Unsteady hydromagnetic laminar flow of a conducting dusty fluid between two parallel plates started impulsively from rest
TL;DR: In this article, the Hartmann number has been used to measure the acceleration of the particles in the laminar motion of an electrically conducting, viscous and incompressible dusty fluid between two infinitely extended nonconducting parallel plates.
Abstract: The unsteady laminar motion of an electrically conducting, viscous and incompressible dusty fluid between two infinitely extended non-conducting parallel plates under a uniform transverse magnetic field, fixed relative to the fluid has been considered. The lower and the upper plate are started impulsively from rest and thereafter move with different but uniform velocities. The velocity fields for the conducting dusty fluid and non-conducting dust particle have been obtained in terms of three non-dimensional parametersl (concentration), σ (relaxation time parameter) andM (Hartmann number). The expressions for the discharge per unit breadth of the plate and the skin-friction at the lower plate are calculated. It is observed, from numerical calculations, that as the Hartmann number increases velocities of the dusty gas and dust particle increase when both the plates are in motion (velocity of the upper plate being equal to, greater than and less than that of the lower plate in the same direction) and decrease in case of Couette motion.
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TL;DR: In this paper, the effects of both magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel are studied analytically and numerically.
155 citations
TL;DR: The effect of the wall slip parameter, viscosity and electric conductivity variation and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed.
Abstract: In this paper, we study the unsteady flow and heat transfer of a dusty fluid between two parallel plates with variable viscosity and electric conductivity. The fluid is driven by a constant pressure gradient and an external uniform magnetic field is applied perpendicular to the plates with a Navier slip boundary condition. The governing non-linear partial differential equations are solved numerically using a semi-implicit finite difference scheme. The effect of the wall slip parameter, viscosity and electric conductivity variation and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed.
89 citations
TL;DR: In this paper, the influence of elasticity of flexible walls on peristaltic transport of a dusty fluid with heat and mass transfer in a horizontal channel in the presence of chemical reaction has been investigated under long wavelength approximation.
Abstract: The influence of elasticity of flexible walls on peristaltic transport of a dusty fluid with heat and mass transfer in a horizontal channel in the presence of chemical reaction has been investigated under long wavelength approximation. Expressions have been constructed for stream function, temperature and concentration by using perturbation technique. The effects of various parameters on heat and mass transfer characteristics of the flow are discussed through graphs.
50 citations
TL;DR: This paper studies the unsteady Couette flow and heat transfer of a dusty conducting fluid between two parallel plates with variable viscosity and electric conductivity with governing non-linear partial differential equations.
47 citations
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...the coefficient viscosity increases with temperature [7,15,17]....
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TL;DR: In this paper, an initial value investigation is made on the motion of an incompressible visco-elastic (Rivlin-Ericksen) fluid with small particles between two infinite moving parallel plates in the presence of a transverse magnetic field.
Abstract: An initial value investigation is made on the motion of an incompressible visco-elastic (Rivlin-Ericksen) fluid with small particles between two infinite moving parallel plates in the presence of a transverse magnetic field. The flow is generated in the fluid particle system due to time dependent pressure gradient and also the motion of the plates in the presence of an external imposed transverse magnetic field. By Laplace transform technique, the velocity distribution and wall shear stress have been obtained for four different cases, when the pressure gradient and both the plate velocities are 1. (i) decreasing exponentially with time, 2. (ii) varying periodically with time, 3. (iii) impulsive type, and 4. (iv) acting for a finite time. In each case, shear stresses at the boundary plates are also calculated.
29 citations
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TL;DR: In this paper, the effect of dust on the stability of a gas is described by two parameters; the concentration of dust and a relaxation time τ which measures the rate at which the velocity of a dust particle adjusts to changes in the gas velocity and depends upon the size of the individual particles.
Abstract: The equations describing the motion of a gas carrying small dust particles are given and the equations satisfied by small disturbances of a steady laminar flow are derived. The effect of the dust is described by two parameters; the concentration of dust and a relaxation time τ which measures the rate at which the velocity of a dust particle adjusts to changes in the gas velocity and depends upon the size of the individual particles. It is shown that if the dust is fine enough for τ to be small compared with a characteristic time scale associated with the flow, then the addition of dust destabilizes a gas flow; whereas if the dust is coarse so that τ is relatively large, then the dust has a stabilizing action.For plane parallel flow, it is shown that the stability characteristics for a dusty gas are still determined by solutions of the Orr-Sommerfeld equation, but with the basic velocity profile replaced by a modified profile which is in general complex. A simple, although unrealistic, example is used to illustrate some features of the action of dust. It is intended to describe the solution of the modified Orr-Sommerfeld equation for plane Poiseuille flow in a later paper.
721 citations
TL;DR: In this paper, the flow formation in Couette motion of an electrically conducting, viscous and incompressible fluid in a transverse magnetic field is studied. But the analysis is limited to the case of small magnetic Reynolds number.
Abstract: Flow formation in Couette motion of an electrically conducting, viscous and incompressible fluid in a transverse magnetic field is studied. The analysis is limited to the case of small magnetic Reynolds number. By the method of Laplace transform the expressions for the velocity distribution and skin friction are obtained. Numerical results show that the flow is retarded and, there fore, the skin friction increases by the effect of the magnetic field. However, at the commencement of motion the manner of flow formation is hardly affected by the magnetic field.
66 citations
"Unsteady hydromagnetic laminar flow..." refers background in this paper
...Katagiri [ 3 ] has investigated the formation of Couette flow of a viscous, incompressible and electrically conducting fluid between two infinite parallel plane walls in presence of a transverse magnetic field....
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51 citations
"Unsteady hydromagnetic laminar flow..." refers background in this paper
...In all the problems [1]-[ 4 ], however, the induced magnetic field produced by the current has been neglected....
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...Gupta [ 4 ] considered the flow of an electrieMly conducting fluid near an accelerated plate in presence of a magnetic field....
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TL;DR: In this paper, the authors define a set of p/p/pt = (r/i7oo) x i7oo/r, (5.1258 X io-87y) (o.224 X 10~)r 0.23igr + 0.4087]
Abstract: (2) T = cp/[cp (R/J)} (3) M = (27) [(0.22147^ + 0.1760 X lO~*Tt 2 0.1258 X io-87y) (o.23igr + 0.0520 x io4 r 2 + 0.2388 X 10-T*)]/7RT (4) p/pt = (r/i7oo) x (i7oo/r,)x exp[(2.753 X 10-)7V (5.134 X 10-*)Tt + 0.7932] X exp[(1.516 X 10")r + (5.224 X 10~)T 0.4087] (5) p/pt = (r/i700) x (1700/r,)x exp[(2.753 X 10-)r, (5.134 X lO" 4 )^ + 0.7932] X exp[(1.516 X 1 0 " 4 ) r + (5.224 X 10~)r 0.4087]
37 citations
16 citations
"Unsteady hydromagnetic laminar flow..." refers background in this paper
...This assumption is considered to be valid for the ease of small magnetic Reynolds number, as done in previous works [1]--[ 5 ]....
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...Baral [ 5 ] solved the problem of the flow of a conducting dusty fluid occupying a semi-infinite space in presence of a transverse magnetic field....
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