Hydromagnetic effects on non-Newtonian Hiemenz flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Magnetic Field ◽  
Free Boundary ◽  
Existence And Uniqueness ◽  
Uniform Magnetic Field ◽  
Magnetic Parameter ◽  
Similarity Transformation ◽  
The Self ◽  
Free Boundary Value Problem ◽  
Uniqueness Of The Solution ◽  
Self Similar

Abstract The stagnation point flow of a non-Newtonian Reiner–Rivlin fluid has been studied in the presence of a uniform magnetic field. The technique of similarity transformation has been used to obtain the self-similar ordinary differential equations. In this paper, an attempt has been made to prove the existence and uniqueness of the solution of the resulting free boundary value problem. Monotonic behavior of the solution is discussed. The numerical results, shown through a table and graphs, elucidate that the flow is significantly affected by the non-Newtonian cross-viscous parameter L and the magnetic parameter M.

On a self-similar solution for the decay of turbulent bursts

1992 ◽  
Vol 3 (4) ◽  
pp. 319-341 ◽  
Author(s):  
S. P. Hastings ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behaviour ◽  
Physical Parameter ◽  
Dimensional Analysis ◽  
Existence And Uniqueness ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Eigenvalue Parameter ◽  
Self Similar ◽  
Similar Solutions

We discuss the self-similar solutions of the second kind associated with the propagation of turbulent bursts in a fluid at rest. Such solutions involve an eigenvalue parameter μ, which cannot be determined from dimensional analysis. Existence and uniqueness are established and the dependence of μ on a physical parameter λ in the problem is studied: estimates are obtained and the asymptotic behaviour as λ → ∞ is established.

A free surface problem arising in the drainage of a uniformly irrigated field: Existence and uniqueness results

1984 ◽  
Vol 36 (3) ◽  
pp. 389-403 ◽  
Author(s):  
John Van Der Hoek ◽  
C. J. Barnes ◽  
J. H. Knight
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Value Problem ◽  
Variational Inequalities ◽  
Existence And Uniqueness ◽  
Free Boundary Value Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Tile Drains ◽  
Porous Soil

AbstractA field comprising uniformly porous soil overlying an impervious subsoil is drained through equally spaced tile drains placed on the boundary between the two layers of soil. When this field is subject to uniform irrigation, a free boundary forms in the porous region above the zone of saturation. We study the free boundary value problem which thus arises using the theory of variational inequalities. Existence and uniqueness results are established.

A study for steady nanofluid flow between parallel plates

2017 ◽  
Vol 34 (8) ◽  
pp. 2514-2527 ◽  
Author(s):  
Syed Tauseef Mohyud-din ◽  
Muhammad Asad Iqbal ◽  
Muhammad Shakeel
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Uniform Magnetic Field ◽  
Design Methodology ◽  
Magnetic Parameter ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Content Type ◽  
Viscosity Parameter ◽  
Variation Of Parameters

Purpose In this paper, the authors study the behavior of heat and mass transfer between parallel plates of a steady nanofluid flow in the presence of a uniform magnetic field. In the model of nanofluids, the essential effect of thermophoresis and Brownian motion has been encompassed. Design/methodology/approach The variation of parameters method has been exploited to solve the differential equations of nanofluid model. The legitimacy of the variation of parameters method has been corroborated by a comparison of foregoing works by many authors on viscous fluid. Findings An analysis of the model is performed for different parameters, namely, viscosity parameter, Brownian parameter, thermophoretic parameter and magnetic parameter. Originality/value The variation of parameters method proves to be very effective in solving nonlinear system of ordinary differential equations which frequently arise in fluid mechanics.

scholarly journals ON THE SELF-SIMILAR HEAT BOUNDARY LAYER PROBLEMS IN MAGNETOHYDRODYNAMICS

2002 ◽  
Vol 7 (1) ◽  
pp. 93-102
Author(s):  
V. Kremenetsky
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Temperature Field ◽  
Joule Heat ◽  
The Self ◽  
Horizontal Flows ◽  
Self Similar Solution ◽  
Steady Magnetic Field ◽  
Self Similar ◽  
Boundary Layer Problems

Usually all self‐similar heat boundary layer problems in presence of magnetic field are solved neglecting the Joule heat, created by current, induced in fluid by interaction of velocity and magnetic field. But the analysis of this heat shows that its influence to the temperature field is very important. For vertical flows it is impossible to find self‐similar solution of boundary layer problems due to the Joule heat influence in temperature field. For horizontal flows only two self‐similar boundary layer problems can be formulated: flow near the critical point in magnetic field with the neutral point and in the transverse steady magnetic field.

Dynamical effects of the ambipolar diffusion in a protoplanetary disc

2020 ◽  
Vol 497 (2) ◽  
pp. 1634-1653 ◽  
Author(s):  
Mahmoud Gholipour
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Numerical Solutions ◽  
Turbulent Viscosity ◽  
Outer Region ◽  
Ambipolar Diffusion ◽  
The Self ◽  
Mhd Equations ◽  
Solution Technique ◽  
Self Similar

ABSTRACT Several recent simulation works in the non-ideal magnetohydrodynamic (MHD) formalism have shown the importance of ambipolar diffusion (AD) within the protoplanetary discs (PPDs) at large radii. In this study, we model the time evolution of a polytropic PPD in the presence of the AD. In this regard, the non-ideal MHD equations are investigated in the outer region of a PPD where the magnetic field evolution is dominated by the AD. The self-similar solution technique is used for a polytropic fluid including the self-gravity and viscosity. The ambipolar diffusivity and its derivative are crucial for the formulation of this study. Hence, this variable is scaled by an important factor, that is the Elsasser number. The self-similar equations are derived, and the semi-analytical and numerical solutions are presented for the isothermal and polytropic cases. The analytical approach enables us to know the asymptotic behaviour of the physical variables in a PPD, such as the angular momentum and magnetic field. Furthermore, the coupling/decoupling of magnetic field with the angular momentum was discussed analytically to find a corresponding model for the angular momentum loss at large radii of a PPD. Regarding this approach, we found that the magnetic braking induced by the AD at large radii has a high potential to loss the angular momentum even if the turbulent viscosity is not efficient. Also, the sign and values of vertical velocity strongly depends on the sign and values of radial field in the polytropic case.

VALUATION OF EUROPEAN INSTALLMENT PUT OPTION: VARIATIONAL INEQUALITY APPROACH

2009 ◽  
Vol 11 (02) ◽  
pp. 279-307 ◽  
Author(s):  
ZHOU YANG ◽  
FAHUAI YI
Keyword(s):  
Variational Inequality ◽  
Free Boundary ◽  
Existence And Uniqueness ◽  
Parabolic Variational Inequality ◽  
Numerical Result ◽  
Put Option ◽  
Uniqueness Of The Solution

In this paper, we consider a parabolic variational inequality arising from the valuation of European installment put option. We prove the existence and uniqueness of the solution to the problem. Moreover, we obtain C∞ regularity and the bounds of the free boundary. Eventually, we show its numerical result by the binomial method.

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