Thermal inertia

On quiescent planets or satellites without substantial atmospheres, the surface temperature is determined by a balance between incident solar flux, thermally emitted radiation, and conductive heat transport into or out of the opaque surface. By measuring the surface temperature and the bolometric albedo the absorbed and emitted radiation can be found and the conductive flux into the solid body derived. After sunset or dining a solar eclipse the cooling rate of the surface depends on the thermal inertia of the subsurface layers. A study of such cooling rates provides a sensitive means of discriminating between powdery, sandy, or solid rock surfaces. We now review the theory behind such an analysis, and discuss examples of thermal inertia measurements. 

The theory of thermal conduction in solids was first applied to lunar studies by Wesselink (1946). The basic equation of heat conduction is 

To separate the variables we take the usual Bernoulli product approach, 

In anticipation of the periodic nature of solar illumination we use a periodic function for the time factor. In general, solar radiation is not a simple sinusoidal term, but must be expressed by a Fourier series. To simplify notation we treat only the lowest diurnal frequency of the series higher order terms can be considered later by superposition of solutions. Substituting Eq. (8.5.5) into Eq. (8.5.4) leads to 

Since the exponential term must approach zero at large depths, only the negative root is acceptable, so that 

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Another popular approach to the isothennal (canonical) MD method was shown by Nose [25]. This method for treating the dynamics of a system in contact with a thennal reservoir is to include a degree of freedom that represents that reservoir, so that one can perform deterministic MD at constant temperature by refonnulating the Lagrangian equations of motion for this extended system. We can describe the Nose approach as an illustration of an extended Lagrangian method. Energy is allowed to flow dynamically from the reservoir to the system and back the reservoir has a certain thermal inertia associated with it. However, it is now more common to use the Nose scheme in the implementation of Hoover [26]. 

Usually this type of anemometer does not provide information on the flow direction. Vice versa, the. sensors are made as independent of the flow direction as possible—omnidirectional. This is an advantage for free-space ventilation measurements, as the flow direction varies constantly and a direction-sensitive anemometer would be difficult to use. Naturally, no sensor is fully omnidirectional, but satisfactory constructions are available. Due to the high sensor thermal inertia, this type of anemometer is unsuitable for high-frequency flow fluctuation measurement. They can be used to monitor low-frequency turbulence up to a given cut-off frequency, which depends on the dynamic properties of the instrument. 

Leung, J. C., Fauske, H. K and Fisher, H. G., Thermal Runaway Reactions In A Low Thermal Inertia Apparatus, Ther-mochimica Acta, 104, 13-29, 1986. 

The thermal inertia of the wall is negligible, i.e., we assumed no phase shift between temperature of the channel wall and the heater. 

Numerous materials have been used to fabricate open tubular columns. Most early studies were conducted using stainless steel tubing and later nickel tubing of capillary dimensions [147-149]. These materials had rough inner surfaces (leading to non-uniform stationary phase films), metal and oxide impurities at their surface which were a cause of adsorption, tailing, and/or decomposition of polar solutes and because their walls were thick, thermal Inertia that prevented the use of fast temperature programming. None of these materials are widely used today. 

The heat capacity (or thermal inertia) of the heating wall is generally higher. 

The differential equations Eqs. (10) and (29)3, which represent the heat transfer in a heat-flow calorimeter, indicate explicitly that the data obtained with calorimeters of this type are related to the kinetics of the thermal phenomenon under investigation. A thermogram is the representation, as a function of time, of the heat evolution in the calorimeter cell, but this representation is distorted by the thermal inertia of the calorimeter (48). It could be concluded from this observation that in order to improve heat-flow calorimeters, one should construct instruments, with a small... 

In any case, thermal inertia may be decreased but never completely removed (48). Data from heat-flow calorimeters must therefore be recorded in such a way that (1) the total amount of heat produced by the phenomenon under investigation is measured with precision, and (2) the correction of the thermograms is easily performed. 

The development of the theory of heat-flow calorimetry (Section VI) has demonstrated that the response of a calorimeter of this type is, because of the thermal inertia of the instrument, a distorted representation of the time-dependence of the evolution of heat produced, in the calorimeter cell, by the phenomenon under investigation. This is evidently the basic feature of heat-flow calorimetry. It is therefore particularly important to profit from this characteristic and to correct the calorimetric data in order to gain information on the thermokinetics of the process taking place in a heat-flow calorimeter. 

However, for a quantitative kinetic analysis of the calorimetric data, corrections must be applied, because the thermal inertia of the calorimeter, which cannot be completely removed, causes in many cases the blurring of the thermogenesis. Several methods have been proposed, with different levels of sophistication. 

The values of thermal inertia, kpc, used in this study were derived in this way and are listed in Table 1. A full description of the method used to derive these parameters is given in (11.). 

Robert Kern, Pressure-Relief Valves for Process Plants, Chemical Engineering (Feb. 28,1977), p. 187. J. C. Leung, H. K. Fauske, and H. G. Fisher, Thermal Runaway Reactions in a Low Thermal Inertia Apparatus, Thermochimica Acta (1986), 104 13-29. 

The property kpc is the thermal inertia the higher it is, the more difficult it is to raise the temperature of the solid. Let us estimate fpy for typical conditions for a wood product... 

It has also been recognized that micro-structured components, because of their low mass and thermal inertia, are able to offer short response times for unsteady state periodic operations. Micro-reactors have been used successfully for fluorination, oxidations and both heterogeneous [63-65] and homogeneous hydrogenations [66]. A review on gas-liquid micro-structured reactors has been published [67]. The very small material inventory when using micro devices offers another advantage, notably as a laboratory tool for screening applications, kinetics determination and process data acquisition, where the main concern is... 

Test Method Section of Chapter 2 Typical Sample Mass (g) Typical Sensitivity (W/kg) Thermal Inertia Phi-factor Principal Applicationa Data Acquired A=Advantage D=Disadvantageb... 

Isoperibolic instruments have been developed to estimate enthalpies of reaction and to obtain kinetic data for decomposition by using an isothermal, scanning, or quasi-adiabatic mode with compensation for thermal inertia of the sample vessel. The principles of these measuring techniques are discussed in other sections. 

Figure 2.26 represents an example of an ARC plot of the logarithm of the self-heat rate versus the reciprocal temperature. This graph shows the temperature at which a sample or mixture starts to decompose or react measurably, and the rate at which the sample or mixture liberates heat as a function of temperature. In the ARC experiment represented in Figure 2.26, exothermic decomposition or reaction is first observed at 80°C with a self-heat rate of 0.025°C/min. The maximum temperature reached is 142°C with a maximum self-heat rate of 6°C/min. The data must be corrected for the thermal inertia () of the system. 

The VSP is a valuable tool in assessing temperature and pressure data with a relatively small sample in a short period of time. The low thermal inertia cells represent an advantage. A disadvantage is the relatively small contents of the test cell, which requires a good representative sample. Also, there is complexity in applying results to the DIERS technology. 

Detailed Hazard Assessment Low Thermal Inertia (41- factor) Adiabatic Calorimeter A UNDESIRED ATonset ATaDIAB dT/dt dP/dt sadf Tm, tMR estimates Vent sizing data Sample size 100 ml to 1 liter Safe for general laboratory work Good mimic of large-scale runaway Ideal for what-if scenario study... 

Proportion of the heat of reaction that heats the container (thermal inertia, phi factor)... 

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