Related papers: Homogenization and simulation of heat transfer thr…
We are investigating the effective heat transfer in complex systems involving porous media and surrounding fluid layers in the context of mathematical homogenization. We differentiate between two fundamentally different cases: Case (a),…
We investigate the effective coupling between heat and fluid dynamics within a thin fluid layer in contact with a solid structure via a rough surface. Moreover, the opposing vertical surfaces of the thin layer are in relative motion. This…
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…
We study the question of periodic homogenization of a variably scaled reaction-diffusion problem with non-linear drift posed for a domain crossed by a flat composite thin layer. The structure of the non-linearity in the drift was obtained…
We consider a thin heterogeneous layer consisted of the thin beams (of radius $r$) and we study the limit behaviour of this problem as the periodicity $\varepsilon$, the thickness $\delta$ and the radius $r$ of the beams tend to zero. The…
The thermodynamic theory of dislocation/grain boundary interaction, including dislocation pile-up against, absorption by, and transfer through the grain boundary, is developed for nonuniform plastic deformations in polycrystals. The case…
We examine the long-term behaviour of non-integrable, energy-conserved, 1D systems of macroscopic grains interacting via a contact-only generalized Hertz potential and held between stationary walls. We previously showed that in homogeneous…
A variational model in the context of the gradient theory for fluid-fluid phase transitions with small scale heterogeneities is studied. In particular, the case where the scale $\varepsilon$ of the small homogeneities is of the same order…
This paper is devoted to the homogenization of the heat conduction equation, with a homogeneous Dirichlet boundary condition, having a periodically oscillating thermal conductivity and a vanishing volumetric heat capacity. A homogenization…
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
In this work we present the homogenization of a reaction-diffusion model that includes an evolving microstructure. Such type of problems model, for example, mineral dissolution and precipitation in a porous medium. Hence, we are dealing…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
Homogenization of a thin micro-structure yields effective jump conditions that incorporate the geometrical features of the scatterers. These jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded.…
In this paper a model for partial melts is constructed using two-scale homogenization theory. While this technique is well known to the mathematics and materials communities, it is relatively novel to problems in the solid Earth. This…
In this paper we have studied the flow and heat transfer in a viscous fluid by a horizontal sheet. The stretching rate and temperature of the sheet vary with time. The governing equations for momentum and thermal energy are reduced to…
A periodic assembly of acoustically-rigid blocks (termed 'grating'), situated between two half spaces occupied by fluid-like media, lends itself to a rigorous theoretical analysis of its response to an acoustic homogeneous plane wave. This…
A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which…
A new two-layer model has been proposed to study microscale heat transfer associated with a developing flow boundary layer. As an example, a cold, microscale film of liquid impinging on an isothermal hot, horizontal surface has been…
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat…