Estimation of effective thermal conductivity enhancement using foam in heat exchangers based on a new analytical model

Abstract

-Thermal performance of open-cell metal foam has been investigated under low Reynolds number by comparing the heat transfer coefficient and thermal conductivity for the flow through a packed channel of high porosity metal foam to that of an open channel. In the case of Al-Air at porosity 0.971, the ratio of heat transfer coefficients is estimated to be 18.5 when the thermal conductivity ratio of foam matrix to fluid conductivity is 130. This demonstrates that the use of foam in the structure of conventional air coolers increases effective thermal conductivity, heat transfer coefficient and thermal performance considerably. To overcome the drawbacks of previous models, a new model to describe the effective thermal conductivity of foam was developed. The model estimates effective thermal conductivity based on a non-isotropic tetrakaidecahedron unit-cell and is not confined only to isotropic cases as in previous models. Effective thermal conductivity is a function of foam geometrical characteristics, including ligament length (L), length of the sides of horizontal square faces (b), inclination angle that defines the orientation of the hexagonal faces with respect to the rise direction (θ), porosity, size, shape of metal lump at ligament intersections and heat transfer direction. Changing dimensionless foam ligament radius or height (d) from 0.1655 to 0.2126 for Reticulated vitreous foam -air (RVC-air) at θ= π 4 and dimensionless spherical node diameter (e) equal to 0.339 raises effective thermal conductivity by 31%. Moreover, increasing θ from π 4 to 0.4π for RVC-air at d=0.1655 and e=0.339 enhances effective thermal conductivity by 33%.

On the effective thermal conductivity of aluminum metal foams: Review and improvement of the available empirical and analytical models

“…3(b). In the literature, several analytical models are developed for 3D tetradecahedron unit cells [8,48,[74][75][76][77]. The original model of Boomsma and Poulikakos [8] was found to be imprecise by Dai et al [48]: in fact, beside a geometrical and an analytical error, its implementation fails to produce the published results.…”

“…(61). A non-isotropic tetrakaidecahedron unit-cell with spherical nodes was used by Haghighi and Kasiri [77,78] for high porosity (ε > 0.97 metal foams). Their aim was to account for the variation of eff k with the heat transfer direction.…”

A Model of Moist Polymer Foam and a Scheme for the Calculation of Its Thermal Conductivity

“…The main part of the polymer is located inside straight bars with a practically constant cross-section, with a slight increase in thickness in the nodes usually caused by the connection of bars. Therefore, for the determination of the thermal conductivity of rigid polymer and other foams (ceramic, metallic), regular and irregular polyhedrons were used [3,4,10,11]. Particular attention is drawn by the latest approach, in which a special method (Voronoy) was used to model the structure of the cellular material [10].…”

Multi-scale design of novel materials for emerging challenges in active thermal management: Open-pore magnesium-diamond composite foams with nano-engineered interfaces

“…is strongly related with pore geometry characteristics [11,16] and performs better as the number of pores lowers [10], as does the thermal conductivity [16]. For the forthcoming generation of materials for active thermal management, it seems consequently necessary to work in two directions: i) on the one hand, we must consider denser foam materials capable of combining a high heat transfer coefficient, while maintaining sound thermal conductivity ( [11] was demonstrated the good performance in the active cooling of aluminum foams with porosities within the 66-69% range); ii) on the other hand, the foamability of monolithic materials needs to move on to new complex materials based on developments of multiphase and multiscale designs with improved thermal properties.…”