Thermal gradients, internal

The proposed model for non-isothermal sorption kinetics can quantitatively describe uptake0data for adsorption of i-octane on 13X and n-pentane on 5A zeolites. The study indicates that the principal resistance to mass transfer for these systems may be confined at the surface of the zeolite crystals. It is also found that the internal thermal resistance of the assemblage of the micron size zeolite crystals used in the kinetic test is significant which produces a substantial thermal gradient within the assemblage and slows down the heat dissipation from it. 

Like other FFF subtechniques, materials are retained in thermal FFF as a result of their field-induced concentration at one wall of the channel. In thermal FFF, that field is a temperature gradient. Several terms are used to express the movement of material in response to a temperature gradient, including thermal diffusion, thermodiffusion, thermophoresis, and the Soret effect. The term thermodiffusion is used here, as it has been adopted by the scientific committee for The International Symposium on Thermodiffusion, which is devoted to the scientific study of this phenomenon. 

This example also shows the effects of mass- and enei y-transfer resistances within the catalyst pellet. The temperature increases toward the center of the pellet and increases the rate, but the oxygen concentration goes down, tending to reduce the rate. The global value of 49.8 x 10" is the resultant balance of both factors. Hence the net error in using the bulk conditions to evaluate the rate would be [(49.8 — 43.6)/49.8] (100), 12.5%. In this case the rate increase due to external and internal thermal effects more than balances the adverse effect of internal mass-transfer resistance. The procedure for calculating the effects of internal gradients on the rate is presented in Chap. 11. 

Following the model proposed by Okamoto et al. [18], in order to derive the magnitude of internal thermal stresses (Ti t) of a thermoelectric material during operation conditions and assuming a uniform temperature gradient, we use ... 

Pyroelectric effect might appear also as a result of non-homogeneous temperature distribution in the sample (i.e. temperature gradient) due to the internal thermal stresses. This phenomenon is ealled teiciaiy pyroelectric effect or the false... 

The temperature gradient is not to be confused with thermal lag, which is another physical property that should also be minimized in DSC experiments. Thermal lag is the difference between the average sample temperature and the sensor temperature and is caused by so-called thermal resistance, which characterizes the ability of the material to hinder the flow of heat. Thermal lag is smaller in DSC than in DTA because of smaller sample size (milligrams in DSCs), but more types of thermal resistance develop in DSC than in DTA. These effects are caused by introduction of the sample and reference pans into the DSC sample and reference holders. Thus, in DTA thermal resistance develops between the sample holder (in some instruments called the sample pod) and the sample (analogously, between the reference holder and the reference material), and within the sample and the reference materials. On the other hand, in DSC thermal resistance will develop between the sample holder and the bottom of the sample pan and the bottom of the sample pan and the sample (these are called external thermal resistances), and within the sample itself (this is called internal thermal resistance). These thermal resistances should be taken into account since they determine the thermal lag. Let us suppose that the cell is symmetric with regard to the sample and reference pods or holders, the instrumental thermal resistances are identical for the sample and reference holders, the contact between the pans and the pods are intimate, no crosstalk exists between the sample and reference sensors (i.e.. 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

Because thermal gradients vary considerably within boilers, a typical BW sample, which is essentially representative of average internal bulk water conditions, is unlikely to provide sufficient valid information necessary for the critical assessment of conditions at boiler surfaces. This makes fine-tune control of coordinated phosphate programs within the areas they are most needed very difficult, if not impossible, especially because caustic and saline concentrations may be much higher under deposits than in the bulk water as a result of localized effects. 

Catalyst pellets often operate with internal temperatures that are substantially different from the bulk gas temperature. Large heats of reaction and the low thermal conductivities typical of catalyst supports make temperature gradients likely in all but the hnely ground powders used for intrinsic kinetic studies. There may also be a him resistance to heat transfer at the external surface of the catalyst. 

Figure 3 illustrates some additional capability of the flow code. Here no pressure gradient is Imposed (this is then drag or "Couette flow only), but we also compute the temperatures resulting from Internal viscous dissipation. The shear rate in this case is just 7 — 3u/3y — U/H. The associated stress is.r — 177 = i/CU/H), and the thermal dissipation is then Q - r7 - i/CU/H). Figure 3 also shows the temperature profile which is obtained if the upper boundary exhibits a convective rather than fixed condition. The convective heat transfer coefficient h was set to unity this corresponds to a "Nusselt Number" Nu - (hH/k) - 1. 

First, we will consider thin objects - more specifically, those that can be approximated as having no spatial, internal temperature gradients. This class of problem is called thermally thin. Its domain can be estimated from Equations (7.11) to (7.12), in which we say the physical thickness, d, must be less than the thermal penetration depth. This is illustrated in Figure 7.7. For the temperature gradient to be small over region d, we require... 

External and internal attachments to piping shall be designed so that they will not cause undue flattening of the pipe, excessive localized bending stresses, or harmful thermal gradients in the pipe wall. It is important that attachments be designed to minimize stress concentration, particularly in cyclic services. 

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