Role of non-integer and integer order differentiations on the relaxation phenomena of viscoelastic fluid

Abro, Kashif Ali; Atangana, Abdon

doi:10.1088/1402-4896/ab560c

Cited by 64 publications

(12 citation statements)

References 50 publications

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“…Finite Fourier sine transform, Laplace, and fractional techniques have been utilized to the governing equations for exhibiting typical and rheological properties of the problem. Although the studies on heat and transfer analysis can be continue yet the relevant studies can be observed therein in categorical format as heat transfer via analytical approaches [16][17][18][19][20][21][22][23], heat transfer via numerical approaches [24][25][26][27][28][29], heat transfer via fractional calculus approaches [30][31][32][33], and heat transfer via multi-dimensional approaches [34][35][36][37]. Motivating by the above consideration, the main theme of this manuscript is to have the significance of convective heating and variable heat source on Azimuthal oscillatory MHD convective flows developed in a cylindrical Darcy-Forchheimer porous medium filled by a radiating second-grade fluid.…”

Section: Introductionmentioning

confidence: 99%

Thermophysical Investigation of Oldroyd-B Fluid with Functional Effects of Permeability: Memory Effect Study Using Non-Singular Kernel Derivative Approach

et al. 2021

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It is well established fact that the functional effects, such as relaxation and retardation of materials, can be measured for magnetized permeability based on relative increase or decrease during magnetization. In this context, a mathematical model is formulated based on slippage and non-slippage assumptions for Oldroyd-B fluid with magnetized permeability. An innovative definition of Caputo-Fabrizio time fractional derivative is implemented to hypothesize the constitutive energy and momentum equations. The exact solutions of presented problem, are determined by using mathematical techniques, namely Laplace transform with slipping boundary conditions have been invoked to tackle governing equations of velocity and temperature. The Nusselt number and limiting solutions have also been persuaded to estimate the heat emission rate through physical interpretation. In order to provide the validation of the problem, the absence of retardation time parameter led the investigated solutions with good agreement in literature. Additionally, comprehensively scrutinize the dynamics of the considered problem with parametric analysis is accomplished, the graphical illustration is depicted for slipping and non-slipping solutions for temperature and velocity. A comparative studies between fractional and non-fractional models describes that the fractional model elucidate the memory effects more efficiently.

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Section: Introductionmentioning

confidence: 99%

Thermophysical Investigation of Oldroyd-B Fluid with Functional Effects of Permeability: Memory Effect Study Using Non-Singular Kernel Derivative Approach

et al. 2021

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“…is new AB derivative is nonsingular and has nonlocal kernel and possesses the long memory due to the existence of Mittag-Lefler kernel which is the generalization of the exponential kernel. is new AB fractional derivative in Caputo sense of order α > 0 is defined as follows [47,48]:…”

Section: Problem Formulationmentioning

confidence: 99%

Fractional Study for Transient Free Convection Flow in a Channel with Mittag-Leffler Memory

Sarwar

Aleem

Asjad

et al. 2022

Mathematical Problems in Engineering

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Fractional-order convective transient flow of viscous and incompressible fluids transiting through two infinite hot parallel upright plates is investigated analytically in the presence of chemical reaction, radiative heat flux, and mass diffusion at the boundary. A physical model for transient incompressible unsteady flow is developed with a comparatively new fractional derivative, namely, Atangana–Baleanu with nonsingular, nonlocal kernel. The developed fractional model is studied with means of an integral transform, i.e., Laplace transform method. Results obtained for the concentration, velocity, and temperature are expressed in the form of generalized M q p y function. The impact of various physical parameters like fractional and flow parametric quantities is demonstrated diagrammatically. At last, we envisioned that for the fractional model, temperature and concentration could be enhanced for smaller fractional parameter α values while velocity for larger values of α , respectively. The proposed model gives the better results in the presence of memory effect besides the Caputo and Caputo–Fabrizio model when compared with the existing literature.

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“…Viscoelasticity has important implications due to the characterization of viscoelastic parameters (relaxation and retardation phenomenon), elastic shearing strain, thermal relaxation, time‐dependent anelastic aspect, and other rheological properties 1‐3 . In this regard, Qi and Jin 4 suggested constitutive relationship of a viscoelastic material based on fractional derivative on the basis of simple harmonic motion or impulsively rotating motion of the outer cylinder.…”

Section: Introductionmentioning

confidence: 99%

Role of single slip assumption on the viscoelastic liquid subject to non‐integer differentiable operators

Saeed

Abro

Almani

2021

Math Methods in App Sciences

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The main focus of this study is to investigate the impact of heat generation/absorption with single slip assumptions based on Newtonian heating on magnetohydrodynamic (MHD) time‐dependent Maxwell fluid over an unbounded plate embedded in a permeable medium. The mathematical modeling based on fractional treatment of governing equation subject to the temperature distribution, shearing stress, and velocity field is developed. The fractionalized analytical solutions have been traced out separately through Atangana‐Baleanu (AB) and Caputo‐Fabrizio (CF) fractional differential operators. These differential operators with and without non‐locality have been employed on the developed governing partial differential equations. The mathematical analysis of developed fractionalized governing partial differential equations has been established by means of systematic and powerful techniques of Laplace transform with its inversion. For the sake of physical investigation of the considered problem, the effective Prandtl number and fractional parameter have been invoked on temperature with and without single slip assumption. Our results suggest that the velocity profile decrease by increasing the effective Prandtl number. The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity. Additionally, the magnetic field and relaxation phenomenon have been analyzed on the profile of velocity with and without single slip assumption.

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Role of non-integer and integer order differentiations on the relaxation phenomena of viscoelastic fluid

Cited by 64 publications

References 50 publications

Thermophysical Investigation of Oldroyd-B Fluid with Functional Effects of Permeability: Memory Effect Study Using Non-Singular Kernel Derivative Approach

Thermophysical Investigation of Oldroyd-B Fluid with Functional Effects of Permeability: Memory Effect Study Using Non-Singular Kernel Derivative Approach

Fractional Study for Transient Free Convection Flow in a Channel with Mittag-Leffler Memory

Role of single slip assumption on the viscoelastic liquid subject to non‐integer differentiable operators

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