Biot small

A large Biot Number means that conduction controls the energy transfer to/from the plastic and large temperature gradients will exist in the plastic. A small Biot Number means that convection is the dominant factor. The above analysis was for conduction heat transfer (B, - oo). When the plastic moulding is taken out of the mould we need to check the value of B,. In this case... 

Two years later Gay-Lussac and J.-B. Biot made a daring balloon ascension to study the behavior of a magnetic needle and the chemical composition of the atmosphere at high altitudes. On another occasion, when Gay-Lussac alone had reached an elevation of 7016 meters and wished to ascend still higher, he threw overboard some small objects to lighten the balloon. A shepherdess in the field was astonished to see a white wooden chair fall from the sky into some bushes, and the peasants who heard her story were at a loss to explain why, if the chair had come direct from Heaven, the workmanship on it should be so crude (3). 

Figure 9 illustrates the effect of the Biot number, s, on the uptake curve for a given r) and p. Figure 10 shows the corresponding dimensionless temperature profiles at x = 0. It may be seen from Figure 9 that s has small effect on the uptake curve at low t but it strongly affects the... 

A high Biot number means that the conductive transfer is small compared to convection and the situation is close to that considered by a Frank-Kamenetskii situation (Section 13.4.1). Inversely, a small Biot number, that is Bi < 0.2, means that the convective heat transfer dominates and the situation is close to a Semenov situation. 

The BIOT-number of the solid particles is so small that the unsteady heat conduction in the particle is neglected. 

In order to reduce the complexity of the model two additional simplifying assumptions were made, (a) With typical residence times of 1 second, particle Reynolds numbers of 800 and tube-to-particle diameter ratios of 3, one would expect small values of the wall Biot number thus, a small number of radial finite difference (or collocation) points should be adequate for the numerical solution of the equations (8). (b) It was assumed... 

Criterion Biot determines the ratio of intensity of external heat exchange processes (numerator) and effective thermal conductivity of a hydride layer (denominator). To carry out frontal chemical reactions of hydrogen sorption -desorption, small numbers Biot (Bi<0.1) are preferable. Number Bi can be decreased by several ways 1) decreasing of the characteristic layer size 2) decreasing of intensity of an external heat transfer (but time of non-stationary processes is growing) 3) increasing of effective hydride bed thermal conductivity. 

From this figure, it can be concluded that the reduction of the effectiveness factor at large values of becomes more pronounced as the Biot number is decreased. This arises from the fact that the reactant concentration at the external pellet surface drops significantly at low Biot numbers. However, a clear effect of interphase diffusion is seen only at Biot numbers below 100. In practice, Bim typically ranges from 100 to 200. Hence, the difference between the overall and pore effectiveness factor is usually small. In other words, the influence of intraparticle diffusion is normally by far more crucial than the influence of interphase diffusion. Thus, in many practical situations the overall catalyst efficiency may be replaced by the pore efficiency, as a good approximation. 

Table 1 gives a summary of calculated times for 50% extraction of solute (t 50%)- Simulations conditions are P = 20 MPa, T = 313 K and Re = 40 for the system DCB/small cylinders and downflow operation. From Table 1, it is seen that for a constant value of Kq, a decrease of De and K lead to a significant increase of 150% irrespective of the Biot number. On the other hand, the influence of Kq is found to be significant only in the higher range of Biot number (Bi = 250) where the external mass transfer gradient may become limiting (Kq is very small). 

A chiral object and its mirror image are enantiomorphous, and they are each other s enantiomorphs. Louis Pasteur (Figure 2-37) was the first who suggested that molecules can be chiral. In his famous experiment in 1848, he recrystallized a salt of tartaric acid and obtained two kinds of small crystals which were mirror images of each other as seen by Pasteur s models in Figure 2-38 preserved at Institut Pasteur at Paris. Originally Pasteur may have been motivated to make these large-scale models because Jean Baptiste Biot, the discoverer of optical activity had very poor vision by the time of Pasteur s discovery [42], Pasteur demonstrated chirality to Biot, who was visibly affected... 

From the analysis of Equation 18> it follows that the main variables that affect the error in the reaction rate are E and P due to their effect on T and TC Thus, very good responses are obtained from a one-dimensional model when reaction conditions are mild (moderate values of E and P). It can also be seen that for these conditions, the influence of the distribution of the radial heat transfer resistances between the bed and the wall, given by the Biot number, is small. E.g., for T = 673°K, Tw = 643°K and E = 12.5 kcal/mol, the maximum er, found for Big -> < is 2.8%. 

