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Symmetric and Non-Symmetric Flows of Burgers’ Fluids through Porous Media between Parallel Plates. Symmetry (Basel) 2021. [DOI: 10.3390/sym13071109] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Unidirectional unsteady flows of the incompressible Burgers’ fluids between two infinite horizontal parallel plates are analytically studied when the magnetic and porous effects are taken into consideration. The fluid motion is induced by the two plates, which move in their planes with time-dependent velocities. Exact general expressions are established both for the dimensionless velocity and shear stress fields as well as the corresponding Darcy’s resistance in the channel using the Laplace transform. If both plates move with equal velocities in the same direction, the fluid motion becomes symmetric with respect to the mid-plane between them. Otherwise, its motion is non-symmetric. To bring to light the behavior of the fluid, the dimensionless velocity profiles versus the spatial variable as well as its time evolution are presented both for the symmetric and asymmetric case. Finally, for comparison, similar graphical representations are presented together for the velocities of the incompressible Oldroyd-B and Burgers’ fluids. For large values of the time t, as expected, the behavior of the two different fluids is almost identical. The Darcy’s resistance against y is also graphically represented for the symmetric flow at different values of the time t. The influence of the magnetic field on the fluid motion is graphically revealed and discussed.
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A Comprehensive Review on Theoretical Aspects of Nanofluids: Exact Solutions and Analysis. Symmetry (Basel) 2020. [DOI: 10.3390/sym12050725] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In the present era, nanofluids are one of the most important and hot issue for scientists, physicists, and mathematicians. Nanofluids have many important and updated characteristics compared to conventional fluids. The thermal conductivity, thermal expansion, and the heat transfer rate of conventional fluids are not up to the mark for industrial and experimental uses. To overcome these deficiencies, nanoparticles have been dispersed into base fluids to make them more efficient. The heat transfer characteristics through symmetry trapezoidal-corrugated channels can be enhanced using nanofluids. In the present article, a literature survey has been presented for different models of nanofluids and their solutions—particularly, exact solutions. The models for hybrid nanofluids were also mentioned in the present study. Furthermore, some important and most used models for the viscosity, density, coefficient of thermal expansion, coefficient of mass expansion, heat capacitance, electrical conductivity, and thermal conductivity are also presented in tabular form. Moreover, some future suggestions are also provided in this article.
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Khan M, Khan WA. Three-dimensional flow and heat transfer to burgers fluid using Cattaneo-Christov heat flux model. J Mol Liq 2016. [DOI: 10.1016/j.molliq.2016.06.041] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Polyanin AD, Vyazmin AV. Decomposition of three-dimensional linearized equations for Maxwell and Oldroyd viscoelastic fluids and their generalizations. THEORETICAL FOUNDATIONS OF CHEMICAL ENGINEERING 2013. [DOI: 10.1134/s004057951304026x] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Jamil M, Zafar AA, Fetecau C, Khan NA. EXACT ANALYTIC SOLUTIONS FOR THE FLOW OF A GENERALIZED BURGERS FLUID INDUCED BY AN ACCELERATED SHEAR STRESS. CHEM ENG COMMUN 2011. [DOI: 10.1080/00986445.2011.570389] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- M. Jamil
- Abdus Salam School of Mathematical Sciences, GC University , Lahore, Pakistan
| | - A. A. Zafar
- Abdus Salam School of Mathematical Sciences, GC University , Lahore, Pakistan
| | - C. Fetecau
- Abdus Salam School of Mathematical Sciences, GC University , Lahore, Pakistan
| | - N. A. Khan
- Department of Mathematics, University of Karachi , Karachi, Pakistan
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