Fujio Kuwahara

A unified integral solution procedure has been proposed to analyze all possible Darcian local thermal nonequilibrium (LTNE) free, forced, and mixed convective boundary layer flows, commonly encountered in porous media engineering applications. The heated body may be arbitrarily shaped, and its temperature may vary over the surface. The integral energy equation for the solid phase yields an algebraic equation between the dimensionless fluid thermal boundary layer thickness and its ratio to the solid-phase counterpart, while the integral energy equation for the fluid phase reduces to a first order ordinary differential equation in terms of the dimensionless fluid thermal boundary layer thickness. This set of the equations for determining the local Nusselt number of our primary interest proved to be valid for all possible Darcian cases of LTNE free, forced, and mixed convective boundary layer flows over an arbitrarily shaped nonisothermal body in a fluid saturated porous medium. Asymptotic expressions for the cases of arbitrary shapes were also obtained analytically for both leading edge and far downstream regions. The results are found to agree well with available direct numerical integration results. Furthermore, the regime map has been constructed to show the boundary layer transition point from the LTNE to equilibrium. The proposed unified method is found quite useful when designing thermal engineering systems associated with fluid saturated porous media.

Estimating and increasing limiting current density (LCD) levels is of fundamental importance for the development of electrodialysis (ED) systems, and it is becoming clear that the use of porous spacers can significantly increase such LCD levels. In this study, a three-dimensional numerical simulation was proposed for evaluating the mass transfer within a porous spacer unit cell and for estimating LCD levels. It was found that our proposed method is effective for estimating the minimum value of an LCD, which is a significant factor related to the safe operation of ED systems. Furthermore, it was found that increasing the minimum effective Sherwood number provides a key to increasing LCD levels. Porous spacer design guidelines were proposed based on the numerical simulation results, after which a new spacer was introduced, designed according to those guidelines. It was found that flow disturbances on the membrane caused by porous spacer structures can lead to increases in effective Sherwood numbers and that LCD levels could be increased by eliminating the flow stagnation behind the structures on the membrane. The LCD of our new spacer was found to be higher than that of the spacers with the highest LCD levels in use at present. Therefore, we can conclude that the proposed design guidelines are effective for increasing LCD levels.

Fully developed forced convective heat transfer within a channel filled with a functionally graded metal foam matrix was investigated analytically for the case of constant wall heat flux. A series of functionally graded metal foam matrices of the same mass (i.e., the same solidity) were examined in views of their heat transfer performances. The porosity either increases or decreases toward the heated wall following a parabolic function. Among the metal foam matrices of the same mass, the maximum heat transfer coefficient exists for the case in which the porosity decreases toward the heated wall (i.e., more metal near the wall). The heat transfer coefficients in such channels filled with a functionally graded metal foam matrix are found 20–50% higher than that expected from the increase in the effective thermal conductivity. Hence, functionally graded metal foam matrices are quite effective to achieve substantially high heat transfer coefficient with an acceptable increase in pressure drop.

A porous media approach was proposed to investigate the characteristics of the bifurcating airflow and mass transfer within a lung. The theory of porous media was introduced in order to deal with a large number of bifurcations and a vast scale difference resulting from bifurcations. Upon introducing a two-medium treatment for the air convection and the diffusion in its surrounding wall tissue, the oxygen mass transfer between the inhaling air and the tissue was considered along with the effects of the blood perfusion on the mass transfer within the tissue. The overall mass transfer resistance between the inlet of the trachea and the blood in the capillaries was obtained on the basis of the porous media approach. The analysis reveals that there exists the optimal number of the bifurcation levels, namely, 23, that yields the minimum overall mass transfer resistance for the mass transport from the external air to the red blood cells. The finding is consistent with Bejan's constructal law, namely, that for a flow system to persist in time, it must evolve in such a way that it provides easier access to its currents.