Universal effective medium theory to predict the thermal conductivity in nanostructured materials. (February 2022)

• Record Type: Journal Article
• Authors: Aria Hosseini, S.; Khanniche, Sarah; Alex Greaney, P.; Romano, Giuseppe
• Is Part Of: International journal of heat and mass transfer. Volume 183:Part A(2022)
• Publication Date: 2022-02
• Subjects: Effective medium theory -- Nanoporous Materials -- Nanoscale heat transfer -- Nanoporous Thermoelectrics -- Thermal conductivity; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2021.122040
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: Nanoscale heat transport does not obey Fourier's law and, at the very least, the Boltzmann transport equation (BTE) must be employed. The BTE is computationally expensive to compute since it entails tracking phonon trajectory both in real- and momentum-space. We develop a new method that allows us to compute the effective thermal conductivity in porous materials using precomputed key parameters associated with the material's geometry and underlying bulk system. Precomputed parameters are provided for several combinations of geometries and bulk materials and disseminated on GitHub. Abstract: Nanostructured materials enable high thermal transport tunability, holding promises for thermal management and heat harvesting applications. Predicting the effect that nanostructuring has on thermal conductivity requires models, such as the Boltzmann transport equation (BTE), that capture the non-diffusive transport of phonons. Although the BTE has been well validated against several key experiments, notably those on nanoporous materials, its applicability is computationally expensive. Several effective model theories have been put forward to estimate the effective thermal conductivity; however, most of them are either based on simple geometries, e.g., thin films, or simplified material descriptions such as the gray-model approximation. To fill this gap, we propose a model that takes into account the whole mean-free-path (MFP) distribution as well as the complexity of the material's boundaries in infinitely thick films with extruded porosity using uniparameter logistic regression. We validate our approach, which is called the "Ballistic Correction Model" (BCM), against full BTE simulations of a selection of three base materials (GaAs, InAs, and Si) with nanoscale porosity, obtaining excellent agreement. While the key parameters of our method, associated with the geometry of the bulk material, are obtained from the BTE, they can be decoupled and used in arbitrary combinations and scales. We tabulated these parameters for a few cases, enabling the exploration of systems that are beyond those considered in this work. Providing a simple yet accurate estimation of thermal transport in nanostructures, our work sets out to accelerate the discovery of materials for thermal-related applications.