Thermal diffusion depth

The thermal diffusion depth is also related to the modulation frequency ... 

A discussion of surface analysis requires a review of the depth being sampled during PA-FTIR spectroscopy. The depth being sampled during PA-FTIR analyses of rubbers is the thermal diffusion depth (Dt). This is a function of the thermal diffusivity of the sample, the wavenumber, and the mirror velocity. 

Table 2.2 Thermal diffusion depth as a function of mirror velocity (for thermal diffusivity = 1.3 x 10 3) ...

This distance or a multiple thereof is generally known as the thermal diffusion distance for the particular problem and is a handy quantity to use when scaling the effects of laser heating. It is often useful to know how the optical absorption depth compares with the thermal diffusion distance during a laser irradiation. To see the meaning of the thermal diffusion depth more clearly, consider the following particular solutions of Eq. (32) ... 

When a is very large or the optical absorption depth 0 is very small compared to the thermal diffusion depth (/cip) /. Here ip is the duration of the irradiation. 

The constant modulation frequency also produces a thermal diffusion depth which is independent of wavelength and thus allows more straightforward interpretation of spectral depth profiling data from heterogeneous samples [54],... 

This definition is in terms of a pool of liquid of depth h, where z is distance normal to the surface and ti and k are the liquid viscosity and thermal diffusivity, respectively [58]. (Thermal diffusivity is defined as the coefficient of thermal conductivity divided by density and by heat capacity per unit mass.) The critical Ma value for a system to show Marangoni instability is around 50-100. 

Thermal imaging is sensitive to iafrared radiation that detects temperature changes over the surface of a part when heat has been appHed. Thermal diffusion ia a soHd is affected by variatioa ia composition or by the preseace of cracks, voids, delamiaatioas, etc the effects are detected by surface temperature changes. Defects cannot be detected if their depth below the surface is more than two to three times their diameter. Nondestmctive testing has been primarily used for composites and analysis of adhesive bonds or welds. Several studies are documented ia the Hterature (322—327). 

Less pronounced thermal diffusion provides better lateral and depth resolution and is the basis of successful application of femtosecond pulses in material processing and microstructuring [4.231, 4.232]. All-solid-state femtosecond lasers with a pulse duration of 100-200 fs and a pulse energy of approximately 1 mj have recently become commercially available [4.233, 4.234]. 

A large block of material of thermal diffusivity Du — 0.0042 cm2/s is initially at a uniform temperature of 290 K and one face is raised suddenly to 875 K and maintained at that temperature. Calculate the time taken for the material at a depth of 0.45 m to reach a temperature of 475 K on the assumption of unidirectional heat transfer and that the material can be considered to be infinite in extent in the direction of transfer. 

In addition, the thermal diffusivity of the soil at both locations varies from a = 10 to 0 = 10 m /s. The post hole depth must be below the frost line, so that we do not have frost heave on our posts. The frost line would be at the depth where temperature never goes below freezing, T = 0°C. We should set the cosine term from equation (E4.2.2) to -1 and set the temperature to 0°C to determine this depth ... 

T = (Dq2) 1 is the collective diffusion time constant, DT the thermal diffusion coefficient. In Eq. (18), the low modulation depth approximation c( M c0, resulting in c(x,t)(l-c(x,t)) c0(l-c0)y has been made, which is valid for experiments not too close to phase transitions. Eqs. (16) and (20) provide the framework for the computation of the temperature and concentration grating following an arbitrary optical excitation. 

For illustrative purposes a thermal diffusivity of 1.3 x 10 3 cm2/s is often used as being typical of rubber and polymers. Some values from the literature for various materials are given in Table 2.1. Using the value of 1.3 x 10"3 it can be calculated that a depth of 3 to 11 Jim is being sampled at 2000 cm"1 as indicated in Table 2.2. This is an order of magnitude greater than that sampled by ATR techniques. 

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