Temperature-gradient effects

Sysoev, V. V. Kiselev, I. Frietsch, M. Goschnick, J., Temperature gradient effect on gas discrimination power of a metal-oxide thin-film sensor microarray, Sensors 2004,... 

In practice the temperature gradient effect on diffusion is neglected and this gives for eq. (28) and eq. (29) respectively ... 

This section discusses several ways in which temperature gradients effect a solute flux. The phenomena involved occur in the absence of convection and are treated with models like those developed for diffusion in Chapters 2 and 3. Thus the approach is again based on a distributed-parameter model and is more fundamental than the approach based on mass transfer coefficients and used in earlier sections of this chapter. 

The effect can be important in mass-transfer problems (see Ref. 57 and citations therein). The Marangoni instability is often associated with a temperature gradient characterized by the Marangoni number Ma ... 

The coefficients, L., are characteristic of the phenomenon of thermal diffusion, i.e. the flow of matter caused by a temperature gradient. In liquids, this is called the Soret effect [12]. A reciprocal effect associated with the coefficient L. is called the Dufour effect [12] and describes heat flow caused by concentration gradients. The... 

When developing the dusty gas model flux relations in Chapter 3, the thermal diffusion contributions to the flux vectors, defined by equations (3.2), were omitted. The effect of retaining these terms is to augment the final flux relations (5.4) by terms proportional to the temperature gradient. Specifically, equations (5.4) are replaced by the following generalization... 

Strain-gauge load cells are sensitive to temperature gradients induced by, for example, radiant heat from the sun or resulting from high temperature wash down. Load cells should be shielded from such effects or given time to stabilize before use. 

Thermal Stresses. When the wak of a cylindrical pressure vessel is subjected to a temperature gradient, every part expands in accordance with the thermal coefficient of linear expansion of the steel. Those parts of the cylinder at a lower temperature resist the expansion of those parts at a higher temperature, so setting up thermal stresses. To estimate the transient thermal stresses which arise during start-up or shutdown of continuous processes or as a result of process intermptions, it is necessary to know the temperature across the wak thickness as a function of radius and time. Techniques for evaluating transient thermal stresses are available (59) but here only steady-state thermal stresses are considered. The steady-state thermal stresses in the radial, tangential, and axial directions at a point sufficiently far away from the ends of the cylinder for there to be no end effects are as fokows ... 

Maintenance of isothermal conditions requires special care. Temperature differences should be minimised and heat-transfer coefficients and surface areas maximized. Electric heaters, steam jackets, or molten salt baths are often used for such purposes. Separate heating or cooling circuits and controls are used with inlet and oudet lines to minimize end effects. Pressure or thermal transients can result in longer Hved transients in the individual catalyst pellets, because concentration and temperature gradients within catalyst pores adjust slowly. 

In 1857, Thomson (Lord Kelvin) placed the whole field on firmer footing by using the newly developing field of thermodynamics (qv) to clarify the relationship between the Seebeck and the Peltier effects. He also discovered what is subsequently known as the Thomson effect, a much weaker thermoelectric phenomenon that causes the generation or absorption of heat, other than Joule heat, along a current-carrying conductor in a temperature gradient. 

The primary thermoelectric phenomena considered in practical devices are the reversible Seebeck, Peltier, and, to a lesser extent, Thomson effects, and the irreversible Eourier conduction and Joule heating. The Seebeck effect causes a voltage to appear between the ends of a conductor in a temperature gradient. The Seebeck coefficient, L, is given by... 

Mass Transport. An expression for the diffusive transport of the light component of a binary gas mixture in the radial direction in the gas centrifuge can be obtained directly from the general diffusion equation and an expression for the radial pressure gradient in the centrifuge. For diffusion in a binary system in the absence of temperature gradients and external forces, the general diffusion equation retains only the pressure diffusion and ordinary diffusion effects and takes the form... 

For catalytic investigations, the rotating basket or fixed basket with internal recirciilation are the standard devices nowadays, usually more convenient and less expensive than equipment with external recirculation. In the fixed basket type, an internal recirculation rate of 10 to 15 or so times the feed rate effectively eliminates external diffusional resistance, and temperature gradients. A unit holding 50 cm (3.05 in ) of catalyst can operate up to 800 K (1440 R) and 50 bar (725 psi). 

The governing equations for the combined effect of concentration and temperature gradient are ... 

The temperature of pressing has also a noticeable effect [226,227] as it does influence the surface/core temperature gradient and has a direct influence on the temperature rise in the board core layer. In short, the higher the press temperature, the faster the heat conduction and the faster the development of the steam gradient across the wood mat. The press temperature will influence the steam front transfer time to the core layer. The higher the initial temperature, the faster the steam front enters the mat core. Increasing the press temperature will cause the maximum steam pressure peak to appear earlier but does not result in a higher core temperature. 

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