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Free convection effects on a perfectly conducting couple stress fluid

Ezzat M., Zakaria M., Samaan A., Abd-el Bary A.

Journal of Technical Physics

2006

Vol. 47, no 1

5-30

We have introduced a magnetohydrodynamic model of boundary-layer equations for a perfectly conducting couple-stress fluid. This model is applied to study the effects of free convection currents with thermal relaxation on the flow of a polar fluid through a porous medium, which is bounded by a vertical plane surface. The state space formulation developed in EZZAT [1] and [2j is introduced. The formulation is valid for problems with or without heat sources. The resulting formulation, together with the Laplace transform technique, are applied to a variety of problems. The solution to a thermal shock problem and to the problem of the flow in the whole space with a plane distribution of heat sources are obtained. It is also applied to a semispace problem with a plane distribution of heat sources located inside the fluid. A numerical method is employed for the inversion of the Laplace transforms. The effects of Grashof number, material parameters, Alfven velocity, relaxation time, Prandtl number and the permeability parameter on the velocity, the temperature and the angular velocity distributions are discussed. The effects of cooling and heating of a couple-stress fluid have also been discussed. Numerical results are given and illustrated graphically for the problems considered.

A general model of generalized thermoelasticity with temperature-dependent modulus of elasticity

Ezzat M. A., Zakaria M., El-Karamani A. S.

Journal of Technical Physics

2005

Vol. 46, no 2

67-82

A new formula of generalized thermoelasticity equations for isotropic media is established. The present model does apply to generalizations, the Lord-Shulman theory with one relaxation time and the Green-Lindsay theory with two relaxation times, as well as to the coupled theory. The normal mode analysis is used to obtain the exact expressions for the temperature distribution, thermal stresses, and the displacement components. The resulting formulation is applied to three different concrete problems. The first one deals with a thick plate subject to heating on parts of the upper and lower surfaces of the plate; the second one concerns the case of a heated punch moving across the surface of a semi-infinite thermoelastic half-space subject to appropriate boundary conditions; and the third problem deals with a plate with thermo-insulated surfaces subjected to time-dependent compression. Numerical results are given and illustrated graphically for the problem considered. A comparison was made with the results obtained in the case of temperature-independent modulus of elasticity in each theory.