scholarly journals Effect of slip condition on viscoelastic mhd oscillatory forced convection flow in a vertical channel with heat radiation

2013 ◽  
Vol 18 (4) ◽  
pp. 1237-1248 ◽  
Author(s):  
K.D. Singh
Keyword(s):  
Magnetic Field ◽  
Oscillatory Flow ◽  
Slip Flow ◽  
Vertical Channel ◽  
Magnetic Reynolds Number ◽  
Slip Condition ◽  
Heat Radiation ◽  
Convection Flow ◽  
Parallel Plates ◽  
Electrically Conducting

Abstract In this paper an oscillatory flow of a viscoelastic, incompressible and electrically conducting fluid through a porous medium bounded by two infinite vertical parallel plates is discussed. One of these plates is subjected to a slip-flow condition and the other to a no-slip condition. The pressure gradient in the channel oscillates with time. A magnetic field of uniform strength is applied in the direction perpendicular to the plates. The induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The temperature difference of the two plates is also assumed high enough to induce heat transfer due to radiation. A closed form analytical solution to the problem is obtained. The analytical results are evaluated numerically and then presented graphically to discuss in detail the effects of different parameters entering into the problem. A number of particular cases have been shown by dotted curves in the figures. During the analysis it is found that the physical and the mathematical formulations of the problems by Makinde and Mhone (2005), Mehmood and Ali (2007), Kumar et al. (2010) and Choudhury and Das (2012) are not correct. The correct solutions to all these important oscillatory flow problems are deduced.

scholarly journals Span-Wise Fluctuating MHD Convective Flow of a Viscoelastic Fluid through a Porous Medium in a Hot Vertical Channel with Thermal Radiation

2016 ◽  
Vol 21 (3) ◽  
pp. 667-681 ◽  
Author(s):  
K.D. Singh
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Vertical Channel ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Temperature Fields ◽  
Convection Flow ◽  
Electrically Conducting ◽  
Unsteady Mixed Convection ◽  
Phase Angles

Abstract An unsteady mixed convection flow of a visco-elastic, incompressible and electrically conducting fluid in a hot vertical channel is analyzed. The vertical channel is filled with a porous medium. The temperature of one of the channel plates is considered to be fluctuating span-wise cosinusoidally, i.e., $T^* \left( {y^* ,z^* ,t^* } \right) = T_1 + \left( {T_2} - {T_ 1} \right)\cos \left( {{{\pi z^* } \over d} - \omega ^* t^* } \right)$ . A magnetic field of uniform strength is applied perpendicular to the planes of the plates. The magnetic Reynolds number is assumed very small so that the induced magnetic field is neglected. It is also assumed that the conducting fluid is gray, absorbing/emitting radiation and non-scattering. Governing equations are solved exactly for the velocity and the temperature fields. The effects of various flow parameters on the velocity, temperature and the skin friction and the Nusselt number in terms of their amplitudes and phase angles are discussed with the help of figures.

scholarly journals Skin-friction for unsteady free convection MHD flow between two heated vertical parallel plates

2006 ◽  
Vol 33 (4) ◽  
pp. 259-280 ◽  
Author(s):  
Gopal Singha ◽  
P.N. Deka
Keyword(s):  
Free Convection ◽  
Skin Friction ◽  
Mhd Flow ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Convection Flow ◽  
Fluid Temperature ◽  
Parallel Plates ◽  
Electrically Conducting ◽  
Induced Field

Unsteady viscous incompressible free convection flow of an electrically conducting fluid between two heated vertical parallel plates is considered in the presence of a uniform magnetic field applied transversely to the flow. The induce field along the lines of motion varies transversely to the flow and the fluid temperature changing with time. An analytical solution for velocity, induced field and the temperature distributions are obtained for small and large magnetic Reynolds numbers. The skin-friction at the two plates is obtained. Velocity distribution, induced field and skin-friction are plotted against the distance from the plates. It has been observed that with the increase in Rm, the magnetic Reynolds number, at constant M, the Hartmann number, leads to an increase in the skin-friction gradually. But with the increase in M, at constant Rm, the skin-friction decreases.

scholarly journals Separation of species of a binary fluid mixture confined in a channel in presence of a strong transverse magnetic field

2012 ◽  
Vol 66 (2) ◽  
pp. 171-180
Author(s):  
Bishwaram Sharma ◽  
Niroj Sing ◽  
Rupam Gogoi ◽  
Kabita Nath
Keyword(s):  
Magnetic Field ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic ◽  
Magnetic Reynolds Number ◽  
Parallel Plates ◽  
Separation Processes ◽  
Fluid Mixture ◽  
Electrically Conducting ◽  
Basic Fluid ◽  
Cartesian Coordinate

