On three models of magneto-hydrodynamic free-convection flow

2009 ◽  
Vol 87 (12) ◽  
pp. 1213-1226 ◽  
Author(s):  
Magdy A. Ezzat ◽  
A. A. El-Bary
Keyword(s):  
Convection Flow ◽  
Heat Sources ◽  
Space Problem ◽  
State Space Approach ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Whole Space ◽  
Plane Distribution ◽  
The One ◽  
Space Approach

In this work, we introduce a model of the boundary-layer equations of a generalized thermofluid for an electrically conducting pourous medium in the presence of a constant magnetic field. This model is applied to each generalization, Cattaneo theory with one relaxation time, Chandrasekharaiah–Tzou theory, as well as classical Fourier law. The state space approach developed by Ezzat (Can. J. Phys. 86, 1241 (2008)), is adopted for the one-dimensional problems including heat sources. The resulting formulation is applied to a problem for the whole space with a plane distribution of heat sources. The reflection method together with the solution obtained for the whole space is applied to a semi-space problem with a plane distribution of heat sources located inside the fluid. Numerical results for the velocity, temperature, and induced-magnetic and electric field distributions are given and illustrated graphically for both problems. The comparisons are made for all functions with the results obtained in the three theories.

State space formulation for boundary-layer magneto-hydrodynamic free convection flow with one relaxation time

2002 ◽  
Vol 80 (10) ◽  
pp. 1157-1174 ◽  
Author(s):  
M A Ezzat ◽  
A A Samaan ◽  
A Abd-El Bary
Keyword(s):  
Boundary Layer ◽  
Relaxation Time ◽  
State Space ◽  
Boundary Layer Equation ◽  
Convection Flow ◽  
Heat Sources ◽  
Space Problem ◽  
Whole Space ◽  
Space Formulation ◽  
Plane Distribution

We introduce a magnetohydrodynamic model of a boundary-layer equation for a conducting viscous fluid. The state space approach is adopted for one-dimensional problems including heat sources with one relaxation time. The resulting formulation is applied to a problem for the whole space with a plane distribution of heat sources. The reflection method together with the solution obtained for the whole space is applied to a semi-space problem with a plane distribution of heat sources located inside the fluid. Numerical results for the velocity, temperature, and induced-magnetic- and induced-electric-field distributions are given and illustrated graphically for both problems. PACS No.: 47.65+a

scholarly journals Free convection flow of conducting micropolar fluid with thermal relaxation including heat sources

2004 ◽  
Vol 2004 (4) ◽  
pp. 271-292 ◽  
Author(s):  
Magdy A. Ezzat
Keyword(s):  
Free Convection ◽  
Micropolar Fluid ◽  
Vertical Plane ◽  
Thermal Relaxation ◽  
Convection Flow ◽  
Heat Sources ◽  
Free Convection Flow ◽  
Space Technique ◽  
Whole Space ◽  
Plane Distribution

The present work is concerned with unsteady free convection flow of an incompressible electrically conducting micropolar fluid, bounded by an infinite vertical plane surface of constant temperature. A uniform magnetic field acts perpendicularly to the plane. The state space technique is adopted for the one-dimensional problems including heat sources with one relaxation time. The resulting formulation is applied to a problem for the whole space with a plane distribution of heat sources. The reflection method together with the solution obtained for the whole space is applied to a semispace problem with a plane distribution of heat sources located inside the fluid. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for the temperature, the velocity, and the angular velocity distributions are given and illustrated graphically for the problems considered.

