Energies 2021, 14, 6308. https://doi.org/10.3390/en14196308 www.mdpi.com/journal/energies Article Equivalent Parallel Strands Modeling of Highly-Porous Media for Two-Dimensional Heat Transfer: Application to Metal Foam Nihad Dukhan Department of Mechanical Engineering, University of Detroit Mercy, Detroit, MI 48221, USA; dukhanni@udmercy.edu Abstract: A new geometric modeling of isotropic highly-porous cellular media, e.g., open-cell metal, ceramic, and graphite foams, is developed. The modelling is valid strictly for macroscopically two- dimensional heat transfer due to the fluid flow in highly-porous media. Unlike the current geomet- rical modelling of such media, the current model employs simple geometry, and is derived from equivalency conditions that are imposed on the model’s geometry a priori, in order to ensure that the model produces the same pressure drop and heat transfer as the porous medium it represents. The model embodies the internal structure of the highly-porous media, e.g., metal foam, using equivalent parallel strands (EPS), which are rods arranged in a spatially periodic two-dimensional pattern. The dimensions of these strands and their arrangement are derived from equivalency con- ditions, ensuring that the porosity and the surface area density of the model and of the foam are indeed equal. In order to obtain the pressure drop and heat transfer results, the governing equations are solved on the geometrically-simple EPS model, instead of the complex structure of the foam. By virtue of the simple geometry of parallel strands, huge savings on computational time and cost are realized. The application of the modeling approach to metal foam is provided. It shows how an EPS model is obtained from an actual metal foam with known morphology. Predictions of the model are compared to experimental data on metal foam from the literature. The predicted local temperatures of the model are found to be in very good agreement with their experimental counterparts, with a maximum error of less than 11%. The pressure drop in the model follows the Forchheimer equation. Keywords: metal foam; graphite foam; geometric modelling; heat transfer; porous media 1. Introduction Highly-porous open-cell media include open-cell metal foam (e.g., aluminum, cop- per, nickel) and graphite foam. These foams can have porosities exceeding 90%. They are composed of cells and ligaments that form pores or windows, which is shown in Figure 1. Many of these highly-porous media, such as well-produced aluminum foam made by casting over polymeric pre-forms, are practically isotropic and have uniform average ge- ometrical properties [1,2]. There are a few thermal advantages of metal foams. The ad- vantages stem from their high solid-phase conductivities, very large surface area (up to 10,000 m 2 /m 3 ) [3–5], and their good permeability, which is in the order of 10 −8 m 2 [6–9]. Additionally, the foams’ internal structure causes vigorous mixing, which augments con- vection heat transfer. Thermal applications of metal foams have been sought in compact heat exchangers [10–14], the thermal management of fuel cells [15,16], and high-power batteries [17]. Combining aluminum foam with phase change materials caused a 50% tem- perature drop and provided a uniform temperature of Li-Ion batteries [18]. The combina- tion has been considered for the cooling of portable [19,20] and other electronics [21,22]. Citation: Dukhan, N. Equivalent Parallel Strands Modeling of Highly-Porous Media for Two-Dimensional Heat Transfer: Application to Metal Foam. Energies 2021, 14, 6308. https://doi.org/10.3390/en14196308 Academic Editors: Moghtada Mobedi and Kamel Hooman Received: 6 July 2021 Accepted: 30 September 2021 Published: 2 October 2021 Publisher’s Note: MDPI stays neu- tral with regard to jurisdictional claims in published maps and institu- tional affiliations. Copyright: © 2021 by the author. Li- censee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and con- ditions of the Creative Commons At- tribution (CC BY) license (http://crea- tivecommons.org/licenses/by/4.0/).