Time-dependent flow model of a generalized Burgers’ fluid with fractional derivatives through a cylindrical domain: An exact and numerical approach

Safdar, Rabia; Imran, Muhammad; Khalique, Chaudry Masood

doi:10.1016/j.rinp.2018.02.053

Cited by 9 publications

(5 citation statements)

References 26 publications

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“…Next, it will be shown that û is the representation solution of (16). If the limit is taken both sides of Equation ( 27), the following equation can be written:…”

Section: Convergence Of Reproducing Kernel Solutionmentioning

confidence: 99%

“…A hybrid technique for the unsteady flow of a Burgers' fluid is given by Raza et al [15]. Laplace and finite Hankel transformations were proposed by Safdar et al for generalized Burgers' fluid with fractional derivative [16]. Time-fractional coupled Burgers' equations were solved with generalized differential transform method by Liu and Hou [17].…”

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of Fractional Order Burgers’ Equation with Dirichlet and Neumann Boundary Conditions by Reproducing Kernel Method

2020

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In this research, obtaining of approximate solution for fractional-order Burgers’ equation will be presented in reproducing kernel Hilbert space (RKHS). Some special reproducing kernel spaces are identified according to inner products and norms. Then an iterative approach is constructed by using kernel functions. The convergence of this approach and its error estimates are given. The numerical algorithm of the method is presented. Furthermore, numerical outcomes are shown with tables and graphics for some examples. These outcomes demonstrate that the proposed method is convenient and effective.

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“…Next, it will be shown that û is the representation solution of (16). If the limit is taken both sides of Equation ( 27), the following equation can be written:…”

Section: Convergence Of Reproducing Kernel Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Fractional Order Burgers’ Equation with Dirichlet and Neumann Boundary Conditions by Reproducing Kernel Method

2020

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“…Ramzan et al 10 studied the flow of the Jeffrey magneto-nanofluid at the stretching cylinder. Safdar et al 11 deliberated the unsteady rotational flow of a generalized Burgers fluid by an infinite circular pipe. Waqas et al 12 deliberated the mixed convective Burgers fluid flow on a moving surface influenced by variable thermal conductivity.…”

Section: Introductionmentioning

confidence: 99%

Heat and mass transfer investigation of a chemically reactive Burgers nanofluid with an induced magnetic field over an exponentially stretching surface

Khan

Nadeem

Zidan

2021

Proceedings of the Institution of Mechanical Engineers, Part E:

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The flow of a chemically reactive Burgers nanofluid with an induced magnetic field over an exponentially stretching surface is considered in this analysis. The thermal slip and concentration slip boundary conditions are considered to analyze the flow at the exponentially stretching surface in the current analysis. Furthermore, a heat transfer analysis is presented with the influence of heat generation/absorption and a variable thermal conductivity effect. Appropriate similarity variables are used to transfer the flow model into the coupled ordinary differential equations. These coupled equations are computed numerically by using the Boundary value problem (BVP) midrich technique. The impact of emerging parameters is examined graphically. It is found that the fluid velocity augments for the several values of relaxation parameters, while it shows the opposite trend for the retardation parameter. Further, it is found that the transfer rate of heat and mass boosted by increasing the values of relaxation and retardation parameters. A comparative investigation of the present article with the prevailing literature shows a remarkable agreement.

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“…The former is the simplest model described by using a simple constitutive equation and the Navier-Poisson-Stokes classical theory is based on this simple equation. 8,9 The latter includes glycerin, grease, polymer melts, blood, liquid crystals, heavy oils, etc., in which the flow behavior cannot be described by the former constitutive equation as the relaxation and retardation phenomena are not properly represented in the constitutive equation. 10 Some important characteristics of non-Newtonian fluids are shear thinning and shear thickening, whereby the apparent yield stresses of such fluids are apparent.…”

Section: Introductionmentioning

confidence: 99%

Towards the exact solutions of Burger’s fluid flow through arteries with fractional time derivative magnetic field and thermal radiation effects

Yakubu

Abdulhameed

Tahiru

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part E:

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We consider the unsteady flow of Burger fluid within a circular cylindrical tube, driven by a time-dependent pressure gradient, a body acceleration and a magnetic field acting normal to the flow direction. The solutions of the fractional constitutive equations governing the unsteady Burger’s fluid flow through arterial walls were obtained via the Laplace transform and the finite Hankel transform. The effects of magnetic field on parameters such as blood temperature and velocity were studied by Caputo time-fractional derivatives. We note that the solutions of many particular models such as fractional Oldroyd-B fluid, fractional Maxwell fluid, fractional second grade fluid and fractional Newtonian fluid models can be recovered from the solutions of the fractional constitutive equations governing the unsteady Burger’s fluid flow by particularizing the material coefficients (i.e. special and limiting cases of the earlier Burger’s fluid model). The numerical computations have been carried out to analyze the effects of fractional parameter α, similarity parameter β, relaxation time λ1, retardation time λ3, radius of the circular cylinder R0 and material parameter λ2 on the blood velocity and temperature. Some interesting flow and temperature characteristics are presented graphically and discussed. The study reveals that blood velocity, temperature and fractional parameters are reduced in the presence of magnetic field. The importance of this study can be found in the application fields of magnetic field control of biotechnological processes, bio magnetic device technology, biomedical engineering, medicine, etc.

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Time-dependent flow model of a generalized Burgers’ fluid with fractional derivatives through a cylindrical domain: An exact and numerical approach

Cited by 9 publications

References 26 publications

Numerical Solution of Fractional Order Burgers’ Equation with Dirichlet and Neumann Boundary Conditions by Reproducing Kernel Method

Numerical Solution of Fractional Order Burgers’ Equation with Dirichlet and Neumann Boundary Conditions by Reproducing Kernel Method

Heat and mass transfer investigation of a chemically reactive Burgers nanofluid with an induced magnetic field over an exponentially stretching surface

Towards the exact solutions of Burger’s fluid flow through arteries with fractional time derivative magnetic field and thermal radiation effects

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