Freezing heat conductivity

Since the soil normally means poorer heat conduction than the rock an unexpected large depth of soil results in a too short borehole. This will lead to under dimensioning and a risk of freezing in the casing. 

Varying rock thermal conduction If there is one type of rock that is conducting more heat than the surrounding rock, the rock with greater heat conduction will stay warmer than the surrounding one. In such cases water would be trapped and overpressure would occur when freezing. 

As the pressure increases from low values, the pressure-dependent term in the denominator of Eq. (101) becomes significant, and the heat transfer is reduced from what is predicted from the free molecular flow heat transfer equation. Physically, this reduction in heat flow is a result of gas-gas collisions interfering with direct energy transfer between the gas molecules and the surfaces. If we use the heat conductivity parameters for water vapor and assume that the energy accommodation coefficient is unity, (aA0/X)dP — 150 I d cm- Thus, at a typical pressure for freeze drying of 0.1 torr, this term is unity at d 0.7 mm. Thus, gas-gas collisions reduce free molecular flow heat transfer by at least a factor of 2 for surfaces separated by less than 1 mm. Most heat transfer processes in freeze drying involve separation distances of at least a few tenths of a millimeter, so transition flow heat transfer is the most important mode of heat transfer through the gas. 

The total pressure during freeze drying may be measured by several methods, though only two are mostly used heat conductivity, and the membrane pressure difference gauge. Their operating principles and their advantages and disadvantages are described below. 

Here w u = 5 1, and the freezing time depends mostly on the heat conductivity of the material. 

To insure an undisturbed water vapor transport (see Section 1.2.4) the leak rate of a freeze-drying plant must allow BTM with sufficient accuracy. This applies for vapor pressures with ice temperatures ranging between -50 and -10 °C corresponding to 0.04—2.5 mbar. The pressure range for DR measurements is normally one decade below the above data and this has to be considered in the specification of the plant. All measurements discussed above have to be carried out with a capacitance vacuum gauge, because these instruments measure pressure independently of the type of gas. All vacuum gauges based on the change of heat conductivity as a function of pressure show a result which depends not only on the pressure of the gas mixture but also on the type of gas. Leybold AG [1.67] indicate that for instruments based on heat con-... 

After freezing, the time to sublimate the solvent is given by the drying expressions in Tables 8.3 and 8.4, where the enthalpy of vaporization for drying is replaced by the enthalpy of sublimation. The enthalpy of sublimation is often equal to the sum of the heats of fusion and vaporization [16]. The enthalpy of sublimatian is also substituted for the enthalpy of vaporization in the Clausius Clapeyron equation (8.9) required for the calculation of the solvent partial pressure. The same rate determining steps of boundaiy layer mass transfer and heat transfer as well as pore diffusion and porous heat conduction are applicable in sublimation. 

Cho, S.H. Sunderland, J.E. Heat conduction problems with melting or freezing. J. Heat Transfer 91 (1969) 421-426... 

Besides temperature (Figure 5a), the cold and warm scenarios differ by the structure of the snowpack. In both cases, the snow water equivalent have the same temporal evolution 2 cm at the end of October, 11 cm at the end of January and 15.7 cm in late April. Stratigraphies and heat conductivities are very different. In the cold scenario, depth hoar layers of low densities (0.21 to 0.26 g.cm O alternate with denser windpacks (0.38 to 0.48). Transient layers of fresh snow and of faceted crystals are also present. values range from 0.06 W.m K for aged depth hoar to 0.46 W.m K for dense windpacks. In the warm scenario, two melt-freeze layers (densities 0.40 to 0.55) alternate with hard windpacks (0.34 to 0.41) while layers of fresh snow are sometimes included in the mean monthly stratigraphies, kr values are 0.45 and 0.63 W.m K for the melt-freeze layers and range from 0.36 to 0.48 W.m K for dense windpacks. Recent snow has values around 0.2 W.m lC Overall, the warm snowpack has a greater heat conductivity than the cold one. 

Under conditions typical of competitive speedskating, frictional melting, squeeze flow and heat conduction into the ice all play an important role in determining skate blade lubrication. Pressure-induced freezing point depression and the quasi-liquid layer are accounted for in the model, but they play only a minor role in determining the kinetic ice friction coefficient. 

Another example is a method of increasing heat conduction to accelerate the freeze drying of meat. Spikes of metal in the frozen meat conduct heat more rapidly into the insides of the meat. 

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