In this work, we studied the role played by the particle-particle contact over the effective properties appearing in upscaled thermal models, for heat transport at the fluid-porous medium interfacial region under conductive regime. Using closure problems recently reported in the literature, the various effective properties were predicted as functions of position in rhe inter-region and of the degree of interconnection between solid particles. To this end, the associated closure problems were solved in unit cells containing squares connected by rectangular ramifications. It is shown that the existence of contact between particles yields results significantly different from those without contact. This may be an important source of error in modeling, specially when the solid (or the fluid) is highly conductive in comparison with the other phase.

En este trabajo, se estudió el papel del contacto partícula-partícula sobre las propiedades efectivas que aparecen en los modelos escalados, para el transporte de calor en la región interfacial entre un medio poroso y un fluido bajo régimen conductivo. Utilizando problemas de cerradura reportados recientemente en la literatura, se predijeron las propiedades efectivas en función de la posición en la inter-región y del grado de interconección entre las partículas sólidas. Para esto, los problemas de cerradura se resolvieron en celdas unitarias que contienen cuadrados conectados entre sí por medio de brazos rectangulares. Se encontró que la existencia de contacto entre las partículas produce resultados significativamente diferentes a aquellos originados sin contacto. Esto puede representar una importante fuente de error en el modelamiento, especialmente cuando el sólido (o el fluido) es mucho más conductivo en comparación con la otra fase.

This paper deals with the derivation of a macroscopic model for columnar dendritic solidification of binary mixtures using the volume averaging method with closure. The main originalities of the model are first related to the explicit description of evolving heterogeneities of the dendritic structures and their consequences on the derivation of averaged conservation equations, where additional terms involving porosity gradients are present, and on the determination of effective transport properties. These average properties are defined by the associated closure problems taking into account the geometry of the dendrites and the local intensity of the flow. The macroscopic solute transport is obtained by considering macroscale non-equilibrium giving rise to macroscopic dispersion and interfacial exchange phenomena. Mass exchange coefficients are accurately explicited as a function of the local geometry.