**1. Introduction**

With the rapid development of electronic technology, miniaturization and intelligence have become important directions in the development of contemporary equipment. The size of the electronic devices used in industrial production equipment is gradually decreasing, and the chip achieves a continuous increase in the operating frequency as well as integration density. This leads to a rapid increase in the heat flow density of the chip, and its temperature directly affects the stability of the performance. As a result, higher demands are placed on the thermal design of electronic chips. To ensure the operational stability of electronic devices, higher requirements for the reliability of electronic equipment are required. Through a high standard of thermal design work arrangements, reasonable cooling methods are chosen to ensure that the heat escaping from the device is removed from the surface more quickly and that the temperature around the component is always within the safe operating temperature range.

In recent years, metal porous materials have been used due to their unique properties and the combination of structural and functional material properties [1–3]. Widely used in biological, medical [4–6], aerospace [7] and industrial applications [8–12], the high demand for green materials in various fields has driven the development of metal foam. Porous metal foam structures with high specific surface area, high permeability properties and high mechanical strength are being explored as an alternative material to conventional heat exchangers. In the field of heat transfer [13–16], metal foam holds great promise for applications in multifunctional heat exchangers [17–19], cooling systems [20–23], highpower batteries, compact electronic heat sinks [23–28] and so on. Porous metal foam can significantly reduce the size and mass of equipment when used in heat transfer equipment due to their light mass and low density. They have great potential for application in

**Citation:** Shan, X.; Liu, B.; Zhu, Z.; Bennacer, R.; Wang, R.; Theodorakis, P.E. Analysis of the Heat Transfer in Electronic Radiator Filled with Metal Foam. *Energies* **2023**, *16*, 4224. https://doi.org/10.3390/en16104224

Academic Editors: Marco Marengo, Artur Bartosik and Dariusz Asendrych

Received: 25 January 2023 Revised: 10 May 2023 Accepted: 17 May 2023 Published: 20 May 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

industrial production as well as in related fields such as high technology, gaining more attention and importance.

The use of metal foam as a new compact heat exchanger has been investigated by numerical simulations. Chen et al. [13] presented a three-dimensional numerical simulation to reveal the flow and heat transfer characteristics of a new tube bundle design covered with metal foam. The results showed that tube bundles covered with metal foam with low porosity and low pore density have a strong advantage over bare tube bundles. For example, Kotresha et al. [16] discussed a numerical simulation of a metal foam heat exchanger system performed by a commercial software. The aim is to improve the thermal performance of the heat exchanger by reducing the pressure drop and increasing the heat transfer rate to the maximum.

Metal foam has also been investigated experimentally. Kim et al. and Shen et al. [14,15] found that the use of metal foam significantly reduces the overall thermal resistance compared to a conventional finned heat pipe heat sink. Hsieh et al. [29] experimentally investigated the effects of porosity, pore density (PPI) and air flow rate on the heat transfer characteristics of the aluminum foam heat sinks and found that the increase in porosity and pore density enhanced the non-local thermal equilibrium phenomenon. Liu et al. [30], based on the Reynolds number range of the equivalent spherical diameter of the foam from 32 to 1289, found that the porosity range was 0.87 to all seven types of the aluminum foams, and an empirical Equation was developed to relate the unexpected pressure drop to the unexpected flow rate. Dukhan et al. [31] presented heat transfer measurements within a rectangular block of commercially available aluminum foam subjected to constant heat flow on one side. The temperature profile decays in an exponential fashion as the distance from the heat base increases. Boomsma and Poulikakos [32] experimentally showed that varying the fluid conductivity has a relatively small effect on increasing the effective heat transfer rate.

The heat transfer performance of metal foam under forced convection and natural convection conditions has also been investigated by researchers. Shih et al. [33,34] demonstrated that under impact jet flow conditions for all values of jet–jet spacing, an increase in the pore density was accompanied by an increase in the heat transfer. Bhattacharya et al. [35] investigated forced convection heat transfer in a new finned metal foam heat sink, showing that when fins were added to the metal foam, the heat transfer was significantly enhanced, and the heat transfer coefficient increased with the number of fins until the addition of more fins would lead to the interference with the thermal boundary layer and retard heat transfer. Shen et al. [15] conducted a systematic study and analysis of the thermal and flow characteristics at different air speeds and thermal powers through experiments. It was found that the introduced metal foam significantly reduced the overall thermal resistance by 25.5% compared to a conventional finned heat pipe heat sink.

This paper focuses on the implementation of enhanced heat transfer analysis for metalfilled radiator components with 96% porosity and 10 PPI pore density of copper foam, aluminum foam and 20 PPI pore density of copper foam. The heat transfer performance of the devices at different flow rates and at certain flow conditions is clarified, and the heat transfer geometrical parameters of the metal foam-filled radiators and their heat transfer performance are obtained.
