An evaluation of heat transfer coefficients in moist porous media,

Abstract

Heat transfer in moist porous media has been given extensive theoretical consideration. In attempting to define the problem mathematically, either one of two approaches has been followed. There is the mechanistic approach which is based upon the diffusion of vapor and the capillary movement of liquids, and there is the approach which applies the theory of the thermodynamics of irreversible processes. The latter is the more general but both approaches give rise to simultaneous equations for the steady-state flow of matter and energy. These equations contain coefficients which are measures of physical properties of the particular medium under study. In this dissertation two heat transfer coefficients are evaluated: "real" thermal conductivity and "real" thermal diffusivity. Real thermal conductivity is one of the coefficients referred to above and real thermal diffusivity is a coefficient that appears in the equations for the transient flow of heat in moist porous media. Both thermal constants are those that would be obtained if measurements could be made without the interference of moisture transfer. A large-diameter, cylindrical thermal probe was designed and used for evaluation of these real thermal constants. The probe is heated uniformly at a constant rate and as the heat is dissipated in the surrounding medium, the probe temperature is recorded as a function of time. Thermal constants are obtained by comparing a theoretical expression with the experimental data. The theoretical expression includes the probe diameter, the heat capacity per unit length of the probe, and the thermal contact "resistance" between the probe and the surrounding medium. The analysis requires evaluation of the thermal contact resistance from the experimental data and independent determination of the volumetric heat capacity of the surrounding medium. Thermal constants close to real values but which include effects of distillation are obtained from the initial portion of the experimental record. These are then corrected for distillation by subtracting out a small quantity which can be evaluated theoretically. Values of real thermal conductivity and diffusivity were obtained at different moisture contents for 20/30 mesh Ottawa sand and for a sandy loam soil. Real thermal conductivity of the Ottawa sand (with a dry bulk density of approximately 1,7 gms/cm³) increases rapidly from a value of 0.000870 cal/°C/cm/sec when dry to 0.00Lt4 cal/°C/cm/sec at about 15% of saturation. Thereafter it apparently increases at a rate equal to the rate of increase of the volumetric heat capacity of the sand-water system to a value of 0.00755 cal/°C/cm/sec at saturation. Real thermal diffusivity of this material increases from 0.00275 cm²/sec when dry to 0,012 cm²/sec at about 15% of saturation. It remains nearly constant with further increase in water content. In a similar manner, real thermal conductivity of the sandy loam soil (with a dry bulk density of approximately 1.5 gms/cm³) increases rapidly from a value of 0,000605 cal/°C/cm/sec when dry to 0.0036 cal/°C/cm/sec at about 30% of saturation. It then increases at a rate approximately equal to the rate of increase of the volumetric heat capacity of the soil-water system to 0.00595 cal/°C/cm/ sec at saturation. Real thermal diffusivity for this material increases from 0.00223 cm²/sec when dry to 0.0090 cm²/sec at about 30% of saturation. Thereafter it remains essentially constant with further increase in water content. Thus, a single measurement of thermal diffusivity in the saturated sand and soil is sufficient to define real thermal diffusivity over a wide range of moisture contents.