Mass Transfer In Media Research Articles

Mathematical Model of Heat Conduction for a Semi-Infinite Body, Taking into Account Memory Effects and Spatial Correlations

One of the promising approaches to the description of many physical processes is the use of the fractional derivative mathematical apparatus. Fractional dimensions very often arise when modeling various processes in fractal (multi-scale and self-similar) environments. In a fractal medium, in contrast to an ordinary continuous medium, a randomly wandering particle moves away from the reference point more slowly since not all directions of motion become available to it. The slowdown of the diffusion process in fractal media is so significant that physical quantities begin to change more slowly than in ordinary media.This effect can only be taken into account with the help of integral and differential equations containing a fractional derivative with respect to time. Here, the problem of heat and mass transfer in media with a fractal structure was posed and analytically solved when a heat flux was specified on one of the boundaries. The second initial boundary value problem for the heat equation with a fractional Caputo derivative with respect to time and the Riesz derivative with respect to the spatial variable was studied. A theorem on the semigroup property of the fractional Riesz derivative was proved. To find a solution, the problem was reduced to a boundary value problem with boundary conditions of the first kind. The solution to the problem was found by applying the Fourier transform in the spatial variable and the Laplace transform in time. A computational experiment was carried out to analyze the obtained solutions. Graphs of the temperature distribution dependent on the coordinate and time were constructed.

FRACTAL HEAT AND MASS TRANSFER FOR SIMULATION OF PROCESSES IN THE TWO-PHASE ZONE OF METAL SOLIDIFICATION

The work is devoted to the development of the fundamental foundations of mathematical modeling of non-local processes of heat and mass transfer in media with a fractal structure - in complex systems modeled by fractals, the study of initial and mixed boundary value problems for the main types of local and non-local differential equations of state and transfer.

Parametric modelling and numerical simulation of natural-convective transport of radon-222 from a phosphogypsum stack into open air

An existing finite-volume computational simulator for heat and mass transfer in media fully or partially filled with porous material has been adapted to predict radon-222 exhalation rates. For validation purposes, this paper numerically examines the extent of natural-convective effects on radon-222 steady-state transfer from a phosphogypsum stack into the surrounding atmosphere. The stack is approximated by a dry rectangular porous matrix having uniform porosity and isotropic permeability whereas the supposedly laminar buoyancy-driven air flow is modelled following Darcy–Brinkman–Boussinesq approach. Differential governing equations are cast in dimensionless form in order to encompass simultaneous effects from physical factors involved. Dimensionless groups related to decay and emanation processes are put forward apart from usual controlling parameters such as Prandtl, Schmidt, Darcy and Grashof numbers. Results are reported for 10 6 ⩽ Gr ⩽ 10 8 and 10 −13 ⩽ Da ⩽ 10 −7. Natural-convective effects on typical low-permeability phosphogypsum stacks proved to be of minor importance, as radon-222 transfer becomes diffusive dominant as expected.

Numerical simulation of mass transfer in porous media of blood vessel walls.

The tunica media of a blood vessel wall is modeled as a heterogeneous medium composed of a periodic array of cylindrical smooth muscle cells and a continuous interstitial fluid phase of proteoglycan and collagen fibers. By applying Brinkman's model to describe the behavior of the interstitial flow, we obtain an analytical solution for the transmural flow field through the periodic array of smooth muscle cells in the form of a power series, making it possible to compute the convection of solutes in the interstitial phase. With reaction of solutes at the surface of smooth muscle cell membranes being treated as boundary conditions and the diffusion of species being limited to the interstitial fluid phase only, mass transfer in the media of blood vessel walls is simulated numerically using Cray supercomputers. It is found that the Sherwood number (the dimensionless mass-transfer coefficient) is not only constant for all interior smooth muscle cells but also minimally sensitive to changes of parameters controlling the relative rates of diffusion and convection in the interstitial fluid phase and the reaction on the smooth muscle cell surface. In addition, the Sherwood number is not very sensitive to changes in the volume fraction of smooth muscle cells. A homogeneous, one-dimensional model (effective-medium model) is also developed to predict the bulk concentration profile in the media, based on the equivalent properties of the effective medium derived from the heterogeneous medium. A comparison of results from the one-dimensional model and two-dimensional simulation is quite satisfactory for all practical ranges of parameters. It is also determined that, for a small molecule such as ATP, the mass transfer to the surface of smooth muscle cells is "reaction limited" as assumed previously in the literature, whereas, for a large molecule such as low-density lipoprotein, the mass transfer might not be reaction limited.

Analysis of pseudo-continuum mass transfer in media with spatially periodic boundaries

The theories developed by Taylor, Aris, and Gill for convective dispersion of soluble matter in nonuniform flow are extended to systems with spatially periodic boundaries. More specifically the generalized theory explains solute retardation and dispersion in columns packed with a regular array of permeable particles, and is thus applicable to most chromatographic processes. The general theory is then specialized to the case of solute dispersion in creeping flow through a body-center-cubic array of impermeable, spherical particles. Preliminary calculations indicate that the present theory predicts correctly solute dispersion at the zero-flow limit. However numerical difficulties are encountered in the calculations for convective dispersion which seriously limit the utility of the theory.