Effects of a transverse magnetic field on separation of a binary mixture of incompressible viscous thermally and electrically conducting fluids confined between two stationary parallel plates are examined. Both the plates are maintained at constant temperatures. It is assumed that one of the components, which is rarer and lighter, is present in the mixture in a very small quantity. The equations governing the motion, temperature and concentration in Cartesian coordinate are solved analytically. The solution obtained for concentration distribution is plotted against the width of the channel for various values of non-dimensional parameters. It is found that the effect of transverse magnetic field is to separate the species of rarer and lighter component by contributing its effect directly to the temperature gradient and the pressure gradient. The effects of increase in the values of Hartmann number, magnetic Reynolds number, barodiffusion number, thermal diffusion number, electric field parameter and the product of Prandtl number and Eckert number are to collect the rarer and lighter component near the upper plate and throw away the heavier component towards the lower plate. The problem discussed here derives its application in the basic fluid dynamics separation processes to separate the rare component of the different isotopes of heavier molecules where electromagnetic method of separation does not work.

scholarly journals Exact Solution Of MHD Mixed Convection Periodic Flow In A Rotating Vertical Channel With Heat Radiation

2013 ◽  
Vol 18 (3) ◽  
pp. 853-869 ◽  
Author(s):  
K.D. Singh
Keyword(s):  
Mixed Convection ◽  
Flow Problem ◽  
Exact Analytical Solution ◽  
Vertical Channel ◽  
Periodic Variation ◽  
Heat Radiation ◽  
Convection Flow ◽  
Large Rotation ◽  
Electrically Conducting ◽  
Upward Direction

Abstract Magnetohydrodynamic (MHD) mixed convection flow of a viscous, incompressible and electrically conducting fluid in a vertical channel is analyzed analytically. A magnetic field of uniform strength is applied perpendicular to the planes of the channel walls. The fluid is acted upon by a periodic variation of the pressure gradient in the vertically upward direction. The temperature of one of the plates is non-uniform and the temperature difference of the walls of the channel is high enough to induce heat transfer due to radiation. The fluid and the channel rotate in unison with an angular velocity about the axis normal to the plates of the channel. An exact analytical solution of the problem is obtained. Two cases of small and large rotation have been considered to assess the effects of different parameters involved in the flow problem. The velocity field, the amplitude and the phase angle of the shear stress are shown graphically and discussed in detail. During analysis it is found that the flow problem studied by Makinde and Mhone (2005) is incorrect physically and mathematically

scholarly journals Oscillatory MHD Convective Flow of Second Order Fluid Through Porous Medium in a Vertical Rotating Channel in Slip-Flow Regime with Heat Radiation

2015 ◽  
Vol 20 (1) ◽  
pp. 33-52 ◽  
Author(s):  
B.P. Garg ◽  
K.D. Singh ◽  
A.K. Bansal
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Convective Flow ◽  
Slip Flow ◽  
Closed Form Solution ◽  
Second Order ◽  
Slip Condition ◽  
Heat Radiation ◽  
Viscoelastic Parameter ◽  
Suction Parameter

Abstract An analysis of an oscillatory magnetohydrodynamic (MHD) convective flow of a second order (viscoelastic), incompressible, and electrically conducting fluid through a porous medium bounded by two infinite vertical parallel porous plates is presented. The two porous plates with slip-flow condition and the no-slip condition are subjected respectively to a constant injection and suction velocity. The pressure gradient in the channel varies periodically with time. A magnetic field of uniform strength is applied in the direction perpendicular to the planes of the plates. The induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The temperature of the plate with no-slip condition is non-uniform and oscillates periodically with time and the temperature difference of the two plates is assumed high enough to induce heat radiation. The entire system rotates in unison about the axis perpendicular to the planes of the plates. Adopting complex variable notations, a closed form solution of the problem is obtained. The analytical results are evaluated numerically and then presented graphically to discuss in detail the effects of different parameters of the problem. The velocity, temperature and the skin-friction in terms of its amplitude and phase angle have been shown graphically to observe the effects of the viscoelastic parameter γ, rotation parameter Ω, suction parameter λ , Grashof number Gr, Hartmann number M, the pressure A, Prandtl number Pr, radiation parameter N and the frequency of oscillation ω .

scholarly journals Transient Free Convective Radiative Flow Between Vertical Parallel Plates Heated/Cooled Asymmetrically with Heat Generation and Slip Condition

2018 ◽  
Vol 23 (2) ◽  
pp. 365-384 ◽  
Author(s):  
P.K. Gaur ◽  
R.P. Sharma ◽  
A.K. Jha
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Momentum Transfer ◽  
Heat Generation ◽  
Convective Flow ◽  
Conducting Fluid ◽  
Slip Condition ◽  
Parallel Plates ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

Abstract Investigation of an MHD convective flow of viscous, incompressible and electrically conducting fluid through a porous medium bounded by two infinite vertical parallel porous plates is carried out. Forchheimer-Brinkman extended Darcy model is assumed to simulate momentum transfer within the porous medium. A magnetic field of uniform strength is applied normal to the plates. The analytical results are evaluated numerically and the presented graphically to discuss in detail the effects of different parameter entering into the problem.

