1. No category

State space approach to magnetohydrodynamic flow of perfectly
conducting micropolar fluid with stretch
Magdy A. Ezzat1,*,† and Shreen El-Sapa2
1
Department of Mathematics, Faculty of Education, Alexandria University, Alexandria,
Egypt
2
Department of Mathematics, Faculty of Science, Damanhour University, Damanhour,
Egypt
Abstract
In this work we introduce a model of the boundary layer equations for a perfect conducting
micropolar fluid with stretch, bounded by an infinite vertical flat plane surface of a constant
temperature. This model is applied to study the effects of free convection currents on the
flow of the fluid in the presence of a constant magnetic field. The state space technique is
adopted for the solution of a one-dimensional problem for any set of boundary conditions.
The resulting formulation together with the Laplace transform techniques are
applied to a thermal shock problem. The inversion of the Laplace transforms is carried out
using a numerical approach. Numerical results are given and illustrated graphically for the
problem
KEY WORDS: magnetohydrodynamic; boundary layer; micropolar fluid with stretch; free
convection flow;
generalized heat equation; state space approach; numerical results
Published in: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN
FLUIDS
REFERENCES
1. Eringen AC. Theory of micropolar fluids with stretch. International Journal of
Engineering Science 1969;
7:115–125.
2. Eringen AC. Simple of micro-fluids. International Journal of Engineering Science 1964;
2:205–217.
3. Eringen AC. Thermo-microstretch and bubbly fluids. International Journal of
Engineering Science 1990;
28:133–143.
4. Eringen AC. Theory of microstretch liquid crystals. Journal of Mathematical Physics
1992; 23:4078–4086.
5. Eringen AC. Electrodynamics of microstretch liquid polymers. International Journal of
Engineering Science 2000;
38:959–987.
6. Rao SK, Rajo KV. Stability solutions for microstretch fluid flows. International Journal
of Engineering Science
1979; 17:465–473.
7. Rao SK, Rajo KV. Existence solutions for microstretch fluid flows. International Journal
of Engineering Science
1980; 18:1411–1419.
8. Iesan D. Uniqueness solutions for microstretch fluid flows. International Journal of
Engineering Science 1997;
35:669–679.
9. Sherief HH, Faltas MS, Ashmawy EA. Galerkin representations and fundamental
solutions for an axisymmetric
microstretch fluid flow. Journal of Fluid Mechanics 2009; 619:277–293.
10. Narasimhan MN. A mathematical model of pulsatile flows of microstretch fluid in
circular tubes. International
Journal of Engineering Science 2003; 41:231–247.
11. Aydemir NU, Venart JE. Flow of a thermomicropolar fluid with stretch. International
Journal of Engineering Science
1990; 28:1211–1222.
12. Ezzat MA. State space approach to solids and fluids. Canadian Journal of Physics 2008;
86:1242–1250.
13. Raptis A, Kafousian N. Magnetohydrodynamic free convection flow and mass Transfer
through a porous medium
bounded by an infinite vertical porous plate with Constant heat flux. Canadian Journal of
Physics 1982;
60:1725–1729.
14. Elbashbeshy V. Free convection flow with variable viscosity and thermal diffusivity
along a vertical plate in the
presence of magnetic field. International Journal of Engineering Science 2000; 38:207–
213.
15. Hossain MA. Viscous and joule heating effects on MHD-free convection flow with
variable plate temperature.
International Journal of Heat and Mass Transfer 1992; 35:3485–3487.
16. Cattaneo C. Sullacodizion del calore, Atti. Sem. Mat. Fis. Univ. Modena 1948; 3.
17. Joseph DD, Preziosi L. Heat waves. Reviews of Modern Physics 1989; 61:41–73.
18. Ezzat MA. Free convection effects on perfectly conducting fluid. International journal
of Engineering Science 2001;
39:799–819.
19. Ezzat MA. Free convection effects on extracellular fluid in the presence of a transverse
magnetic field. Applied
Mathematic and Computations 2004; 151:455–482.
20. Ezzat MA, Othman MI, Helmy KA. A problem of a micropolar magnetohydrodynamic
boundary layer flow.
Canadian Journal of Physics 1999; 64:813–827.
21. Ezzat MA, El-Bary AA. On three models of magneto-hydrodynamic free convection
flow. Canadian Journal of
Physics 2009; 87:1213–1226.
22. Honig G, Hirdes U. A method for the numerical inversion of Laplace transforms.
Journal of Computational and
Applied Mathematics 1984; 10:113–132.
23. Aydemir N. Free convection boundary-layer flow of a thermomicropolar fluid with
stretch. International Journal of
Engineering Science 1990; 23:1223–1233.
24. Ishak A, Nazar R, Pop I. Boundary-layer of a micropolar fluid on a continuously
moving or fixed permeable surface.
International Journal of Heat and Mass Transfer 2007; 50:4743–4748.
25. Brigadnov IA, Dorfmann A. Mathematical modeling of magnetoreheological fluid.
Continuum Mechanics and
Thermodynamics 2005; 17:29–42.
26. Ezzat MA, Zakaria M, Shaker O, Barakat F. State space formulation to viscoelastic fluid
flow of magnetohydrodynamic
free convection through a porous medium. Acta Mechanica 1996; 119:147–164.
27. Ezzat MA, OthmanMI, Smaan AA. State space approach to two-dimensional
electromagneto-thermoelastic problem
with two relaxation times. International Journal of Engineering Science 2001; 39:1383–
1404.
28. Ezzat MA. Fundamental solution in generalized magneto-thermoelasticity with two
relaxation times for perfect
conductor cylindrical region. International Journal of Engineering Science 2004; 42:1503–
1519.
29. Ezzat MA, Zakaria MA. Heat transfer with thermal relaxation to a perfectly conducting
polar fluid. Heat and Mass
Transfer 2005; 41:189–198.
30. Ezzat MA, El-Bary AA, Ezzat SM. Combined heat and mass transfer for unsteady
MHD flow of perfect conducting
micropolar fluid with thermal relaxation. Energy Conversion and Management 2011;
52:934–945.