Analytical Model of a Side-Heated Free Convection Loop Placed in a Transverse Magnetic Field

1998 ◽  
Vol 120 (1) ◽  
pp. 62-69 ◽  
Author(s):  
Nesreen Ghaddar
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Transverse Magnetic Field ◽  
Hartmann Number ◽  
Transverse Magnetic ◽  
Hydrodynamic Characteristics ◽  
Loop Model ◽  
Grashof Number ◽  
Prandtl Numbers ◽  
Buoyancy Driven Convection

The hydrodynamic characteristics of a buoyancy-driven convection loop containing an electrically-conducting fluid in a transverse magnetic field are investigated analytically using a one-dimensional model. One side of the loop is isothermally heated and the other side isothermally cooled, and the upper and lower sections are insulated. The model which is based on the use of the Hartmann Plane-Poiseuille flow solution for estimating loop shear stress, predicts the flow velocity and the induced current of the magnetohydrodynamic generator in terms of the flow and geometric parameters. The study covers ranges of Grashof number, Gr, from 102 to 106, the Hartmann number, Ha, from 0 to 20, the Prandtl number, Pr, from .003 to 7, and loop height to thickness ratio, L/d, from 10 to 50. It is shown that at low Prandtl numbers, Pr ≪ 1, there exists an optimal Hartmann number, Haopt, that maximizes the induced electric current. This Haopt depends weakly on the Grashof number. The side-heated loop performance is also compared with the bottom heated loop model of Ghaddar, (1997a). It is found that at a low Prandtl number, side heated loop induces the higher velocity whereas at high Prandtl numbers the bottom heated loop induces higher velocity.

Heat Transfer in Magnetohydrodynamic Flow in an Entrance Section

1965 ◽  
Vol 87 (2) ◽  
pp. 231-236 ◽  
Author(s):  
A. M. Dhanak
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Prandtl Number ◽  
Flat Plate ◽  
Hartmann Number ◽  
Transverse Magnetic ◽  
Entrance Section ◽  
Pressure Distributions ◽  
Prandtl Numbers ◽  
Iterative Procedures

Based on the Ka´rma´n-Pohlhausen method and the associated iterative procedures developed herein the analysis shows that the presence of a transverse magnetic field in the entrance section of a channel has significant effects on the velocity and pressure distributions, and on the displacement and momentum thicknesses. The calculations further reveal that the heat transfer from the channel, in contrast with the flat plate case, increases with the Hartmann number. This increase is, however, significant only at high Prandtl numbers. The influence of Joulean dissipation appears to be negligible for a Joulean parameter up to 1.0 and at a Prandtl number of unity.

Natural Convection Heat Transfer in a Rectangular Enclosure With a Transverse Magnetic Field

1995 ◽  
Vol 117 (3) ◽  
pp. 668-673 ◽  
Author(s):  
S. Alchaar ◽  
P. Vasseur ◽  
E. Bilgen
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Transverse Magnetic Field ◽  
Hartmann Number ◽  
Convection Heat Transfer ◽  
Transverse Magnetic ◽  
Temperature Profiles ◽  
Flow Approximation ◽  
Buoyancy Driven Convection ◽  
The Magnetic Field

In this paper the effect of a transverse magnetic field on buoyancy-driven convection in a shallow rectangular cavity is numerically investigated (horizontal Bridgman configuration). The enclosure is insulated on the top and bottom walls while it is heated from one side and cooled from the other. Both cases of a cavity with all rigid boundaries and a cavity with a free upper surface are considered. The study covers the range of the Rayleigh number, Ra, from 102 to 105, the Hartmann number, Ha, from 0 to 102, the Prandtl number, Pr, from 0.005 to 1 and aspect ratio of the cavity, A, from 1 to 6. Comparison is made with an existing analytical solution (Garandet et al., 1992), based on a parallel flow approximation, and its range of validity is delineated. Results are presented for the velocity and temperature profiles and heat transfer in terms of Ha number. At high Hartmann numbers, both analytical and numerical analyses reveal that the velocity gradient in the core is constant outside the two Hartmann layers at the vicinity of the walls normal to the magnetic field.

