Thermally thick/thin

The thermally thin case holds for d of about 1 mm. Let us examine when we might approximate the ignition of a solid by a semi-infinite medium. In other words, the backface boundary condition has a negligible effect on the solution. This case is termed thermally thick. To obtain an estimate of values of d that hold for this case we would want the ignition to occur before the thermal penetration depth, <5T reaches x d. Let us estimate this by... 

We will develop an analytical formulation of the statement in Equation (8.2). This will be done for surface flame spread on solids, but it can be used more generally [1], As with the ignition of solids, it will be useful to consider the limiting cases of thermally thin and thermally thick solids. In practice, these solutions will be adequate for first-order approximations. However, the model will not consider any effects due to... 

The solution to this boundary value problem was approximated by Rosencwaig and Gersho for six different cases (4) one of which, a thermally thick but optically thin sample, often applies to layers adsorbed on heterogeneous catalysts. The photoacoustic signal arises from the chemisorbed species and the support. 

As observed earlier, the material thickness plays a significant role in the rate of flame spread, either through the mode of heat transfer or through the losses that can occur through the solid. Materials are generally defined as thermally thin, where Sp = L or thermally thick, where 5p thermal thickness 8p needs to be carefully defined, and generally, is given by... 

The diffusivity, a2, is subsequently determined under the condition that the intercepts of the linear fits for the thermally thick and thin conditions are equal. For the PA6 nanocomposite, when the diffusivity is equal to 0.9 x 10 7m2/s, the intercepts are almost the same at about 11.5kW/m2. These intercepts are equal to the 0.64 fraction of the critical heat flux (below which there is no ignition) for ignition [21], and thus the critical heat flux can be calculated equal to 11.5/0.64 = 17.9 kW/m2. The ignition temperature can then be calculated by considering the critical heat flux equal to surface reradiation and convection losses ... 

Here, L is the material thickness, T is the tlame temperature, v, is the velocity of the incoming oxidant flow if there is no external supply, v, is controlled by natural convection. A solid fuel which is heated throughout its depth prior to flame arrival is said to be thermally thin. If the thickness (L) of the material is more than that of the layer heated prior to flame arrival the material is said to be thermally thick. 

In small-scale laboratory tests (characteristic sample dimensions of less than 0.2-0.3 m), conduction or convection are the dominant heat transfer routes. It has been shown horizontally or vertically, that 90% of the heat generated in a laminar flame spreading along a thermally thick PMMA sample is transferred by conduction across the condensed phase, and only about 10% by convection through the gas phase. In the case of thermally thin samples, on the other hand, the heat is predominantly transferred through the gas phase, independent of the flame propagation direction... 

At the sample stage, a flat mirror is mounted perpendicular to the sample on a rotation stage. As part of the laser beam is reflected by the mirror, it interferes with the nonreflected part to form an interference pattern on the photoresist. The period P is given as P = where 6 is the incident angle [44]. After lithography and baking, the templates are then transferred into an electron-beam or a thermal evaporation thin film deposition system for metallization. As the thickness of the metal film is larger than the skin depth of metal, the metallic arrays are considered as semi-infinitely thick. 

Preliminary experiments showed that when thermally stabilized thin films (80 p thickness) of vinyl chloride-methyl vinyl ketone copolymers were subject to UV radiation they became brittle without color formation. When the ketone concentration in the ci olymer was approximately 6 mol-%, the time to brittleness in the Accelerometer was less than 20 hr, whereas 40 to 50 hr were required if the ketone concentration was only 2%. Samples of PVC homcpolymer, identically stabilized, were photolyzed along with the copolymers. No color or chemical change was apparent in these samples, even after 100 hr photolysis. 

Figure 18.8. Calculated thermal conductivity (thick line, left-hand y-axis) and thermal diffusivity (thin line, right-hand y-axis) of polystyrene as a function of the temperature.

Minimum thicknesses of the oil-bearing bed are based on limits of tolerable heat losses that take place into the overlying and underlying strata. However, in oil fields with multiple petroliferous horizons the indicated minimum thicknesses of individual oil-beaiing beds may be even smaller. In these cases, the heat lost from one thermally treated thin horizon may be effectively recaptured by the next overlying or underlying oil-bearing stratum. 

If the thickness of a solid exposed to heat flux is higher than it is considered thermally thick otherwise it is thermally thin. The critical thickness depends on the thermal properties of the material (a) and on the duration of exposure (t). 

The interaction between the thermal diffusion length, optical absorption length, and sample thickness (/) is used to describe the photoacoustic properties of a sample. Thus, a sample is described as opaque if the optical absorption length is less than the sample thickness, and light cannot be transmitted through the sample. However, when ii and /is are greater than I the sample is described as optically and thermally thin, respectively, and when jj, and /is are less than I the sample is described as optically and thermally thick, respectively. 

Thermal Response Parameter (TRP) in VJ/xv for thermally thin polymer and in kW-s / m for thermally thick polymer... 

Polymer heat flux (kW/m ) Thermally thick (kW-s Vm ) Thermally thin (kJ/m )... 

Fire scientists tend to classify materials as being either thermally thick or thermally thin. By thermally thin means that heat absorbed on one surface of the material will penetrate its thickness sufficiently rapidly, so that there will be no significant temperature gradient through the material depth.i Textiles in the form of single-layered fabric assemblies are usually dimensionally thin and hence could be classed as thermally thin materials. 

Figure 13 shows representative HRR histories for thermally thick and thin samples of polymers that gasify completely or form a char during burning. It is apparent that none of these heat release rate histories show a constant (steady-state) value of heat release rate over the burning interval as presumed in equation 45. 

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