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DOI：http://dx.doi.org/10.26855/jamc.2021.09.009

# Analytical Solutions for a General Mixed Initial-Boundary Value Problem Corresponding to Hydromagnetic Flows of Second Grade Fluids through Porous Medium

Date: September 24,2021 |Hits: 4811 Download PDF How to cite this paper

Constantin Fetecau1,*, Dumitru Vieru2

1Section of Mathematics, Academy of Romanian Scientists, 050094 Bucharest, Romania.

2Department of Theoretical Mechanics, Technical University of Iasi, 700050 Iasi, Romania.

*Corresponding author: Constantin Fetecau

### Abstract

A general mixed initial-boundary value problem describing hydro magnetic flows of the incompressible second grade fluids (ISGF) between infinite horizontal parallel plates embedded in a porous medium is analytically studied.  The fluid motion is induced by the lower plate that applies an arbitrary time-dependent shear stress to the fluid.  Closed form expressions are established for the dimensionless velocity field and the volume flux per unit width of a plane normal to the flow direction.  They can generate exact solutions for any flow of this type of ISGF and the problem in discussion is completely solved.  For illustration, three motions with technical relevance are taken into consideration and the necessary time to touch the steady or permanent state for two motions which become steady in time is graphically determined.  In addition, it is proved that the solutions corresponding to motions induced by ramp-type shear stresses on the boundary can be easily determined if the similar solutions for the motion generated by a constant shear stress on the boundary are known.

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### How to cite this paper

Analytical Solutions for a General Mixed Initial-Boundary Value Problem Corresponding to Hydromagnetic Flows of Second Grade Fluids through Porous Medium

How to cite this paper: Constantin Fetecau, Dumitru Vieru. (2021) Analytical Solutions for a General Mixed Initial-Boundary Value Problem Corresponding to Hydromagnetic Flows of Second Grade Fluids through Porous Medium. Journal of Applied Mathematics and Computation5(3), 225-236.

DOI: http://dx.doi.org/10.26855/jamc.2021.09.009

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