Link to this article: http://journals.cambridge.org/abstract_S0956792501004582How to cite this article: ZAKARIA BELHACHMI, BERNARD BRIGHI and KHALID TAOUS (2001). On a family of differential equations for boundary layer approximations in porous media.Free convection along a vertical flat plate embedded in a porous medium is considered, within the framework of boundary layer approximations. In some cases, similarity solutions can be obtained by solving a boundary value problem involving an autonomous third-order nonlinear equation, depending on a parameter related to the temperature on the wall. The paper deals with existence and uniqueness questions to this problem, for every value of the parameter.

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An experimental study on samples from a fresh human femur highlighted the viscoelastic behaviour of bone. The memory aspect of the behaviour is weak compared to the elastic aspect. A theoretical and numerical approach based on the finite element method illustrates the existing bond between the structure and the micro behaviour on the one hand, and the macro behaviour on the other. The orthotropic elastic behaviour observed by various authors is shown numerically. The memory functions of compact and spongy bone are given. The numerical results illustrate the behaviour observed in the experiments.

On estime le module équivalent de rigidité à la torsion pour un cylindre dont la section multiconnexe présente une double porosité irrégulière. On met en évidence les complications du modèle générées par le contraste d'échelles entre les zones poreuses et compactes.