Department Seminar of Michal Sagirr Nisim - Effective thermal conductivity of media with randomly distributed convective hollow spheres
SCHOOL OF MECHANICAL ENGINEERING SEMINAR
Wednesday. May 18, 2022 at 14:00
Effective thermal conductivity of media with randomly distributed convective hollow spheres
Michal Sagirr Nisim
M.Sc. student of Avinoam Rabinovich
Effective properties of composite or heterogeneous materials, (media, composed of domains of different materials); have been investigated for many years and as far back as Maxwell (1873), Rayleigh (1892) and even Einstein (1906). Estimating thermal effective conductivity is important for modeling and understanding the heat transfer mechanisms in these media. This is relevant to many applications of heat transfer in both natural media, such as soil and porous reservoir rocks, or industrial materials such as composites, foams and concrete building blocks. One of the most common models for calculating effective thermal conductivity is the Maxwell model which considers the problem of a dilute dispersion of spherical inclusions scattered in a continuous matrix, where the inclusions are small relative to the distance between them. Therefore, interaction between the inclusions is ignored and an expression is derived using the solution for a single sphere. Only conduction is considered, and convection or radiation heat transfer is typically neglected in the Maxwell model.
In this work we present an extension to the Maxwell effective conductivity (kef) model, which considers fluid filled spherical inclusions and takes into account natural convection in the spheres. We use a novel numerical approach for calculation of kef. Results are presented for a range of dimensionless parameters and shown to converge to the classical Maxwell expression when convection is negligible. Furthermore, an analytical approximation for air filled voids was fitted to the results, allowing for rapid calculations of kef. Other fluids rather than air are also considered and results are presented.
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