Unsteady Incompressible Flow of a Generalized Oldroyd-B Fluid between Two Oscillating Infinite Parallel Plates in Presence of a Transverse Magnetic Field

Bose, Dhiman; Basu, U.

doi:10.4236/am.2015.61011

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…MHD OBF through fractional calculus approach under several conditions has been examined by Liu et al [38]. Solutions for OBF between two oscillating plates with transverse magnetic field have been investigated by Bose and Basu [39]. Zhao et al [40] carried out numerical solutions for fractional OBF in porous medium under the influence of heat transfer.…”

Section: Introductionmentioning

confidence: 99%

Functional Application of G-Functions of Lorenzo and Hartley on the Free Convection Flow of Oldroyd-B Fluid with Ordinary and Fractional Techniques

et al. 2021

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In this article, free convection flow of an Oldroyd-B fluid (OBF) through a vertical rectangular channel in the presence of heat generation or absorption subject to generalized boundary conditions is studied. The fractionalized mathematical model is established by Caputo time-fractional derivative through mechanical laws (generalized shear stress constitutive equation and generalized Fourier’s law). Closed form solutions for the velocity and temperature profiles are obtained via Laplace coupled with sine-Fourier transforms and have been embedded with regards to the special functions, namely, the generalized G-functions of Lorenzo and Hartley. Solutions of the known results from recently published work (Nehad et al. Chin. J. Phy., 65, (2020) 367–376) are recovered as limiting cases. Finally, the effects of fractional and various physical parameters are graphically underlined. Furthermore, a comparison between Oldroyd-B, Maxwell and viscous fluids (fractional and ordinary) is depicted. It is found that, for short time, ordinary fluids have greater velocity as compared to the fractional fluids.

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Section: Introductionmentioning

confidence: 99%

Functional Application of G-Functions of Lorenzo and Hartley on the Free Convection Flow of Oldroyd-B Fluid with Ordinary and Fractional Techniques

et al. 2021

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“…The general solution for velocity of OBF between two parallel walls has been investigated by Zafar et al 24 Solutions for OBF between two oscillating infinite parallel plates with transverse magnetic field has been explored by Bose and Basu. 25 Khan and Zaman 26 determined the solutions for velocity of OBF between two moving plates via Fourier and Laplace transformations. Zhao et al 27 evaluated the numerical solutions for fractional OBF in porous medium under the influence of heat transfer.…”

Section: Introductionmentioning

confidence: 99%

Local and Nonlocal Differential Operators: A Comparative Study of Heat and Mass Transfers in MHD Oldroyd-B Fluid With Ramped Wall Temperature

2020

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Study of heat and mass transfers is carried out for MHD Oldroyd-B fluid (OBF) over an infinite vertical plate having time-dependent velocity and with ramped wall temperature and constant concentration. It is proven in many already published articles that the heat and mass transfers do not really or always follow the classical mechanics process that is known as memoryless process. Therefore, the model using classical differentiation based on the rate of change cannot really replicate such dynamical process very accurately, thus, a different concept of differentiation is needed to capture such process. Very recently, a new class of differential operators were introduced and have been recognized to be efficient in capturing processes following the power-law, the decay law and the crossover behaviors. For the study of heat and mass transfers, we applied the newly introduced differential operators to model such flow and compare the results with integer-order derivative. Laplace transform and inversion algorithms are used for all the cases to find analytical solutions and to predict the influences of different parameters. The obtained analytical solutions were plotted for different values of fractional orders [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] on the velocity field. In comparison, Atangana–Baleanu (ABC) fractional derivatives are found to be the best to explain the memory effects than the classical, Caputo (C) and Caputo–Fabrizio (CF) fractional derivatives. Some calculated values for Nusselt number and Sherwood number are presented in tables. Moreover, from the present solutions, the already published results were found as limiting cases.

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A finite element method for the numerical solution of Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives

Dehghan

Abbaszadeh

2016

Engineering with Computers

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Unsteady Incompressible Flow of a Generalized Oldroyd-B Fluid between Two Oscillating Infinite Parallel Plates in Presence of a Transverse Magnetic Field

Abstract: In this paper an attempt has been made to study the unsteady incompressible flow of a genera-

Cited by 4 publications

References 8 publications

Functional Application of G-Functions of Lorenzo and Hartley on the Free Convection Flow of Oldroyd-B Fluid with Ordinary and Fractional Techniques

Functional Application of G-Functions of Lorenzo and Hartley on the Free Convection Flow of Oldroyd-B Fluid with Ordinary and Fractional Techniques

Local and Nonlocal Differential Operators: A Comparative Study of Heat and Mass Transfers in MHD Oldroyd-B Fluid With Ramped Wall Temperature

A finite element method for the numerical solution of Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives

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