MHD free convection flow of a micropolar fluid past a vertical porous plate

2002 ◽  
Vol 80 (12) ◽  
pp. 1661-1673 ◽  
Author(s):  
K A Helmy ◽  
H F Idriss ◽  
S E Kassem
Keyword(s):  
Micropolar Fluid ◽  
Porous Plate ◽  
Infinite Plate ◽  
Numerical Approach ◽  
Convection Flow ◽  
Heated Plate ◽  
Governing Equations ◽  
State Space Approach ◽  
The Laplace Transform ◽  
Space Approach

The present work is concerned with the unsteady flow of an incompressible, viscous, conducting micropolar fluid, through a porous medium, over an infinite plate that is started into motion in its own plane by an impulse. A uniform magnetic field acts in a direction perpendicular to the plate. The governing equations are solved using a state space approach and the inversion of the Laplace transform is carried out, using a numerical approach. The technique is applied to a heated-plate problem and to a problem pertaining to a plate under uniform heating. Numerical results concerning temperature (for both problems), velocity, and microrotation are given and are illustrated graphically. PACS Nos.: 47.00, 65.00, 47.50, 76.00

State space approach to one-dimensional magneto-thermoelasticity under the Green–Naghdi theories

2009 ◽  
Vol 87 (8) ◽  
pp. 867-878 ◽  
Author(s):  
Magdy A. Ezzat ◽  
A. S. El-Karamany ◽  
A.A. Bary
Keyword(s):  
State Space ◽  
Generalized Thermoelasticity ◽  
Heat Sources ◽  
State Space Approach ◽  
One Dimensional ◽  
Laplace Transform Technique ◽  
Isotropic Media ◽  
The Laplace Transform ◽  
Space Approach ◽  
Coupled Theory

A model of the equations of generalized magneto-thermoelasticity for perfectly conducting isotropic media is given. The formulation is applied to the generalized thermoelasticity theories: Green–Naghdi of type II and type III as well as to the dynamic coupled theory. The state space approach is adopted for the solution of one-dimensional problems in the absence of heat sources with time-dependent heating on the boundary. The Laplace-transform technique is used. Numerical results are given and illustrated graphically employing numerical method for the inversion of the Laplace transforms. Comparisons are made with the results predicted by the three theories.

scholarly journals Hall Effects on Steady MHD Heat and Mass Transfer Free Convection Flow along an Inclined Stretching Sheet with Suction and Heat Generation

2014 ◽  
Vol 6 (3) ◽  
pp. 457-466
Author(s):  
M. Ali ◽  
M. S. Alam
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Heat Generation ◽  
Integration Scheme ◽  
Convection Flow ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
Secondary Velocity ◽  
Stretching Plate

The heat and mass transfer of a steady flow of an incompressible electrically conducting fluid over an inclined stretching plate under the influence of an applied uniform magnetic field with heat generation and suction and the effects of Hall current are investigated. Using suitable similarity transformations the governing boundary layer equations for momentum, thermal energy and concentration are reduced to a set of coupled ordinary differential equations which are then solved numerically by the shooting method along with Runge- Kutta fourth-fifth order integration scheme. The numerical results concerned with the velocity, secondary velocity, temperature and concentration profiles effects of various parameters on the flow fields are investigated and presented graphically. The results have possible technological applications in liquid-based systems involving stretchable materials. © 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v6i3.16903 J. Sci. Res. 6 (3), 457-466 (2014)

scholarly journals One-Dimensional Problem of a Conducting Viscous Fluid with One Relaxation Time

2011 ◽  
Vol 2011 ◽  
pp. 1-23
Author(s):  
Angail A. Samaan
Keyword(s):  
Relaxation Time ◽  
Thermal Relaxation ◽  
Heat Sources ◽  
One Dimensional ◽  
Boundary Layer Equations ◽  
Laplace Transform Technique ◽  
The Matrix ◽  
The Laplace Transform ◽  
Magnetohydrodynamic Model ◽  
Plane Distribution

We introduce a magnetohydrodynamic model of boundary-layer equations for conducting viscous fluids. This model is applied to study the effects of free convection currents with thermal relaxation time on the flow of a viscous conducting fluid. The method of the matrix exponential formulation for these equations is introduced. The resulting formulation together with the Laplace transform technique is applied to a variety problems. The effects of a plane distribution of heat sources on the whole and semispace are studied. Numerical results are given and illustrated graphically for the problem.

Sign in / Sign up

Export Citation Format

Share Document