scholarly journals Influence of Magnetic Field on the Peristaltic Flow of a Viscous Fluid through a Finite-Length Cylindrical Tube

2010 ◽  
Vol 7 (3) ◽  
pp. 169-176 ◽  
Author(s):  
S. K. Pandey ◽  
Dharmendra Tripathi
Keyword(s):  
Magnetic Field ◽  
Viscous Fluid ◽  
Transverse Magnetic Field ◽  
Finite Length ◽  
Flow Rate ◽  
Hartmann Number ◽  
Volume Flow Rate ◽  
Critical Value ◽  
Transverse Magnetic ◽  
Volume Flow

The paper presents an analytical investigation of the peristaltic transport of a viscous fluid under the influence of a magnetic field through a tube of finite length in a dimensionless form. The expressions of pressure gradient, volume flow rate, average volume flow rate and local wall shear stress have been obtained. The effects of the transverse magnetic field and electrical conductivity (i.e. the Hartmann number) on the mechanical efficiency of a peristaltic pump have also been studied. The reflux phenomenon is also investigated. It is concluded, on the basis of the pressure distribution along the tubular length and pumping efficiency, that if the transverse magnetic field and the electric conductivity increase, the pumping machinery exerts more pressure for pushing the fluid forward. There is a linear relation between the averaged flow rate and the pressure applied across one wavelength that can restrain the flow due to peristalsis. It is found that there is a particular value of the averaged flow rate corresponding to a particular pressure that does not depend on the Hartmann number. Naming these values ‘critical values’, it is concluded that the pressure required for checking the flow increases with the Hartmann number above the critical value and decreases with it below the critical value. It is also inferred that magneto-hydrodynamic parameters make the fluid more prone to flow reversal. The conclusion applied to oesophageal swallowing reveals that normal water is easier to swallow than saline water. The latter is more prone to flow reversal. A significant difference between the propagation of the integral and non-integral number of waves along the tube is that pressure peaks are identical in the former and different in the latter cases.

scholarly journals Study of hydrodynamic characteristics of particles in liquid–solid fluidized bed with uniform transverse magnetic field

2013 ◽  
Vol 245 ◽  
pp. 314-323 ◽  
Author(s):  
Shuyan Wang ◽  
Yanli Shen ◽  
Yimei Ma ◽  
Jinsen Gao ◽  
Xingying Lan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Fluidized Bed ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic ◽  
Hydrodynamic Characteristics

scholarly journals Free convective flow of a couple stress fluid through a vertical porous channel in the presence of a transverse magnetic field

2018 ◽  
Vol 12 (1) ◽  
pp. 49-62
Author(s):  
M. Prasad Siddalinga ◽  
B. S. Shashikala
Keyword(s):  
Magnetic Field ◽  
Transverse Magnetic Field ◽  
Couple Stress ◽  
Hartmann Number ◽  
Transverse Magnetic ◽  
Porous Channel ◽  
Couple Stress Fluid ◽  
Physical Parameters ◽  
Stress Parameter ◽  
Buoyancy Parameter

Nonlinear oberbeck convection of a couple stress fluid in a vertical porous channel in the presence of transverse magnetic field is investigated in this paper. Analytical solution is obtained using the perturbation technique for vanishing values of the buoyancy parameter. Numerical solution of the nonlinear governing equations is obtained using the finite difference technique to validate the results obtained from the analytical solutions. The influence of the physical parameters on the flow, such as couple stress parameter, Hartmann number, temperature parameter, porous parameter and buoyancy parameter are evaluated and presented graphically. A new approach is used to analyse the flow for strong, weak and comparable porosity cases. It is found that increase in porous parameter, couple stress parameter, Hartmann number and temperature parameters decrease the velocity considerably.Kathmandu University Journal of Science, Engineering and Technology Vol. 12, No. I, June, 2016, Page: 49-62

scholarly journals Study of Blood Flow with Effects of Slip in Arterial Stenosis Due to Presence of Transverse Magnetic Field

2013 ◽  
Vol 4 (2) ◽  
pp. 215-226
Author(s):  
Sarfraz Ahmed
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Blood Flow ◽  
Transverse Magnetic Field ◽  
Hartmann Number ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Circulatory System ◽  
Transverse Magnetic ◽  
Arterial Stenosis

