Abstract
The thermal conductivity measurement of fluid-saturated porous material by transient line source method must consider the effects of natural convection, if the measurement time becomes large. Since the occurrence of natural convection along the vertical needle probe generally enhances the heat transfer rate, the measured thermal conductivity may give a higher value than the true thermal conductivity of the medium. In the present paper the error associated with the convection in a saturated-porous material is studied using a mathematical model and a numerical technique. The variation of flow and temperature field due to different Rayleigh numbers is studied for four different values of slenderness ratio; 48, 96, 240 and 490. In general as the measurement time becomes larger, the effect of convection is more pronounced. For instance, the measurement at t=100 contains only a slightest error, if the Rayleigh number is less than 0.01, and the slenderness ratio of the probe is between 48 and 490. On the other hand, for a fixed value of the Rayleigh number, the convection is felt earlier as the slenderness ratio becomes smaller. For instance, for Ra=1 and h/a=490 the convection deteriorates the measurement only slightly at t=60, but it requires Ra=0.1 or even less for the same amount of error at t=60 if the slenderness ratio is decreased to h/a=48. The general criterion for the maximum allowable measurement time, within which the measurement may contain less than 10% error, is established as a function of Ra and h/a.
