On the Governing Equations for Velocity and Shear Stress of some Magnetohydrodynamic Motions of Rate-type Fluids and their Applications

Constantin Fetecau

doi:10.61927/igmin144

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Engineering Group Mini Review 記事ID: igmin144

On the Governing Equations for Velocity and Shear Stress of some Magnetohydrodynamic Motions of Rate-type Fluids and their Applications

Mechanical Engineering

Constantin Fetecau ^*

Affiliation

Section of Mathematics, Academy of Romanian Scientists, 050094 Bucharest, Romania

DOI10.61927/igmin144 全文HTML 全文PDF この記事を引用する

要約

The governing equations for the shear stress corresponding to some magnetohydrodynamic (MHD) motions of a large class of rate-type fluids are brought to light. In rectangular domains, the governing equations of velocity and shear stress are identical as form. The provided governing equations can be used to solve motion problems of such fluids when shear stress is prescribed on the boundary. For illustration, the motion in an infinite circular cylinder with shear stress on the boundary is discussed.

参考文献

Renardy M. Recent advances in the mathematical theory of steady flow of viscoelastic fluids. J Nonnewton. Fluid Mech. 1988; 29: 11-24. DOI: 1016/0377-0257 (88) 85047-X
Renardy M. An alternative approach to inflow boundary conditions for Maxwell fluids in three space dimensions. J Nonnewton Fluid Mech. 1990; 36: 419-425. DOI: 10.1016/0377-0257(90)85022-Q
Fetecau C, Rauf A, Qureshi TM, Vieru D. Steady-state solutions for MHD motions of Burgers fluids through porous media with differential expressions of shear on boundary and Applications. Mathematics. 2022; 10(22): 4228. DOI: 10.3390/math 10224228
Tong D. Starting solutions for oscillating motions of a generalized Burgers’ fluid in cylindrical domains. Acta Mech. 2010; 214; 395-407. DOI: 10.1007/s00707-010-0288-7
Sultan Q, Nazar M, Imran M, Ali U. Flow of generalized Burgers fluid between parallel walls induced by rectified sine pulses stress. Bound Value Probl. 2014; 152. DOI: 1186/s13661-014-0152-0
Sultan Q, Nazar M. Flow of generalized Burgers’ fluid between side walls induced by sawtooth pulses stress. J Appl Fluid Mech. 2016; 9: 2195-2204. DOI: 10.18869/acadpub.jafm.68.236.24660
Abro KA, Hussain M, Baig MM. Analytical solution of magnetohydrodynamics generalized Burgers’ fluid embeded with porosity. Int J Advances Appl Sci. 2017; 4: 80-89. DOI: 10.21833/ijaas.2017.07.012
Alqahtani AM, Kha I. Time-dependent MHD flow of a non-Newtonian generalized Burgers’ fluid (GBF) over a suddenly moved plate with generalized Darcy’s law. Front Phys. 2019; id.214. DOI: 3389/fphy.2019.00214
Hussain M, Quayyum M, Sidra A. Modeling and analysis of MHD oscillatory flows of generalized Burgers’ fluid in a porous medium using Fourier transform. J Math. 2022; 2373084. DOI: 10.1155/2022/2373084
Fetecau C, Akhtar S, Morosanu C, Porous and magnetic effects on modified Stokes’ problems for generalized Burgers fluids. Dynamics. 2023; 3: 803-819. DOI: 10.3390/dynamics3040044
Hamza SEE. MHD flow of an Oldroyd-B fluid through porous medium in a circular channel under the effect of time-dependent gradient. Am J Fluid Dyn. 2017; 7: 1-11. DOI: 10.5923/j.ajfd.20170701.01
Bandelli R, Rajagopal KR. Start-up flows of second-grade fluids in domains with one finite dimension. Int J Non-Linear Mech. 1995; 30: 817-839. DOI: 10.1016/0020-7462(95)00035-6

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[1] Renardy M. Recent advances in the mathematical theory of steady flow of viscoelastic fluids. J Nonnewton. Fluid Mech. 1988; 29: 11-24. DOI: 1016/0377-0257 (88) 85047-X

[2] Renardy M. An alternative approach to inflow boundary conditions for Maxwell fluids in three space dimensions. J Nonnewton Fluid Mech. 1990; 36: 419-425. DOI: 10.1016/0377-0257(90)85022-Q

[3] Fetecau C, Rauf A, Qureshi TM, Vieru D. Steady-state solutions for MHD motions of Burgers fluids through porous media with differential expressions of shear on boundary and Applications. Mathematics. 2022; 10(22): 4228. DOI: 10.3390/math 10224228

[4] Tong D. Starting solutions for oscillating motions of a generalized Burgers’ fluid in cylindrical domains. Acta Mech. 2010; 214; 395-407. DOI: 10.1007/s00707-010-0288-7

[5] Sultan Q, Nazar M, Imran M, Ali U. Flow of generalized Burgers fluid between parallel walls induced by rectified sine pulses stress. Bound Value Probl. 2014; 152. DOI: 1186/s13661-014-0152-0

[6] Sultan Q, Nazar M. Flow of generalized Burgers’ fluid between side walls induced by sawtooth pulses stress. J Appl Fluid Mech. 2016; 9: 2195-2204. DOI: 10.18869/acadpub.jafm.68.236.24660

[7] Abro KA, Hussain M, Baig MM. Analytical solution of magnetohydrodynamics generalized Burgers’ fluid embeded with porosity. Int J Advances Appl Sci. 2017; 4: 80-89. DOI: 10.21833/ijaas.2017.07.012

[8] Alqahtani AM, Kha I. Time-dependent MHD flow of a non-Newtonian generalized Burgers’ fluid (GBF) over a suddenly moved plate with generalized Darcy’s law. Front Phys. 2019; id.214. DOI: 3389/fphy.2019.00214

[9] Hussain M, Quayyum M, Sidra A. Modeling and analysis of MHD oscillatory flows of generalized Burgers’ fluid in a porous medium using Fourier transform. J Math. 2022; 2373084. DOI: 10.1155/2022/2373084

[10] Fetecau C, Akhtar S, Morosanu C, Porous and magnetic effects on modified Stokes’ problems for generalized Burgers fluids. Dynamics. 2023; 3: 803-819. DOI: 10.3390/dynamics3040044

[11] Hamza SEE. MHD flow of an Oldroyd-B fluid through porous medium in a circular channel under the effect of time-dependent gradient. Am J Fluid Dyn. 2017; 7: 1-11. DOI: 10.5923/j.ajfd.20170701.01

[12] Bandelli R, Rajagopal KR. Start-up flows of second-grade fluids in domains with one finite dimension. Int J Non-Linear Mech. 1995; 30: 817-839. DOI: 10.1016/0020-7462(95)00035-6

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On the Governing Equations for Velocity and Shear Stress of some Magnetohydrodynamic Motions of Rate-type Fluids and their Applications

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