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

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.

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.

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.

Effect of Nanofluid on Heat Transfer Enhancement for Mixed Convection Flow Over a Corrugated Surface

2020 ◽  
Vol 45 (4) ◽  
pp. 373-383
Author(s):  
Nepal Chandra Roy ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Local Nusselt Number ◽  
Richardson Number ◽  
Thermal Boundary Layer ◽  
Volume Fraction ◽  
Convection Flow ◽  
Mixed Convection Flow

AbstractA mathematical model for mixed convection flow of a nanofluid along a vertical wavy surface has been studied. Numerical results reveal the effects of the volume fraction of nanoparticles, the axial distribution, the Richardson number, and the amplitude/wavelength ratio on the heat transfer of Al2O3-water nanofluid. By increasing the volume fraction of nanoparticles, the local Nusselt number and the thermal boundary layer increases significantly. In case of \mathrm{Ri}=1.0, the inclusion of 2 % and 5 % nanoparticles in the pure fluid augments the local Nusselt number, measured at the axial position 6.0, by 6.6 % and 16.3 % for a flat plate and by 5.9 % and 14.5 %, and 5.4 % and 13.3 % for the wavy surfaces with an amplitude/wavelength ratio of 0.1 and 0.2, respectively. However, when the Richardson number is increased, the local Nusselt number is found to increase but the thermal boundary layer decreases. For small values of the amplitude/wavelength ratio, the two harmonics pattern of the energy field cannot be detected by the local Nusselt number curve, however the isotherms clearly demonstrate this characteristic. The pressure leads to the first harmonic, and the buoyancy, diffusion, and inertia forces produce the second harmonic.

Cylindrically Anisotropic Tubes Containing a Line Dislocation

2006 ◽  
Author(s):  
Chung-Hao Wang
Keyword(s):  
State Space ◽  
Dislocation Line ◽  
Longitudinal Axis ◽  
The State ◽  
Fourier Series Expansion ◽  
General Solutions ◽  
Mixed Dislocation ◽  
Line Dislocation ◽  
Space Formulation ◽  
Cylindrically Anisotropic

An analytical solution of the problem of a cylindrically anisotropic tube which contains a line dislocation is presented in this study. The state space formulation in conjunction with the eigenstrain theory is proved to be a feasible and systematic methodology to analyze a tube with the existence of dislocations. The state space formulation which expediently groups the displacements and the cylindrical surface traction can construct a governing differential matrix equation. By using Fourier series expansion and the well developed theory of matrix algebra, the asymmetrical solutions are not only explicit but also compact in form. The dislocation considered in this study is a kind of mixed dislocation which is the combination of edge dislocations and a screw dislocation and the dislocation line is parallel to the longitudinal axis of the tube. The degeneracy of the eigen relation and the technique to determine the inverse of a singular matrix are thoroughly discussed, so that the general solutions can be applied to the case of isotropic tubes, which is one of the novel features of this research. The results of isotropic problems, which are belong to the general solutions, are compared with the well-established expressions in the literature. The satisfied correspondences of these comparisons indicate the validness of this study. A cylindrically orthotropic tube is also investigated as an example and the numerical results for the displacements and tangential stress on the outer surface are displayed. The effects on surface stresses due to the existence of a dislocation appear to have a characteristic of localized phenomenon.

The laminar boundary-layer equation: a method of solution by means of an automatic computer

1955 ◽  
Vol 51 (2) ◽  
pp. 320-332 ◽  
Author(s):  
D. C. F. Leigh
Keyword(s):  
Boundary Layer ◽  
Asymptotic Solution ◽  
Laminar Boundary Layer ◽  
Iterative Process ◽  
Boundary Layer Equation ◽  
Algebraic Equations ◽  
Automatic Computer ◽  
Linear Algebraic Equations ◽  
Method Of Solution ◽  
Incompressible Boundary

ABSTRACTA method, very suitable for use with an automatic computer, of solving the Hartree-Womersley approximation to the incompressible boundary-layer equation is developed. It is based on an iterative process and the Choleski method of solving a simultaneous set of linear algebraic equations. The programming of this method for an automatic computer is discussed. Tables of a solution of the boundary-layer equation in a region upstream of the separation point are given. In the upstream neighbourhood of separation this solution is compared with Goldstein's asymptotic solution and the agreement is good.

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