Exact solution for the flow of Oldroyd-B fluid due to constant shear and time dependent velocity

Mathur, Vatsala; Khandelwal, Kavita

doi:10.9790/5728-10423845

Cited by 5 publications

(5 citation statements)

References 14 publications

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“…These solutions, which are presented in series form in terms of some generalized functions, satisfy all imposed initial and boundary conditions and are easily reduced to similar solutions for Newtonian and ordinary Maxwell fluids. It is worth pointing out the fact that our limiting solution (28) for the shear stress corresponding to a Newtonian fluid is identical to that obtained in [45,Eq. (24)], while the adequate velocity field (29) corrects a similar result from the same reference.…”

Section: Numerical Results and Conclusionsupporting

confidence: 73%

“…Consequently, in the existing literature, there is no exact solution about the motions of fractional rate type fluid developed by an infinite cylinder that applies a constant, accelerated, or oscillating shear stress to the fluid. Such solutions for ordinary rate type fluids were recently obtained by Fetecau et al [35] and Rauf et al [36] for constant and oscillating stress, respectively, which is on the boundary, while the solutions from [28] and [37] do not examine the constant shear on the boundary as the researchers claimed there. On the other hand, as it was shown by Renardy [38,39], the boundary conditions on tangential stresses are very significant and a well-posed boundary problem can be generated in this way.…”

Section: Introductionmentioning

confidence: 96%

“…Based on the above-mentioned remarks, in the last decade many researchers used the fractional derivatives as a remarkable tool to analyze the properties of viscoelastic fluids [26][27][28][29][30][31][32][33][34]. However, in all these works the motion of the fluid is generated by a cylinder that is rotating around its axis with a given velocity or applies to the fluid a shear stress that is given by a partial differential equation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Rotational motion of fractional Maxwell fluids in a circular duct due to a time-dependent couple

et al. 2019

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The rotational motion of fractional Maxwell fluids in an infinite circular cylinder that applies a time-dependent but not oscillating couple stress to the fluid is investigated using the integral transform technique. Such a flow model was not analyzed in the past both for ordinary and fractional rate type fluids. This is due to their constitutive equations which contain differential expressions acting on the shear stresses. The obtained solutions fulfill all the enforced initial and boundary conditions and are easily reduced to the solutions of Newtonian or ordinary Maxwell fluids having similar motion. At the end, the influence of pertinent parameters on velocity and shear stress variations is graphically underlined and discussed.

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Section: Numerical Results and Conclusionsupporting

confidence: 73%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Rotational motion of fractional Maxwell fluids in a circular duct due to a time-dependent couple

et al. 2019

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“…Afzal et al [9] obtained the exact solution for the viscoplastic medium in the regime of two circular pipes. Khandelwal and Mathur [10] examined the unsteady transient flow of rate type fluid with fractional derivative in annular region. They discussed the unidirectional flow by taking the constant velocity of inner cylinder.…”

Section: Introductionmentioning

confidence: 99%

Heat transfer analysis of viscoelastic fluid flow with fractional Maxwell model in the cylindrical geometry

2020

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This investigation deals with the study of heat transfer analysis of fractional Maxwell fluid in a vertical circular cylinder which is initially at rest. Semi-analytical elucidations for velocity as well as temperature fields have been established by using a hybrid technique which has less time cost and mathematical calculations as compared to other techniques existing in the literature. This problem is also solved exactly with the help of integral transform technique which involves Laplace along with finite Hankel transforms Exact solutions that satisfy all prescribed initial and boundary conditions have been particularized to get the similar solutions for Newtonian and ordinary Maxwell fluids. Impact of distinct physical parameters for example fractional parameter, Prandtl number, Grashof number on fluid function and heat transfer is illustrated through graphical and tabular discussion in the end. Moreover, the fractional Maxwell model helps us to choose the non-integer parameter α for the validation of results between theoretical and experimental findings.

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“…Annular flow between concentric cylinders (including purely tangential, purely longitudinal as well as helical deformation) is not new, and has been addressed in the literature for both classical [7,8,9,10,11] and fractional viscoelastic models considering the generalised Maxwell [12,13,14,15,16,17] and the generalised Oldroyd-B [18,19,20,21,22,23,24] models. Apart from the different fractional models considered, these works differ from each other in the boundary conditions used, and the method in which theoretical results are derived.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and numerical analysis of unsteady fractional viscoelastic flows in simple geometries

et al. 2018

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In this work we discuss the connection between classical and fractional viscoelastic Maxwell models, presenting the basic theory supporting these constitutive equations, and establishing some background on the admissibility of the fractional Maxwell model. We then develop a numerical method for the solution of two coupled fractional differential equations (one for the velocity and the other for the stress), that appear in the pure tangential annular flow of fractional viscoelastic fluids. The numerical method is based on finite differences, with the approximation of fractional derivatives of the velocity and stress being inspired by the method proposed by Sun and Wu for the fractional diffusion-wave equation [ Z.Z. Sun, X. Wu, A fully discrete difference scheme for a diffusion-wave system, Applied Numerical Mathematics 56 (2006) 193-209]. We prove solvability, study numerical convergence of the method, and also discuss the applicability of this method for simulating the rheological response of complex fluids in a real concentric cylinder rheometer. By imposing a torsional step-strain, we observe the different rates of stress relaxation obtained with different values of α and β (the fractional order exponents that regulate the viscoelastic response of the complex fluids).

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Exact solution for the flow of Oldroyd-B fluid due to constant shear and time dependent velocity

Cited by 5 publications

References 14 publications

Rotational motion of fractional Maxwell fluids in a circular duct due to a time-dependent couple

Rotational motion of fractional Maxwell fluids in a circular duct due to a time-dependent couple

Heat transfer analysis of viscoelastic fluid flow with fractional Maxwell model in the cylindrical geometry

Theoretical and numerical analysis of unsteady fractional viscoelastic flows in simple geometries

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