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1

Flow through porous media induced by an impervious rotating disk in the presence of magnetic field

Sharma P. K., Chaudhary R. C.

Engineering Transactions

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2005

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Vol. 53, iss. 1

43-53

EN

The flow of an electrically conducting viscous incompressible fluid, due to an infinite impervious rotating disk bounded by porous medium is discussed. It is assumed that the flow between the disk and the porous medium is governed by Navier-Stokes equations and that in the porous medium - by Brinkman equations. A uniform magnetic field is applied in the direction normal to flow. At the interface (porous medium - clear fluid boundary), a modified set of boundary conditions is applied. Analytical expressions for the velocity and shearing stress are calculated and effects of various parameters upon them are examined.

2

Nonlinear regression problem of material functions identification for porous media plastic flow

Nowak Z., Stachurski A.

Engineering Transactions

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2001

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Vol.49, iss.4

637-661

EN

In the paper we present the identification problem arising in modelling the processes of nucleation and growth of voids in the elastic-plastic media. Identification is carried out on the basis of Fisher's data measured on the cylindrical steel specimens subjected to the uniaxial tension. The identification problem is formulated as the standard nonlinear regression problem. Our aim was to select appropriate formulae of the material functions appearing in the porosity model in the right-hand side of the differential equation, and to identify their unknown parameters. The resulting nonlinear regression problem was solved by means of the global optimization method of Boender et al. As the local minimizer we have implemented the modified famous BFGS quasi-Newton method. Modifications were necessary to take into account box constraints posed on the parameters. As the directional minimizer we have prepared a special procedure joining quadratic and cubic approximations and including a new switching condition. We have tested two variants of the porosity model; in the first one with variable shape of the material function g, and the second one - with constant g. The results suggest that the model with material function g ş 1 describes well the nucleation and growth of voids. However, our attempt to identify that constant has brought an unexpected value smaller than 1, and approximately equal to 0.84.

3

FEM analysis of binary dilute system solidification using the anisotropic porous medium model of a mushy zone

Banaszek J., Furmański P.

Computer Assisted Mechanics and Engineering Sciences

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2000

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Vol. 7, No. 3

341-362

EN

Finite Element Method (FEM) calculations have been performed to address the problem of the influence of anisotropy of permeability and of thermal conductivity of a mushy region on a temporary flow pattern and temperature during solidification of binary mixtures. Computationally effective FEM algorithm is based on the combination of the projection method, the semi-implicit time marching scheme and the enthalpy-porosity model of the two-phase region. Example calculations are given for two different dilute solutions of ammonium chloride and water. The effect of permeability anisotropy considerably changes the shape of the mushy zone. Three different models of thermal conductivity, the first - based on a mixture theory, the second - fully anisotropic one and the third - the model of isotropic effective conductivity, have been analyzed and mutually compared. It has been found that the impact of the thermal conductivity anisotropy is visible only in the case when this property differs significantly in both phases.