Sensitivity analysis of effective thermal conductivity of open-cell ceramic foams using a simplified model based on detailed structure

The Effective Thermal Conductivity (ETC) of open-cell porous foams can be predicted from the detailed numerical simulation, considering the complex foam structure obtained from three-dimensional (3D) Computed Tomography (CT)-scan images. An alternative approach could be to consider simplified models for a quick and accurate estimation of the ETC. A model for ETC of open-cell porous foams, using such a simplified approach, has been proposed recently which relies upon a single numerical prediction of the dimensionless ETC under vacuum condition, evaluated using the detailed foam structure obtained from 3D CTscan information. This model is applied in the present study in order to analyze the influence of different parameters, namely the microscopic porosity within the bulk solid material and the direction of heat transfer, on the ETC of open-cell ceramic foams. The present investigation demonstrates that the considered simplified modeling approach offers reasonable accuracy with reduced computational effort for the sensitivity analysis of ETC to different parameters. INTRODUCTION Porous foams are commonly used for a wide range of applications in numerous technological fields due to their special structural and thermo-physical properties. In this respect, the evaluation of their Effective Thermal Conductivity (ETC) has become a major requirement for the accurate prediction of heat transfer behavior of many systems, such as heat exchangers, thermal insulators, combustion systems, evaporators, etc., using homogenization approach [1-3]. The complex morphology of foam structures plays an important role in the overall heat transfer characteristics and hence the ETC can vary substantially among different foams of same material and porosity. Moreover, owing to the very high porosity of foams, total heat transfer can take place by both conduction as well as thermal radiation, particularly when the operating temperature as well as the applied temperature difference are relatively high [4]. The present investigation, however, is restricted only to the conduction heat transfer at room temperature, where the contribution of thermal radiation is seemingly small. The ETC of porous foams can be numerically predicted from simulations of conduction heat transfer through them due to imposed temperature gradient by considering their detailed morphology. The structural information of foams, required by these simulations, nowadays can be obtained from the high resolution 3D CT-scan images. Such detailed approach is generally quite accurate, as well as time consuming. Therefore, in order to achieve a reasonable compromise between the accuracy and the computational effort, an alternative approach is to use simplified models for quick and accurate evaluation of the ETC, ideally presenting a wide range of applicability. A review on models for the ETC, presenting different levels of complexity, has been presented by Coquad et al. [5]. Recently, a model for evaluating the ETC of opencell porous foams, using a simplified approach with one adjustable parameter, has been proposed by Mendes et al. [6]. This, parameter appearing in an explicit expression for the ETC, can be uniquely determined from a single numerical prediction of the dimensionless ETC under vacuum condition (made dimensionless with respect to the thermal conductivity of solid phase), based on the detailed geometry of foam. Quite obviously, evaluation of the dimensionless ETC under vacuum condition requires significantly reduced computational time, which scales at least to the order of porosity of foams and owing to the definition, the result is independent of the thermal conductivity of solid phase. Most importantly, as has been demonstrated by Mendes et al. [6], the dimensionless ETC under vacuum condition implicitly contains the relevant quantitative morphological