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This study investigates the effect of heat conduction through the support fiber on a droplet's evaporation in a weakly convective flow. Experimentally, a droplet of n-heptane or n-hexadecane with an initial diameter of 700 or 1000 μm was suspended at the tip of a horizontal or vertical quartz fiber (diameter 50, 150, or 300 μm) to evaporate in an upward hot gas flow (at 490 or 750 K). A simple one-dimensional model of transient conduction is formulated in combination with evaporation of the droplet. The calculations agree well with the experiments. In general, heat conduction through the fiber enhances evaporation, with a stronger effect for a lower gas temperature and a thicker fiber. However, the total heat inputs are attenuated when the fiber's diameter is 300 μm. Orientation of the fiber is unimportant. Also, the evaporation rate is enhanced in an oxygen-containing gas flow, due to the additional heating from oxidation around the droplet.

This study aims to solve the discrepancies between the theoretical and experimental results for droplet evaporation. In the literature, all the experiments for microgravity droplet evaporation have been conducted in a hot furnace with the droplet suspended by a fiber. We propose that the discrepancies result from the fact that current theoretical models ignored the conduction into the droplet through the fiber and the liquid-phase absorption of the radiation from the furnace wall. For verification, we formulate a comprehensive model with the effects of fiber conduction and liquid-phase radiative absorption accounted for. For the droplet size variation and evaporation rate constant, good agreement is found between our calculations and the experimental data of H. Nomura, Y. Ujiie, H.J. Rath, J. Sato, M. Kono [Proceedings of 26th Symposium (Int.) on Combustion, 1996, pp. 1267–1273]. Radiative absorption and fiber conduction enhance the evaporation rate significantly. At a low temperature of 470 K, the discrepancies are mainly due to the additional fiber conduction, while at a high temperature of 750 K, the liquid-phase radiative absorption becomes mainly responsible.

The effect of anisotropy on transport phenomena in anisotropic porous media is studied in this paper. For convenience, a bank of circular cylinders which can be treated as an anisotropic porous medium is employed such that both Darcy-Forchheimer drag and effective thermal conductivity can be accurately determined. Two problems including a forced flow and a natural convection are illustrated to investigate the effect of anisotropy on fluid flow and heat transfer through a bank of circular cylinders. The solutions reveal that inclination of the cylinder bundle could give rise to an influence of more than 100% on the heat transfer rate for both forced convection and natural convection. Hence, the anisotropy of an anisotropic porous medium should not be ignored.

Based on the microscale temperature, the effective thermal conductivity in the principal direction of an anisotropic porous medium is evaluated. A correlation of the effective thermal conductivity then is employed to predict the volume-averaged temperature of a two-dimensional nonhomogeneous anisotropic porous medium. Through the example, the present model is found to possess an excellent performance even when the principal direction of the anisotropic medium is not parallel to the physical coordinates. The results also reveal that using the classic mixing rule could lead to a significant error when the thermal conductivity ratio of the solid and fluid is large. The present numerical procedure is believed to be able to determine the effective thermal conductivity for most porous media as long as their microstructure is regular and known.

In the present investigation, an incompressible fluid flow across a bank of circular cylinders is studied and modeled as a non-Darcy flow through a porous medium. The continuity equation and the momentum equation in pore scale are solved on a Cartesian grid system. To circumvent the numerical difficulties arising from the flow domain of irregular shape, the weighting function scheme along with the APPLE algorithm and the SIS solver is employed. The Darcy-Forchheimer drag is then determined from the resulting volumetric flow rate under a prescribed pressure drop. The result indicates that the permeability approaches zero at the particular porosity of 0.2146 when the fluid flow across the cylinders becomes impossible. In addition, the pressure drag (Forchheimer drag) is found to contribute a significant resistance at large porosities and/or large granule Reynolds numbers. A correlation of Darcy-Forchheimer drag is proposed for 0.2146 ⩽ e ⩽ 1 and 0 ⩽ Red ⩽ 50.