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A New Exact Solution for the Flow of a Fluid through Porous Media for a Variety of Boundary Conditions

1
Department of Mathematics, Davangere University, Shivagangothri, Davangere 577 007, India
2
Department of Mathematics, SHDD Government First Grade College, Paduvalahippe, Hassan 573 211, India
3
Department of Mathematics, Government Engineering College, Hassan 573 201, India
4
Faculty of Mechanical Engineering and Informatics, Institute of Machine and Product Design, University of Miskolc, 3515 Miskolc-Egyetemvaros, Hungary
5
Department of Mathematics, University BDT College of Engineering, Davangere 577 004, India
*
Author to whom correspondence should be addressed.
Fluids 2019, 4(3), 125; https://doi.org/10.3390/fluids4030125
Received: 23 May 2019 / Revised: 28 June 2019 / Accepted: 29 June 2019 / Published: 8 July 2019
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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Abstract

The viscous fluid flow past a semi-infinite porous solid, which is proportionally sheared at one boundary with the possibility of the fluid slipping according to Navier’s slip or second order slip, is considered here. Such an assumption takes into consideration several of the boundary conditions used in the literature, and is a generalization of them. Upon introducing a similarity transformation, the governing equations for the problem under consideration reduces to a system of nonlinear partial differential equations. Interestingly, we were able to obtain an exact analytical solution for the velocity, though the equation is nonlinear. The flow through the porous solid is assumed to obey the Brinkman equation, and is considered relevant to several applications. View Full-Text
Keywords: Brinkman equation; viscosity ratio; first- and second-order slip; similarity transformation; porous medium Brinkman equation; viscosity ratio; first- and second-order slip; similarity transformation; porous medium
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Mahabaleshwar, U.S.; Vinay Kumar, P.N.; Nagaraju, K.R.; Bognár, G.; Nayakar, S.N.R. A New Exact Solution for the Flow of a Fluid through Porous Media for a Variety of Boundary Conditions. Fluids 2019, 4, 125.

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