New exact solutions corresponding to the first problem of Stokes for Oldroyd-B fluids

This paper presents the new exact analytical solutions for magnetohydrodynamic (MHD) flows of an Oldroyd-B fluid. The explicit expressions for the velocity field and the associated tangential stress are established by using the Laplace transform method. Three characteristic examples: (i) flow due to impulsive motion of plate, (ii) flow due to uniformly accelerated plate, and (iii) flow due to non-uniformly accelerated plate are considered. The solutions for the hydrodynamic flows are special cases of the presented solutions. Moreover, the similar solutions corresponding to Maxwell and Newtonian fluids in the presence as well as absence of a magnetic field appear as the limiting cases of our solutions. The influences of the exerted magnetic field on the flow are also graphically presented and discussed. In particular, graphical results for the Oldroyd-B fluid are compared with those of a Newtonian fluid.

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“…Now taking the inverse Laplace transform of Eq. (26) and following the procedure given in the reference [17], we get…”

Section: Flow Due To Impulsive Motion Of the Platementioning

confidence: 99%

“…For M = 0, Eqs. (27)and (28) can be reduce to the similar solutions for a hydrodynamic Oldroyd-B fluid, performing the same motion, as obtained by Vieru et al[17] …”

mentioning

confidence: 96%

New exact solutions for magnetohydrodynamic flows of an Oldroyd-B fluid

Khan

Mahmood

Fetecău

2008

Z. Angew. Math. Phys.

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“…For example, Fetecau and Fetecau [1] investigated Stokes' first problem for an Oldroyd-B fluid; Tan et al [2,3] studied the problem for a second grade fluid in a porous half-space with heated boundary and an Oldroyd-B fluid in a porous half-space, respectively; Shen et al [4] discussed the Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative model; Akyildiz et al [5] investigated Stokes' first problem for a Newtonian fluid in a non-Darcian porous half-space using a Laguerre-Galerkin method; Vierua et al [6] presented a new exact solution to the problem for Oldroyd-B fluids; Shahzada et al [7] considered the problem for the rotating flow of a third grade fluid; Devakar and Iyengar [8] analyzed the problem for a micropolar fluid through the state-space approach.…”

Section: Introductionmentioning

confidence: 99%

Numerical methods with fourth-order spatial accuracy for variable-order nonlinear Stokes’ first problem for a heated generalized second grade fluid

Chen¹,

Liu²,

Turner³

et al. 2011

Computers & Mathematics with Applications

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a r t i c l e i n f o Keywords:The variable-order nonlinear Stokes' first problem Heated generalized second grade fluid Stability Convergence Fourier analysis Fourth-order spatial accuracy Improved numerical method a b s t r a c t Stokes' first problem has in recent years received much attention. In this paper, we focus on the variable-order nonlinear Stokes' first problem for a heated generalized second grade fluid. A numerical scheme with fourth-order spatial accuracy is developed to solve the problem. The stability, solvability and convergence of the numerical scheme are discussed via Fourier analysis. An improved numerical scheme is also developed. In addition, a numerical example is given and the numerical results support the effectiveness of our theoretical analysis results.

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“…In another paper, Fetecau and Fetecau [11] extended the idea of MF to an Oldroyd-B fluid (OBF, non-Newtonian) and examined exact solutions for the first problem of Stokes'. Vieru et al [12] also determined exact solution for the flow situation of an OBF over an infinite rigid plate.…”

Section: Introductionmentioning

confidence: 99%

Time-Dependent MHD Flow of Non-Newtonian Generalized Burgers' Fluid (GBF) Over a Suddenly Moved Plate With Generalized Darcy's Law

Alqahtani

Khan

2020

Front. Phys.

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Time-dependent magnetohydrodynamic (MHD) motion of a generalized Burgers' fluid (GBF) is investigated in this article. GBF is a highly complicated non-Newtonian fluid and is of highest degree in the class of rate type fluids. GBF is taken electrically conducting by using the restriction of small magnetic Reynolds number. Darcy's law has been used here in its generalized form using the GBF constitutive relation; hence, the medium is made porous. The impulsive motion in the fluid is induced due to sudden jerk of the plate. Exact expressions for velocity as well as for shear stress fields are obtained using the Laplace transform method. The solutions for hydrodynamic fluid (absence of MHD) in a non-porous medium as well as those for a Newtonian fluid (NF) executing a similar motion are also recovered. Results are sketched in terms of several plots and discussed for embedded parameters. It is found that the Hartmann number and porosity of the medium have strong influence on the velocity and shear stress fields.

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New exact solutions corresponding to the first problem of Stokes for Oldroyd-B fluids

Cited by 14 publications

References 20 publications

New exact solutions for magnetohydrodynamic flows of an Oldroyd-B fluid

New exact solutions for magnetohydrodynamic flows of an Oldroyd-B fluid

Numerical methods with fourth-order spatial accuracy for variable-order nonlinear Stokes’ first problem for a heated generalized second grade fluid

Time-Dependent MHD Flow of Non-Newtonian Generalized Burgers' Fluid (GBF) Over a Suddenly Moved Plate With Generalized Darcy's Law

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