When Re and dp/dt vary, while both the activation energy and the ratio between the radial heat transfer and heat generation rate at the inlet are kept constant, the values of 7 and T do not vary significantly. On the other hand, since the effect of the Biot number on the error is small, no variations in the difference between models are expected. 

When the Biot number is small, Bi < 0.2, the temperature of the solid is nearly uniform and a lumped analysis is acceptable. The solution to the lumped analysis of (5-18) is... 

When a solid body is being heated by the hotter fluid surrounding it (such as a potato being baked in an oven), heat is first convected to the body and subsequently conducted within the body. The Biot number is the ratio of the internal resistance of a body to heat conduction (o its external resistance to heat conveetton. Therefore, a small Biot number represents small resistance to heat conduction, and thus small temperature gradients within the body. 

Note that the Biot number is tlic ratio of the convection at the surface to conduction within the body, and this number should be as small as possible for lumped system analysis to be applicable. Therefore, small bodies with high tlieniial conductivity are good candidates for lumped system analysis, especially when they are in a medium that is a poor conductor of heat (such as air or another gas) and motionless. Thus, Ihe hot small copper ball placed in quiescent air, discussed eailier, is most likely to satisfy the criterion for lumped system analysis (Fig. 4-6). 

Wc discussed the physical significance of the Biot number earlier and indicated that it is a measure of the relative magnitudes of the two heal transfer mechanisms convection at the surface and conduction through the solid. A small value of Bi indicates tliat the inner resistance of the body to heat conduction is smalt relative to the resistance to convection between the surface and the fluid. As a result, the temperature distribution within the solid becomes fairly uniform, and lumped system analysis becomes applicable. Recall that when Bi <0.1, the error in assuming the temperature within the body to be uniform is negligible. 

I which is practically identical to the result obtained above using the Hetsler charts. Therefore, we can use lumped system analysis with confidence when the Biot number is sufficiently small. 

Concerning the heat transfer, the experimental difficulties must be underlined. When dimensions become smaller the heat flow does not go directly through the walls. For very small dimensions and temperature difference, the heat transfer coefficients are subject to large uncertainties. The use of a longitudinal Biot number can be of help to estimate the heat flow which may not be used to calculate the heat transfer coefficient. 

Besides, it is self-evident, as stated in the preceding section, that the spatial distribution of temperature, in particular, in the early stages of the self-heating process, or of the oxidatively-heating process, in a small-scale chemical of the TD type, including every small-scale gas-permeable oxidatively-heating substance, subjected to either of the two kinds of adiabatic tests, is the very ultimate of the Semenov model, because the condition, the Biot number = Ur A = 0, holds strictly in such a chemical. 

Popoff MR, Chaves-Olarte E, Lemichez E., et al. (1996) Ras, Rap, and Rac small GTP-binding proteins are targets for Clostridium sordellii lethal toxin glucosyla-tion. In J. Biot Chem. 271, 10217-10224. 

Correlations for hy, and Xeb can be found in the literature. Values of 10 W m" for hy, and of 1 W m K for Xgb are typical. Thermal Biot numbers are generally around 1. It follows from Eqn. (8.115) that much dilution with inert particles and small tube diameters favour radial isothermicity. Also, an inert with a good thermal conductivity should be used whenever possible. 

Fig. 2.5 Influence of the Biot number Bi = aLo/X on the temperature profile near to the surface, a small Biot number, b large Biot number...

A small Biot number means that the resistance to thermal conduction in the body, for example due to its high thermal conductivity, is significantly smaller than the heat transfer resistance at its boundary. With small Biot numbers the temperature difference in the body is small in comparison to the difference ( w — f) between the wall and fluid temperatures. The reverse is valid for large Biot numbers. Examples of these two scenarios are shown for a cooling process in Fig. 2.5. Very large Biot numbers lead to very small values of — J), and for Bi —> oo, according to (2.34) we get (it/y — i p) —> 0. The heat transfer condition (2.34) can be replaced by the simpler boundary condition = -dj. 

The latter of the two methods offers a practical, simple applicable solution to transient heat conduction problems and should always be applied for sufficiently small Biot numbers. 

A simple calculation for the heating or cooling of a body of any shape is possible for the limiting case of small Biot numbers (Bi — 0). This condition is satisfied when the resistance to heat conduction in the body is much smaller then the heat transfer resistance at its surface, cf. section 2.1.5. At a fixed time, only small temperature differences appear inside the thermally conductive body, whilst... 

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