Effects of a Temperature Gradient

Solidification within a temperature gradient can be achieved in two types of experimental setups  

a zone solidification apparatus [37-40] the sample passes slowly through a steep temperature gradient. It melts and crystallizes the crystallization front is formed and moves along the sample. Thus, the crystallization occurs in a temperature gradient, but at a stable temperature at the front. 

a device in which a constant temperature gradient is established between two metal blocks at different temperatures [41]. This better corresponds to polymer processing. 

The morphological patterns are very sensitive to the nucleation density and to its variation with temperature  

According to foregoing model, all the forwardgrowing lamellae will exhibit a monotonic curvature and tend to a horizontal asymptote (direction of temperature gradient). The model also predicts that the lamellae growing in the backward direction should tend to a vertical asymptote, which is not observed experimentally. 

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M Thompson and J R White, The effect of a temperature gradient on residual stresses and distortion in injection mouldings , Polym Eng Sci 1984 24(4) 227-241. 

Storms, E. (1969) Some effects of a temperature gradient on Knudsen effusion. High Temperature Science, 1, 456 65. 

Another form of interaction between the transfer processes is responsible for the phenomenon of thermal diffusion in which a component in a mixture moves under the action of a temperature gradient. Although there are important applications of thermal diffusion, the magnitude of the effect is usually small relative to that arising from concentration gradients. 

So far, we have assumed that the particle is isothermal and have focused only on the diffusional characteristics and concentration gradient within the particle, and their effect on 17. We now consider the additional possibility of a temperature gradient arising from the thermal characteristics of the particle and the reaction, and its effect on tj. 

A flow diagram of an anhydrous phenol solvent extraction plant is shown in Figure 8. Raw distillate is passed through a tower in which it absorbs phenol from the recovery system vapor. The oil is then passed to the treating tower, generally a few sections above the bottom. Anhydrous phenol is introduced at the top of this tower. Phenolic water condensate from the solvent recovery system (about 9.5% phenol) is introduced at the bottom of the tower to effect reflux. A temperature gradient of 10° to 75° F. may be... 

Strictly the mathematical expression to be used for the diffusion process should take account of these constraints however, this kind of counter-diffusion involving two reactants and two products in proportions determined by the stoichiometry of the process is of a complexity which has not yet been considered theoretically. In the absence of such a theoretical treatment, Equation (3) was applied using diffusion coefficients reported in the literature for each of the components for diffusion at room temperature. A small correction for the effect of the temperature gradient in the boundary layer on the diffusion coefficient was made in a manner discussed later. 

Soret effect — When a temperature gradient is applied to an homogeneous mixture of two or more components there is a partial separation of the components by -> migration along the temperature gradient. This phenomenon, known as Soret effect, occurs in condensed phases (i.e., liquids and solids) [i]. Another term that is used to describe the Soret effect is thermo diffusion, which has been observed for either mixtures of gases or liquids and solid solutions [ii]. For electrolytic solutions in a temperature gradient, ions move from a location... 

As the second application of irreversible thermodynamics we consider the Soret effect (1893) for a two-component system a flow of particles under the influence of a temperature gradient produces a gradient in concentration. We are ultimately interested in the magnitude of this effect under steady state conditions. Let J0, Jlt J2 be the entropy and particle fluxes... 

This one-step expression for the reaction rate is adequate for a demonstration of some of the general principles involved in the generation of pressure pulses. The equations are used to show the effects of the temperature gradient around a hot spot and the volumetric heat release rate there upon the propagation of autoignition. 

After the preliminary selection of 300 series stainless steel, these alloys were subjected to further tests to study the effect of stress in the presence of chloride, oxygen, and water vapor, the effect of sensitization, and the rate at which the alloying constituents are leached and transported under the influence of a temperature gradient. A molten salt loop has been in operation for nearly a year as a part of these tests. The... 

As already shown in section 1.2.3, heat transfer between two fluids can be improved if the surface area available for heat transfer, on the side with the fluid which has the lower heat transfer coefficient, is increased by the addition of fins or pins. However this enlargement of the area is only partly effective, due to the existence of a temperature gradient in the fins without which heat could not be conducted from the hn base. Therefore the average overtemperature decisive for the heat transfer to the fluid is smaller than the overtemperature at the hn base. In order to describe this effect quantitatively, the fin efficiency was introduced in section 1.2.3. Its calculation is only possible if the temperature distribution in the hn is known, which we will cover in the following. Results for the hn efficiencies for different hn and pin shapes are given in the next section. 

The diffusion-thermal effect or the Dufour energy flux eff describes the tendency of a temperature gradient under the influence of mass diffusion of chemical species. Onsager s reciprocal relations for the thermod3mamics of irreversible processes imply that if temperature gives rise to diffusion velocities (the thermal-diffusion effect or Soret effect), concentration gradients must produce a heat flux. This reciprocal effect, known as the Dufour effect, provides an additional contribution to the heat flux [89]. 

Effinghausen effect - The appearance of a temperature gradient in a current carrying conductor that is placed in a transverse magnetic field. The direction of the gradient is perpendicular to the current and the field. 

Thomson coefficient (p, x) - The heat power developed in the Thomson effect (whereby heat is evolved in a conductor when a current is flowing in the presence of a temperature gradient), divided by the current and the temperature difference. [1]... 

Direct-contact condensation of steam in Aroclor, with a venturi as mixing device, was reported by Lackey (LI). Working with temperature gradients of about 10, 40, and 70°F between the two fluids, he observed a strong effect of the temperature gradients on the steam flow rate, the latter decreasing... 

Temperature obviously affects the physical properties of the fluids, thus indirectly affecting the transfer coefficients. As in the case of heat transfer in pipes, equations involving viscosity corrections for temperature differences between bulk and interface have been suggested (Eq. 11-14, Table II) and are especially applicable for viscous continuous phases. No correction is needed for water, for instance, especially at > 50. At lower (A Re)c. natural convection is pronounced, especially in liquid systems with low kinematic viscosity. Since the transfer coefficient for natural convection is a function of the Grashof number, one may expect some effects of the temperature gradient. Steinberger and Treybal s equation (Eq. 6) allows for these effects. 

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