ali

et al. 2022

Advances in Mechanical Engineering

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“…Agarwal et al [21,22] investigated some special functions in the analysis of differential equations and some existences and uniqueness results for fractional nonlocal thermistor problem. Chu [23] and his collaborators studied fractional multi-dimensional Navier-Stokes equation. Sunarto et al [24] implemented iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of higher order boundary value problems via wavelet approach

et al. 2021

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This paper presents a numerical scheme based on Haar wavelet for the solutions of higher order linear and nonlinear boundary value problems. In nonlinear cases, quasilinearization has been applied to deal with nonlinearity. Then, through collocation approach computing solutions of boundary value problems reduces to solve a system of linear equations which are computationally easy. The performance of the proposed technique is portrayed on some linear and nonlinear test problems including tenth, twelfth, and thirteen orders. Further convergence of the proposed method is investigated via asymptotic expansion. Moreover, computed results have been matched with the existing results, which shows that our results are comparably better. It is observed from convergence theoretically and verified computationally that by increasing the resolution level the accuracy also increases.

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“…e meshless methods have the ability to compute the solution in regular and irregular domain utilizing scattered or uniform nodes, which increases the priority and the advantages of meshless methods. As these facts show, these methods are really workable and useful numerical methods that can be applied to real-world challenging problems [9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of the Multiterm Time-Fractional Model for Heat Conductivity by Local Meshless Technique

et al. 2021

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Fractional partial differential equation models are frequently used to several physical phenomena. Despite the ability to express many complex phenomena in different disciplines, researchers have found that multiterm time-fractional PDEs improve the modeling accuracy for describing diffusion processes in contrast to the results of a single term. Nowadays, it attracts the attention of the active researchers. The aim of this work is concerned with the approximate numerical solutions of the three-term time-fractional Sobolev model equation using computationally attractive and reliable technique, known as a local meshless method. Because of the meshless character and the simple application in higher dimensions, there is a growing interest in meshless techniques. To assess the reliability and accuracy of the proposed method, three test problems and two types of irregular domains are taken into account.

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Analysis of fractional multi-dimensional Navier–Stokes equation

Cited by 46 publications

References 40 publications

Thermo-convective Arrhenius reactive fluid flow between two parallel plates

Thermo-convective Arrhenius reactive fluid flow between two parallel plates

Numerical solutions of higher order boundary value problems via wavelet approach

Numerical Solution of the Multiterm Time-Fractional Model for Heat Conductivity by Local Meshless Technique

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