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Multicenter Molecular Integrals over Dirac Wave Functions for Several Fundamental Properties
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General-science Group Review Article Article ID: igmin289

General Solutions for MHD Motions of Viscous Fluids with Viscosity Linearly Dependent on Pressure in a Planar Channel

Physics DOI10.61927/igmin289
Constantin Fetecau * 1 and
Costică Moroşanu 2
Affiliation

Affiliation

    1Academy of Romanian Scientists, 3 Ilfov, Bucharest 050044, Romania

    2Department of Mathematics, “Alexandru Ioan Cuza” University, Iasi 700506, Romania

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Abstract

The analytical study examines the isothermal, unsteady flows of viscous incompressible fluids in a planar channel, when viscosity depends linearly on pressure, and a constant magnetic field is present. Exact expressions are derived for the dimensionless initial velocity field, the corresponding non-zero shear stress, and the problem is fully solved. To illustrate and highlight certain fluid behavior characteristics, modified Stokes’ problems are analyzed, and analytical expressions for the corresponding initial velocities are provided. For validation, the steady components are presented in two distinct forms, with their equivalence confirmed through graphical comparison. The effect of the magnetic field on the fluid behavior is explored and discussed visually. The results show that the fluid flows more slowly, and the steady-state is reached sooner when a magnetic field is applied.
2010 Mathematics Subject Classification: 76A05.

Figures

Flow geometry. Figure 1: Flow geometry....
Equivalence of the expressions of ucp(y,t) and usp(y,t) given by relations (28), (36) and (30), (37) for β = 0.5, M = 0.7, ω = Π/3 and three values of the time t. Figure 2: Equivalence of the expressions of ucp(y,t) and usp...
Convergence of starting velocity uc(y,t) from Eq. (27)1 to its steady state component ucp(y,t) for β = 0.2, ω = Π/3, two values of M and increasing values of time t. Figure 3: Convergence of starting velocity uc(y,t) from Eq. ...
Convergence of starting velocity us(y,t) from Eq. (27)2 to its steady state component usp(y,t) for β = 0.2, ω = Π/3, two values of M and increasing values of time t. Figure 4: Convergence of starting velocity us(y,t) from Eq. ...
Convergence of starting velocity uC(y,t) from Eq. (38)1 to its steady component uCp(y) for β = 0.2, ω = Π/3, two values of M and increasing values of time t. Figure 5: Convergence of starting velocity uC(y,t) from Eq. ...

References

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