scholarly journals Homotopy Analysis Solution of Hydromagnetic Mixed Convection Flow Past an Exponentially Stretching Sheet with Hall Current

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Mohamed Abd El-Aziz ◽  
Tamer Nabil
Keyword(s):  
Magnetic Field ◽  
Mixed Convection ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Electrically Conducting ◽  
Hall Parameter ◽  
Homotopy Analysis ◽  
Continuous Sheet ◽  
Exponentially Stretching ◽  
The Magnetic Field

The effect of thermal radiation on steady hydromagnetic heat transfer by mixed convection flow of a viscous incompressible and electrically conducting fluid past an exponentially stretching continuous sheet is examined. Wall temperature and stretching velocity are assumed to vary according to specific exponential forms. An external strong uniform magnetic field is applied perpendicular to the sheet and the Hall effect is taken into consideration. The resulting governing equations are transformed into a system of nonlinear ordinary differential equations using appropriate transformations and then solved analytically by the homotopy analysis method (HAM). The solution is found to be dependent on six governing parameters including the magnetic field parameterM, Hall parameterm, the buoyancy parameterξ, the radiation parameterR, the parameter of temperature distributiona, and Prandtl number Pr. A systematic study is carried out to illustrate the effects of these major parameters on the velocity and temperature distributions in the boundary layer, the skin-friction coefficients, and the local Nusselt number.

A moving fluid interface. Part 2. The removal of the force singularity by a slip flow

1977 ◽  
Vol 79 (2) ◽  
pp. 209-229 ◽  
Author(s):  
L. M. Hocking
Keyword(s):  
Contact Line ◽  
Slip Flow ◽  
Slip Condition ◽  
Solid Boundary ◽  
Parallel Plates ◽  
Fluid Interface ◽  
Slip Coefficient ◽  
Outer Flow ◽  
Normal Contact ◽  
Two Fluids

If the no-slip condition is used to determine the flow produced when a fluid interface moves along a solid boundary, a non-integrable stress is obtained. In part 1 of this study (Hocking 1976), it was argued that, when allowance was made for the presence of irregularities on the solid boundary, an effective slip coefficient could be found, which might remove the difficulty.This paper examines the effect of a slip coefficient on the flow in the neighbourhood of the contact line. Particular cases which are solved in detail are liquid–gas interfaces at an arbitrary angle, and normal contact of fluids of arbitrary viscosity. The contribution of the vicinity of the contact line to the force on the boundary is obtained.The inner region, near the contact line, must be matched with an outer flow, in which the no-slip condition can be applied, in order to obtain the total value of the force on the boundary. This force is determined for the flow of two fluids between parallel plates and in a pipe, with a plane interface. The enhanced resistance produced by the presence of the interface is calculated, and it is shown to be equivalent to an increase in the length of the column of fluid by a small multiple of the pipe radius.

Double Diffusive Marangoni Convection Flow of Electrically Conducting Fluid in a Square Cavity With Chemical Reaction

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
M. Saleem ◽  
M. A. Hossain ◽  
Suvash C. Saha
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Sherwood Number ◽  
Average Nusselt Number ◽  
Marangoni Convection ◽  
Convection Flow ◽  
Square Cavity ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Double Diffusive

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w causes the average Nusselt number to decrease, and average Sherwood number to increase.

Reversed Flow Structure and Heat Transfer Measurements for Buoyancy-Assisted Convection in a Heated Vertical Duct

1992 ◽  
Vol 114 (4) ◽  
pp. 928-935 ◽  
Author(s):  
C. Gau ◽  
K. A. Yih ◽  
W. Aung
Keyword(s):  
Heat Transfer ◽  
Vertical Channel ◽  
Flow Region ◽  
Threshold Value ◽  
Convection Flow ◽  
Parallel Plates ◽  
Reversed Flow ◽  
Recirculating Flow ◽  
Buoyancy Parameter ◽  
Complex Phenomena

Buoyancy-assisted convection flow and heat transfer processes in a heated vertical channel are studied experimentally for situations where the buoyancy parameter Gr/Re2 is relatively large. The channel wall is made of two parallel plates, with one wall heated uniformly and the opposite wall insulated. A uniform air flow is made to enter the channel from the bottom. The reversed flow is visualized, which occurs initially near the channel exit for the case when Gr/Re2 is greater than a threshold value. The cold reversed flow enters the channel from the outside and forms a V-shaped recirculating flow region in the downstream part of the duct. This region gradually propagates upstream as the buoyancy parameter Gr/Re2 increases. The counterflow motion, leading to mixing between the heated buoyant fluid and the V-shaped recirculation, is shown to be highly unstable and characterized by generation of eddies and vortices when the value of Gr/Re2 is large. An increase in Re has the effect of pushing the reversed flow downstream and making the recirculating region wider. Temperature fluctuations are measured to provide insight into the complex phenomena being studied. The penetration depth of the reversed flow is measured and compared with prediction based on a simple model. Local and average Nusselt numbers are also measured and presented.

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