Detailed and simplified models for evaluation of effective thermal conductivity of open-cell porous foams at high temperatures in presence of thermal radiation Miguel A.A. Mendes a,⇑ , Prabal Talukdar b,⇑ , Subhashis Ray a,⇑ , Dimosthenis Trimis a a Institute of Thermal Engineering, Technische Universität Bergakademie Freiberg, Gustav-Zeuner-Strasse 7, D-09596 Freiberg, Germany b Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India article info Article history: Received 24 July 2013 Received in revised form 23 September 2013 Accepted 27 September 2013 Available online 23 October 2013 Keywords: Porous medium Open-cell foam Conduction–radiation Effective thermal conductivity Radiative transport equation Finite volume method abstract Simulations of coupled conduction–radiation heat transfer through open-cell porous foams have been performed in this article in order to evaluate the effective thermal conductivity (ETC) at high tempera- tures due to combined effects. For this purpose, the complex structure of foams has been generated using the knowledge obtained from 3D Computer Tomography (CT)-scan images and both detailed and simpli- fied homogeneous modes have been employed during the present investigation. For detailed models, in addition to the energy conservation equation, the radiative transfer equation has been solved in order to obtain the distribution of radiation intensity using the blocked-off region approach, which can handle the voxel information acquired from the CT-scan data. Proposed simplified models, on the other hand, are based on homogenization approach and the performance of these simplified models has been compared with the reference model in terms of their accuracy. Simplified models mainly require information about the ETC due to pure conduction calculated from detailed 3D simulation and the extinction coefficient estimated from the CT-scan data using the image processing technique. Extensive parametric study has been conducted and the analysis of results show that ETCs estimated from the simplified models rea- sonably agree with those obtained from the most accurate model, depending upon the chosen value of extinction coefficient. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Developmental efforts on producing varieties of ceramic foams have increased significantly in the recent years due to their ever- increasing applications in numerous technological fields. The unique structural properties, such as large surface area to volume ratio of metal/ceramic foams (porous media), makes it very useful for many industrial applications, especially where heat transfer is of primary concern. In this respect, the evaluation of effective ther- mal conductivity (henceforth will be referred to as the ETC, throughout the paper) of porous foams has become a major requirement for accurate prediction of heat transfer behaviour of many systems, such as heat exchangers, thermal insulators or com- bustion systems, to name a few. The complex morphology of foam structures plays an important role in the heat transfer characteris- tics and consequently, the ETC can be quite different for different foams, even with same porosity. If the heat transfer takes place at a high temperature, the ETC has a larger contribution from ther- mal radiation and hence an accurate modelling of radiation heat transfer becomes inevitable. Unfortunately, however, the morphology of porous media is generally quite complex and resolving these structures with a numerical model has always been a challenging task. Available lit- erature on modelling of heat transfer through porous foams can be divided broadly into two categories, (i) a detailed model, consider- ing the complex structure of the foam up to a certain resolution and (ii) use of a homogeneous model with effective thermo-phys- ical and optical properties, calculated using some form of correla- tions or directly measured from experiments. Nowadays, a wide variety of approaches can be found under these two main classifi- cations, which are discussed in the following paragraphs. As far as detailed models are concerned, since actual foam structures are quite complex in nature, several researchers at- tempted to synthetically generate some equivalent regular struc- tures that can reasonably approximate real foams for the purpose of heat transfer simulations. As reported in the literature, ceramic and metallic foam structures can be represented, for example, with cubic [1,2], dodecahedral or tetrakaidecahedral structures. It was 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.09.071 ⇑ Corresponding authors. Tel.: +49 3731 393946 (M.A.A. Mendes), +91 11 26596337 (P. Talukdar), +49 3731 393947 (S. Ray). E-mail addresses: miguel.mendes@iwtt.tu-freiberg.de (M.A.A. Mendes), prabal@- mech.iitd.ac.in, prabal.talukdar@gmail.com (P. Talukdar), ray@iwtt.tu-freiberg.de, juhp_sray@yahoo.co.in (S. Ray). International Journal of Heat and Mass Transfer 68 (2014) 612–624 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt