A synthesis of fluid and thermal transport models for metal foam heat exchangers Shadi Mahjoob, Kambiz Vafai * Mechanical Engineering Department, University of California, Riverside, CA 92521, USA Received 24 October 2007; received in revised form 16 December 2007 Available online 28 March 2008 Abstract Metal foam heat exchangers have considerable advantages in thermal management and heat recovery over several commercially avail- able heat exchangers. In this work, the effects of micro structural metal foam properties, such as porosity, pore and fiber diameters, tor- tuosity, pore density, and relative density, on the heat exchanger performance are discussed. The pertinent correlations in the literature for flow and thermal transport in metal foam heat exchangers are categorized and investigated. Three main categories are synthesized. In the first category, the correlations for pressure drop and heat transfer coefficient based on the microstructural properties of the metal foam are given. In the second category, the correlations are specialized for metal foam tube heat exchangers. In the third category, cor- relations are specialized for metal foam channel heat exchangers. To investigate the performance of the foam filled heat exchangers in comparison with the plain ones, the required pumping power to overcome the pressure drop and heat transfer rate of foam filled and plain heat exchangers are studied and compared. A performance factor is introduced which includes the effects of both heat transfer rate and pressure drop after inclusion of the metal foam. The results indicate that the performance will be improved substantially when a metal foam is inserted in the tube/channel. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Metal foams are a class of porous materials with low densities and novel thermal, mechanical, electrical and acoustic properties [1]. The foams are lightweight, offering high strength and rigidity, nontoxic structure, high surface area and recyclable which improve energy absorption and heat transfer in thermal applications, such as heat exchang- ers. The rate of heat transfer is enhanced by conducting the heat to the material struts, which have a large accessible sur- face area per unit volume, along with high interaction with the fluid flowing through them [2–7]. Normal foam liga- ments in the flow direction results in boundary layer disrup- tion and mixing. Turbulence and unsteady flow occur for pore-scale Reynolds number greater than 100 [8]. The effect of thermal dispersion is essential for a number of applica- tions in the transport processes. Vafai et al. have shown that the effect of transverse dispersion is much more important than the longitudinal dispersion [9,10]. The induced turbu- lence and dispersion cause further enhancement in heat transfer and increase performance and efficiency of the heat exchanger considerably [11,12]. In addition, flow paths through the foam are interconnected, which makes the flow available in all areas. As such, utilizing the metal foam leads to smaller and lighter heat exchangers. Metal foams have considerable applications in multi- functional heat exchangers [13–17], cryogenics [18], com- bustion chambers, cladding on buildings, strain isolation, buffer between a stiff structure and a fluctuating tempera- ture field, geothermal operations, petroleum reservoirs, compact heat exchangers for airborne equipments, air- cooled condenser towers and cooling systems [19], high power batteries [20], compact heat sinks for power elec- tronics and electronic cooling [17,21–24], heat pipes [25,26] and sound absorbers [27–30]. Metal foams can be classified as porous media with typ- ically high porosity that consists of tortuous, irregular 0017-9310/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2007.12.012 * Corresponding author. Tel.: +1 951 827 2135; fax: +1 951 827 2899. E-mail address: vafai@engr.ucr.edu (K. Vafai). www.elsevier.com/locate/ijhmt Available online at www.sciencedirect.com International Journal of Heat and Mass Transfer 51 (2008) 3701–3711