The flow of blood in human circulatory system can be controlled by applying appropriate magnetic field. It is also well known that non-Newtonian nature of blood significantly influences the flows, particularly in the cases where blood vessels are curved, branching or narrow etc. Stenosis refers to localized narrowing of an artery and is a frequent result of arterial disease and is caused mainly due to intravascular atherosclerotic plaque which develops at the arterial wall and protrudes into the lumen of the vessel. Such constrictions disturb normal blood flow through the artery. Here study is made on the flow of blood through a stenosed artery with the effect of slip at the boundary in presence of transverse magnetic field considering blood as Casson fluid (non- Newtonian fluid). The equations of motion has have been solved numerically. The effect of various parameters on the flow characteristics like Hartmann number, Reynolds number has been discussed. Numerical results were obtained for different values of the Hartmann number M and Reynolds number Re. It is observed that the fluid velocity decreases as the Hartmann number increases.

Hydrothermal wave instability of thermocapillary-driven convection in a transverse magnetic field

2000 ◽  
Vol 404 ◽  
pp. 211-250 ◽  
Author(s):  
JĀNIS PRIEDE ◽  
GUNTER GERBETH
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Field Strength ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic ◽  
Base Flow ◽  
Critical Parameters ◽  
Instability Modes ◽  
Small Parameters ◽  
Prandtl Numbers

We study the linear stability of thermocapillary-driven convection in a planar unbounded layer of an electrically conducting low-Prandtl-number liquid heated from the side and subjected to a transverse magnetic field. The thresholds of convective instability for both longitudinal and oblique disturbances are calculated numerically and also asymptotically by considering the Hartmann and Prandtl numbers as large and small parameters, respectively. The magnetic field has a stabilizing effect on the flow with the critical temperature gradient for the transition from steady to oscillatory convection increasing as square of the field strength, as also does the critical frequency, while the critical wavelength reduces inversely with field strength. These asymptotics develop in a strong enough magnetic field when the instability is entirely due to the jet of the base flow confined in the Hartmann layer at the free surface. In contrast to the base flow, the critical disturbances, having a long wavelength at small Prandtl numbers, extend from the free surface into the bulk of the liquid layer over a distance exceeding the thickness of the Hartmann layer by a factor O(Pr−1/2). For Ha [lsim ] Pr−1/2 the instability is influenced by the actual depth of the layer. For such moderate magnetic fields the instability threshold is sensitive to the thermal properties of the bottom of the layer and the dependences of the critical parameters on the field strength are more complicated. In the latter case, various instability modes are possible depending on the thermal boundary conditions and the relative magnitudes of Prandtl and Hartmann numbers.

Natural Convection in an Inclined Fluid Layer With a Transverse Magnetic Field: Analogy With a Porous Medium

1995 ◽  
Vol 117 (1) ◽  
pp. 121-129 ◽  
Author(s):  
P. Vasseur ◽  
M. Hasnaoui ◽  
E. Bilgen ◽  
L. Robillard
Keyword(s):  
Magnetic Field ◽  
Transverse Magnetic Field ◽  
Hartmann Number ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Integral Form ◽  
Transverse Magnetic ◽  
Horizontal Layer ◽  
Governing Equations ◽  
Onset Of Convection

In this paper the effect of a transverse magnetic field on buoyancy-driven convection in an inclined two-dimensional cavity is studied analytically and numerically. A constant heat flux is applied for heating and cooling the two opposing walls while the other two walls are insulated. The governing equations are solved analytically, in the limit of a thin layer, using a parallel flow approximation and an integral form of the energy equation. Solutions for the flow fields, temperature distributions, and Nusselt numbers are obtained explicitly in terms of the Rayleigh and Hartmann numbers and the angle of inclination of the cavity. In the high Hartmann number limit it is demonstrated that the resulting solution is equivalent to that obtained for a porous layer on the basis of Darcy’s model. In the low Hartmann number limit the solution for a fluid layer in the absence of a magnetic force is recovered. In the case of a horizontal layer heated from below the critical Rayleigh number for the onset of convection is derived in term of the Hartmann number. A good agreement is found between the analytical predictions and the numerical simulation of the full governing equations.

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