Heat diffusivity

The eombination in a compact system of an infrared sensor and a laser as excitation source is called a photothermal camera. The surface heating is aehieved by the absorption of the focused beam of a laser. This localisation of the heating permits a three-dimensional heat diffusion in the sample to be examined. The infrared (IR) emission of the surface in the neighbourhood of the heating spot is measured by an infrared detector. A full surface inspection is possible through a video scanning of the excitation and detection spots on the piece to test (figure 1). 

Along with a constant velocity zone (Zone 1), there is a constant temperature zone in a jet. Heat diffusion in a jet is more intense than momentum diffusion therefore the core of constant temperatures fades away faster than that of constant velocities and the temperature profile is flatter than the velocity profile. Thus the length of the zone with constant temperature (Fig. 7.23) is shorter than the length of the constant velocity zone (Zone I... 

In this section we discuss the basic mechanisms of pattern formation in growth processes under the influence of a diffusion field. For simphcity we consider the sohdification of a pure material from the undercooled melt, where the latent heat L is emitted from the solidification front. Since heat diffusion is a slow and rate-limiting process, we may assume that the interface kinetics is fast enough to achieve local equihbrium at the phase boundary. Strictly speaking, we assume an infinitely fast kinetic coefficient. 

Measurements of axial mixing in a hydrogen-a-methylstyrene bubble-column have been reported by Farkas (FI). Measurements of axial heat diffusion were carried out, the diffusion coefficient being of the order of 7.5 cm2/sec at a nominal gas velocity of about 4 cm/sec, a value that is in good agreement with some of the results of Siemes and Weiss. 

Heat diffuses much like mass and is governed by similar equations. The temperature analog of Equation (8.12) is... 

Weisz, P. B. and Hicks, J. S., The behaviour of porous catalyst particles in view of internal mass and heat diffusion effects, Chem. Eng. Sci., 17, 265-275 (1962). 

FIGURE 26.18 Theoretical temperature rise in the contact area of a pad sliding over a semi-infinite solid for different depths from the surface. Width 2b 2 mm, speed 3 m/s, pressure 2 Mp, p—l, heat conductivity 0.15 W/m/K, heat diffusivity 10 " m /s. 

The original problem. The heat diffusion process on a straight line is described by the heat conduction equation... 

The transition between crystalline and amorphous polymers is characterized by the so-called glass transition temperature, Tg. This important quantity is defined as the temperature above which the polymer chains have acquired sufficient thermal energy for rotational or torsional oscillations to occur about the majority of bonds in the chain. Below 7"g, the polymer chain has a more or less fixed conformation. On heating through the temperature Tg, there is an abrupt change of the coefficient of thermal expansion (or), compressibility, specific heat, diffusion coefficient, solubility of gases, refractive index, and many other properties including the chemical reactivity. 

At a later stage of bubble growth, heat diffusion effects are controlling (as point c in Fig. 2.9), and the solution to the coupled momentum and heat transfer equations leads to the asymptotic solutions and is closely approximated by the leading term of the Plesset-Zwick (1954) solution,... 

In the case of 19a, it was found that the typical melting point for linear polyethylene, 134°C, with a heat diffusion of 204 Jg-1, is depressed to -2°C with a heat diffusion of 32 Jg 1. A typical DSC curve is shown in Fig. 6. 

A common method to measure diffusion coefficients consists in the welding of two samples with different concentrations of the element of which the diffusion coefficient is to be known. Upon heating, diffusion asymmetrical profiles are quite commonly obtained which show that different species diffuse at different rates. The concentration-... 

The theory of premixed flames essentially consists of an analysis of factors such as mass diffusion, heat diffusion, and the reaction mechanisms as they affect the rate of homogeneous reactions taking place. Inasmuch as the primary mixing processes of fuel and oxidizer appear to dominate the burning processes in diffusion flames, the theories emphasize the rates of mixing (diffusion) in deriving the characteristics of such flames. 

The heat diffusing from r toward the drop (out of the element) is... 

Figure 1-8 Heat and mass diffusion in a semi-infinite medium in which the diffusion profile propagates according to square root of time, (a) The evolution of temperature profile of oceanic plate. The initial temperature is 1600 K. The surface temperature (at depth = 0) is 275 K. Heat diffusivity is 1 mm /s. (b) The evolution of profile in a mineral. Initial in the mineral is l%o. The surface is 10%o. D= 10 m /s.

Heat conduction distance can be calculated in a similar way as diffusion distance. For example, mean heat conduction distance can be calculated as (xt), where k is the heat diffusivity. Hence, mean time for heat conduction to reach a distance x (for one-dimensional heat conduction) is x /k. Assume that k = 0.8 mm /s for the Earth and for a meteorite. (It is nice that k does not vary much with temperature or phase.)... 

Solution Heat conduction during aging of the plate (that is, as it moves away from the ocean ridge) can be described by the heat-diffusion problem in a semi-infinite medium. The solution is... 

Melting of a single crystal in its own melt may be treated similarly if it is controlled by heat conduction. Assume that the melt reservoir is infinite. Because heat diffusivity k in the melt is about 6 orders of magnitude larger than mass... 

One example would be ice melting or methane hydrate dissociation when rising in seawater. Convective melting rate may be obtained by analogy to convective dissolution rate. Heat diffusivity k would play the role of mass diffusivity. The thermal Peclet number (defined as Pet = 2aw/K) would play the role of the compositional Peclet number. The Nusselt number (defined as Nu = 2u/5t, where 8t is the thermal boundary layer thickness) would play the role of Sherwood number. The thermal boundary layer (thickness 8t) would play the role of compositional boundary layer. The melting equation may be written as... 

Give initial conditions, including the melt composition, density, heat diffusivity, viscosity, crystal density, latent heat of fusion, and the initial crystal radius. 

Heat diffusivity transmission coefficient in the transition-state theory... 

LI. Luikov, A. V., Analytical Heat Diffusion Theory. Academic Press, New York, 1968. Ml. Masliyah, J. H., and Epstein, N., Prog. Heat Mass Transfer 6, 613-632 (1972). 

One other measurement technique that has been used to measure Kl over a shorter time period, and is thus more responsive to changes in wind velocity, is the controlled flux technique (Haupecker et al., 1995). This technique uses radiated energy that is turned into heat within a few microns under the water surface as a proxy tracer. The rate at which this heat diffuses into the water column is related to the liquid film coefficient for heat, and, through the Prandtl-Schmidt number analogy, for mass as well. One problem is that a theory for heat/mass transfer is required, and Danckwert s surface renewal theory may not apply to the low Prandtl numbers of heat transfer (Atmane et al., 2004). The controlled flux technique is close to being viable for short-period field measurements of the liquid film coefficient. 

---