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.

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 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.

Onset of wall-attached convection in a rotating fluid layer in the presence of a vertical magnetic field

2008 ◽  
Vol 600 ◽  
pp. 427-443
Author(s):  
J. J. SÁNCHEZ-ÁLVAREZ ◽  
E. CRESPO DEL ARCO ◽  
F. H. BUSSE
Keyword(s):  
Magnetic Field ◽  
Rotation Rate ◽  
Magnetic Energy ◽  
Fluid Layer ◽  
Travelling Waves ◽  
Critical Rayleigh Number ◽  
Vertical Axis ◽  
Vertical Magnetic Field ◽  
Onset Of Convection ◽  
Magnetic Energy Density

A horizontal fluid layer heated from below and rotating about a vertical axis in the presence of a vertical magnetic field is considered. From earlier work it is known that the onset of convection in a rotating layer usually occurs in the form of travelling waves attached to the vertical sidewalls of the layer. It is found that this behaviour persists when a vertical magnetic field is applied. When the Elsasser number Λ is kept constant and the sidewall is thermally insulating the critical Rayleigh number Rc increases in proportion to the rotation rate described by the square root of the Taylor number, τ. This asymptotic relationship is found for an electrically highly conducting sidewall as well as for an electrically insulating one. At fixed rotation rate for Q≫τ, Rc grows in proportion to Q when the sidewall is electrically highly conducting, and in proportion to Q3/4 when the sidewall is electrically insulating. Here Q is the Chandrasekhar number which is a measure of the magnetic energy density, and a thermally insulating sidewall has been assumed. Of particular interest is the possibility that the magnetic field counteracts the stabilizing influence of rotation on the onset of sidewall convection in the case of thermally insulating sidewalls. When the sidewall is thermally highly conducting, Rc for the sidewall mode grows in proportion to τ4/3. This asymptotic behaviour is found for both cases of electrical boundary conditions, but it no longer precedes the onset of bulk convection for Λ ≳ 1.

Magnetohydrodynamic flow along cylindrical pipes under non-uniform transverse magnetic fields

1968 ◽  
Vol 31 (2) ◽  
pp. 321-342 ◽  
Author(s):  
L. Todd
Keyword(s):  
Magnetic Field ◽  
Hartmann Number ◽  
Transverse Magnetic ◽  
Uniform Field ◽  
Governing Equations ◽  
Azimuthal Magnetic Field ◽  
Electrically Conducting ◽  
Unidirectional Flow ◽  
Plane Transverse ◽  
Field Lines

The unidirectional flow of an incompressible, electrically conducting, viscous fluid along cylindrical pipes is considered. An external magnetic field, B0, which lies in the plane transverse to the flow is applied. It is shown that the governing equations, written in the co-ordinate system traced out by B0, are mathematically very similar to those for a uniform field.The paper deals mainly with ducts whose walls are insulators. Though exact solutions (valid for all values of the Hartmann number) are derived, the limit of high Hartmann number is taken for detailed discussion. Transition layers (or, loosely, ‘wakes’) can arise which are centred on curved field lines. In some cases, reversed flow occurs in part of the core (‘radial-type’ fields). Situations also arise where the magnitude (and sign) of the velocity remains the same as for B0 = 0, whatever the strength of the applied, transverse (azimuthal) magnetic field.

Theory on Thermal Instability of Binary Gas Mixtures in Porous Media

1976 ◽  
Vol 98 (1) ◽  
pp. 35-41 ◽  
Author(s):  
M. L. Lawson ◽  
Wen-Jei Yang ◽  
S. Bunditkul
Keyword(s):  
Fluid Layer ◽  
Perturbation Technique ◽  
Critical Rayleigh Number ◽  
Lower Boundary ◽  
Horizontal Layer ◽  
Linear Perturbation ◽  
Onset Of Convection ◽  
Hurwitz Stability ◽  
Binary Gas Mixture ◽  
The Galerkin Method

A theory is developed which predicts the instability of a horizontal layer of porous medium saturated with a binary gas mixture. The lower boundary of the system is maintained at a higher temperature and the upper one at low temperature. The transport equations and coefficients are developed on the basis of kinetic theory. A linear perturbation technique is employed to reduce the governing equations for momentum, heat, and mass transfer to eigenvalue differential equations which are solved by the Finlayson method, the combination of the Galerkin method and the Routh-Hurwitz stability criterion. Only neutral stationary stability is found to occur in the system. Its criterion can be predicted by a simple algebraic equation. Both the critical Rayleigh and wave numbers for the onset of convection are governed by five independent dimensionless parameters, two of which are most influential. The critical Rayleigh number may be lower or greater than that for pure fluid layer depending upon whether thermal diffusion induces the heavier component of the mixture to move toward the cold or hot boundary, respectively. The theory compares well with the experimental results.

Time-periodic Heating of a Rotating Horizontal Fluid Layer in a Vertical Magnetic Field

2005 ◽  
Vol 60 (8-9) ◽  
pp. 583-592 ◽  
Author(s):  
Beer Singh Bhadauria
Keyword(s):  
Magnetic Field ◽  
Fluid Layer ◽  
Vertical Axis ◽  
Horizontal Layer ◽  
Vertical Magnetic Field ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Dependent Part ◽  
Horizontal Fluid Layer ◽  
Time Periodic

Thermal instability in a horizontal layer of an electrically conducting fluid heated from below has been investigated under the effects of uniform rotation about a vertical axis and an applied uniform vertical magnetic field. The temperature field between the walls of the fluid layer consists of two parts; a steady part and a time-dependent part, which varies periodically. The effect of modulation of the walls temperature on the onset of convection has been studied using Floquets theory. Stabilizing and destabilizing effects on the onset of convective instability have been found. Some comparisons have been made. - 2000 Mathematics Subject Classification: 76E06, 76R10.

Numerical study of magnetohydrodynamics Jeffery–Hamel flow with cu-water nanofluid between two rectangular smooth walls with transverse magnetic field

2020 ◽  
Vol 09 (02) ◽  
pp. 2050010
Author(s):  
Ramakanta Meher ◽  
N. D. Patel
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Transverse Magnetic Field ◽  
Hartmann Number ◽  
Numerical Study ◽  
Transverse Magnetic ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform

In this paper, the MHD Jeffery–Hamel flow with cu-water nanofluid between two smooth rectangular walls with the transverse magnetic field is studied. Differential transform method (DTM) is used to obtain the velocity profile of Jeffery–Hamel flow in both convergent and divergent channels for different values of Reynolds number and Hartmann number. Finally, to examine the accuracy and the validity of the method, the obtained results have been compared with the available collation method results.

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.

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