Exact solutions of MHD second Stokes flow of generalized Burgers fluid

Khan, Masood; Malik, Rabia; Anjum, Aisha

doi:10.1007/s10483-015-1906-7

Cited by 23 publications

(27 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Due to the shear, the fluid begins to move and, in the absence of a pressure gradient in the x-direction, the balance of linear momentum reduces to the partial differential equation as follows [25]:…”

Section: Statement Of the Problemmentioning

confidence: 99%

See 1 more Smart Citation

Analytical Solutions for Two Mixed Initial-Boundary Value Problems Corresponding to Unsteady Motions of Maxwell Fluids through a Porous Plate Channel

Fetecău

Vieru

Zeeshan

2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Two unsteady motions of incompressible Maxwell fluids between infinite horizontal parallel plates embedded in a porous medium are analytically studied to get exact solutions using the finite Fourier cosine transform. The motion is induced by the lower plate that applies time-dependent shear stresses to the fluid. The solutions that have been obtained satisfy all imposed initial and boundary conditions. They can be easily reduced as limiting cases to known solutions for the incompressible Newtonian fluids. For a check of their correctness, the steady-state solutions are presented in different forms whose equivalence is graphically proved. The effects of physical parameters on the fluid motion are graphically emphasized and discussed. Required time to reach the steady-state is also determined. It is found that the steady-state is rather obtained for Newtonian fluids as compared with Maxwell fluids. Furthermore, the effect of the side walls on the fluid motion is more effective in the case of Newtonian fluids.

show abstract

Section: Statement Of the Problemmentioning

confidence: 99%

“…Replacing the expression of u(y, t) from equality (25) in (19) and solving the obtained equation with the initial condition (20), it results that τ(y, t) is given by the following expression:…”

Section: Case τ(0 T)mentioning

confidence: 99%

Analytical Solutions for Two Mixed Initial-Boundary Value Problems Corresponding to Unsteady Motions of Maxwell Fluids through a Porous Plate Channel

Fetecău

Vieru

Zeeshan

2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…Furthermore we suppose that the Laplace transform of the function exists. In the case of parallel flow along the -axis, the velocity vector iŝ = ( ( , ), 0, 0) whereas [15][16][17] lead us to the following governing equation:…”

Section: Mathematical Formulation Of the Problemmentioning

confidence: 99%

Flows with Slip of Oldroyd-B Fluids over a Moving Plate

Shakeel

Ahmad

Khan

et al. 2016

Advances in Mathematical Physics

View full text Add to dashboard Cite

A general investigation has been made and analytic solutions are provided corresponding to the flows of an Oldroyd-B fluid, under the consideration of slip condition at the boundary. The fluid motion is generated by the flat plate which has a translational motion in its plane with a time-dependent velocity. The adequate integral transform approach is employed to find analytic solutions for the velocity field. Solutions for the flows corresponding to Maxwell fluid, second-grade fluid, and Newtonian fluid are also determined in both cases, namely, flows with slip on the boundary and flows with no slip on the boundary, respectively. Some of our results were compared with other results from the literature. The effects of several emerging dimensionless and pertinent parameters on the fluid velocity have been studied theoretically as well as graphically in the paper.

show abstract

“…It is possible to develop specific solutions for the isothermal MHD flow of incompressible Maxwell fluids over infinite plates or between parallel plates embedded in porous media. Notably, these precise answers are influenced by the findings of Khan et al [1], Hayat et al [2], Khan et al [3], Ali et al [4], Ullah et al [5], Fetecau et al [6], Hussain et al [7], and Fetecau et al [8]. However, the majority of these solutions apply to motions where the boundary velocity is predetermined.…”

Section: Introductionmentioning

confidence: 99%

Remarks on some unidirectional flows of Maxwell fluids through a rectangular channel filled with porous medium

Fetecau,

Mirza,

Vieru

et al. 2024

Z Angew Math Mech

View full text Add to dashboard Cite

Exact solutions for the dynamics of incompressible fluids showing rate‐type behavior have mostly been found in circumstances where the boundary velocities are given in the body of existing research. This phenomenon results from the constitutive equation of the corresponding extra‐stress tensor, which specifies the natural relationship between velocity and shear stress. In this paper, we focus on a unique observation of the magnetohydrodynamic (MHD) movements of incompressible Maxwell fluids, and the governing equations regulating velocity and shear stress. We focus our analysis on the case of an infinite plate submerged in a porous substance. Within this framework, we do an analytical analysis of a motion issue with a boundary that has a predetermined shear stress. We can easily ascertain the shear stress associated with the motion brought on by a flat plate in order to be more exact. The fluid is subjected to a shear stress by this plate that changes over time. The velocity field from a boundary motion with a predetermined velocity is used to achieve this. We give two graphical representations of individual solutions for the sake of clarity and result verification. Last but not least, we use graphical depiction to highlight how a magnetic field and a porous media affect the fluid's flow resistance. The results show that the flow resistance of the fluid increases in the presence of a porous media and decreases when a magnetic field is present.

show abstract

Exact solutions of MHD second Stokes flow of generalized Burgers fluid

Cited by 23 publications

References 22 publications

Analytical Solutions for Two Mixed Initial-Boundary Value Problems Corresponding to Unsteady Motions of Maxwell Fluids through a Porous Plate Channel

Analytical Solutions for Two Mixed Initial-Boundary Value Problems Corresponding to Unsteady Motions of Maxwell Fluids through a Porous Plate Channel

Flows with Slip of Oldroyd-B Fluids over a Moving Plate

Remarks on some unidirectional flows of Maxwell fluids through a rectangular channel filled with porous medium

Contact Info

Product

Resources

About