The impact of a wedge-shaped body on the free surface of a weightless inviscid incompressible liquid is considered. Both symmetrical and unsymmetrical entries at constant velocity are dealt with. The differential problem corresponds to the physico-mathematical model of a distribution of potential singularities and, in particular, the flow singularities at the ends of the wetted regions are represented by sinks. A conformal transformation of the flow field is adopted and the unknown intensities of the discontinuities are found by an optimization procedure, together with the solution of the nonlinear free-surface problem. The flow separation at a sideslip is also considered

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The dynamics of gases in permeable media is approached both experimentally and by numerical simulations. The experiments were performed in matrices made of packed beds of spheres in rarefied conditions and a model for the direct simulation of the molecular kinetics is proposed. Comparisons between experimental data and numerical results show the influence of the main parameters of the gas-solid interaction and the range of validity of the model. Moreover it is shown that there is a flow condition for the minimum permeability of the medium to the gas flow. Such a minimum depends upon the Knudsen number, and can be explained by the molecular dynamics as in the well-known Knudsen's experiment on capillaries

A model for a continuum gas flowing through a porous matrix is proposed where the gas kinetics is governed by the Boltzmann equation and the solid phase by the energy equation. In the Boltzmann equation the integral relative to the gas-solid collisions is evaluated as for the collisions of hard spheres molecules against much heavier and longer straight particles (Lebowitz model of a sticks gas), randomly distributed in space according to a Maxwellian function with zero mean velocity. The mean flow is one-dimensional but the molecules are free to move in all three space dimensions. In the continuum limit, the moments of the Boltzmann equation provide the mass continuity, energy and momentum equations, the last one expressing the Darcy law for a compressible gas. The transport coefficients are analytically evaluated and a few examples are dealt with.

Abstract. Heat conduction is considered in a semi-infinite solid subjected to a high step change in surface heat flux, such that melting occurs. A time-dependent relaxation model for the energy flux is assumed, leading to a non-Fourier, non-linear equation for the thermal field, which is solved under suitable conditions on the interface displacement.1. Introduction. Criticism to the Fourier model for heat conduction, which leads to a physically unacceptable infinite speed of propagation of the energy transfer, was put forward, in the past, by several authors. Such a criticism, initially based on purely speculative grounds, follows from a variety of approaches to the problem, from the first consideration in a work by Cattaneo [1], where a model for the heat conduction process was substantiated-in the case of gaseous media-by means of the kinetic theory, to the statistical mechanics of nonequilibrium irreversible processes [2].1In any case, when the Fourier law is rebuted, a time-dependent relaxation model is proposed for the heat flux and the thermal field, which, in the Fourier case, is governed by a parabolic equation, obeys to a hyperbolic wave equation.The temperature distribution evaluated by the latter model more significantly differs from the Fourier model predictions as the involved fluxes of heat and their time variations increase. Recent technological developments have drawn increasing attention to non-Fourier heat transfer models as situations where their effects can start playing a significant role