Anisotropy Effects on Heat and Fluid Flow by Unsteady Natural Convection and Radiation in Saturated Porous Media

ABSTRACT

This article deals with a numerical study of fluid flow and heat transfer by unsteady natural convection and thermal radiation in a vertical channel opened at both ends and filled with anisotropic, in both thermal conductivity and permeability, fluid-saturated porous medium. The bounding walls of the channel are gray and kept at a constant hot temperature.

In the present study we suppose the validity of the Darcy law for motion and of the local thermal equilibrium assumption. The radiative transfer equation (RTE) is solved by the finite-volume method (FVM). The numerical results allow us to represent the time–space variations of the different state variables. The sensitivity of the fluid flow and the heat transfer to different controlling parameters, namely, the single scattering albedo ω, the temperature ratio R, the anisotropic thermal conductivity ratio R_c, and the anisotropic permeability ratio R_k, are addressed. Numerical results indicate that the controlling parameters of the problem, namely, ω, R, R_c, and R_k, have significant effects on the flow and thermal field behavior and also on the transient process of heating or cooling of the medium. Effects of such parameters on time variations of the volumetric flow rate q_v and the convected heat flux Q at the channel's outlet are also studied.     

Spreadable cellular automata: modelling and simulations

The spreadable phenomena which describes the expansion in time of a given spatial property has been studied using models based on partial differential equations. These spreadable dynamics are generally non-linear and then difficult to simulate particularly in two dimensions. In this article, we propose cellular automata (CA) models as an alternative modelling tool that can easily simulate spreadable systems. CA are capable of describing complex systems based on simple evolution rules, which provide numerical schemes directly implemented on computers without approximation or rounding errors. We design local CA dynamics which allow us to maintain a spatial property on non-decreasing subdomains. Several numerical results are performed to illustrate spreadable phenomena. The simulation results corroborate the general shape theory that exhibits the convergence to a specific domain independently on initial conditions.