Journal of Applied Mathematics

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

Magdy A. Ezzat

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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.

Article information

J. Appl. Math. Volume 2004, Number 4 (2004), 271-292.

First available in Project Euclid: 8 November 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76W05: Magnetohydrodynamics and electrohydrodynamics 76D10
Secondary: 76A05


Ezzat, Magdy A. Free convection flow of conducting micropolar fluid with thermal relaxation including heat sources. J. Appl. Math. 2004 (2004), no. 4, 271--292. doi:10.1155/S1110757X04403088.

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  • G. Ahmadi, Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate, Int. J. Engin. Sci. 14 (1976), 639--646.
  • R. Bhargava and M. Rani, Heat transfer in micropolar boundary layer flow near a stagnation point, Int. J. Enging. Sci. 23 (1985), 1331--1335.
  • A. C. Eringen, Theory of micropolar fluids, J. Math. Mech. 16 (1966), 1--18.
  • --------, Theory of thermomicrofluids, J. Math. Anal. Appl. 38 (1972), 480--496.
  • M. A. Ezzat, State space approach to unsteady free convection flow through a porous medium, Appl. Math. Comput. 64 (1994), no. 2-3, 191--205. \CMP1+298+2611 298 261
  • --------, State space approach to unsteady two-dimensional free convection flow through a porous medium, Can. J. Phys. 1 (1994), 311--317.
  • --------, State space approach to generalized magneto-thermoelasticity with two relaxation times in a medium of perfect conductivity, Int. J. Eng. Sci. 35 (1997), no. 8, 741--752.
  • --------, Free convection effects on perfectly conducting fluid, Int. J. Eng. Sci. 39 (2001), no. 7, 799--819.
  • --------, Free convection effects on extracellular fluid in the presence of a transverse magnetic field, Appl. Math. Comput. 151 (2004), no. 2, 455--482. \CMP2+044+2132 044 213
  • M. A. Ezzat and M. I. A. Othman, Thermal instability in a rotating micropolar fluid layer subject to an electric field, Int. J. Eng. Sci. 38 (2000), no. 16, 1851--1867.
  • M. A. Ezzat, M. I. A. Othman, and K. A. Helmy, A problem of a micropolar magnetohydrodynamic boundary-layer flow, Can. J. Phys. 77 (1999), no. 10, 813--827.
  • R. S. Gorla, A. Mohammedan, M. Mansour, and I. Hussein, Unsteady natural convection from a heated vertical plate in micropolar fluid, Numerical Heat Transfer, Part A 28 (1995), 253--262.
  • I. Hassanien and R. Gorla, Mixed convection in stagnation flow of micropolar fluid over vertical surfaces with uniform surface heat flux, Int. J. of Fluid Eng. Mech. 5 (1992), no. 3, 391--412.
  • J. Holman, Heat Transfer, McGraw-Hill, Kogakusha, Tokyo, 1976.
  • G. Honig and U. Hirdes, A method for the numerical inversion of Laplace transforms, J. Comput. Appl. Math. 10 (1984), 113--132.
  • S. K. Jena and M. N. Mathur, Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a non-isothermal vertical flat plate, Int. J. Eng. Sci. 19 (1981), 1431--1439.
  • H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids 15 (1967), 299--309.
  • K. Ogata, State Space Analysis of Control Systems, Prentice-Hall, New Jersey, 1967.
  • J. R. Peddieson and R. P. McNitt, Boundary layer for a micropolar fluid, Recent Adv. Eng. Sci. 5 (1972), 23--28.
  • B. C. Sakiadis, Boundary layer behavior on continuous solid surface, Am. Int. Chem. Eng. J. 7 (1961), 221--225.
  • D. Wiberg, Schaum's Outline Series in Engineering, McGraw-Hill, New York, 1971.