REITERATED HOMOGENIZATION APPLIED TO NANOFLUIDS WITH AN INTERFACIAL THERMAL RESISTANCE
Ernesto Iglesias Rodríguez, Julián Bravo‐Castillero, Manuel E. Cruz, Leslie D. Pérez‐Fernández, Federico J. Sabina · International Journal for Multiscale Computational Engineering · 2020
Heterogeneous media with several spatial scales are often found in heat transfer applications. For instance, two-phase nanofluids made of nanoparticles immersed in a fluid containing both individual particles and clusters, which exhibit at least three structural scales, have shown improved thermal conductivity over the individual constituents. In this work, a problem for the Fourier heat equation with periodic and rapidly oscillating coefficients is studied via a reiterated homogenization method. The constituent phases are assumed to be in imperfect thermal contact, so there is a thermal barrier at the interfaces. The formal procedure to derive the homogenized problem, local problems, and effective coefficients is described for a general three-dimensional problem. The influence of volume fractions, phase conductivities, and interfacial thermal resistances on the effective behavior is exemplified for the case of laminated composites. An application of a simple model for the study of nanofluids is explained. Improvement of the effective conductivity and its dependence on the interfacial resistance is analyzed.