Heating process vector

However, this statement deserves to be examined much more closely. The absolute certainty of an overkill heating process is diminished considerably when the product is not heated or not given sufficient heat to sterilize the container. In addition, there is inevitable manipulation involved before the container is sealed. This uncertainty has resulted in a discussion of the acceptable element of risk in an aseptic process. Unfortunately, this risk cannot be measured directly and various guess factors have been vectored into the discussion, all without scientific foundation. Going back to fundamentals, it is necessary to remind oneself that there are no degrees of sterility—a product is either sterile or it is not. 

Fig. 11.14. Exergy vector diagram for an iron oxide reduction, FeO - Fe + 0.5O2, coupled with a heating process at 2800 K [Ref. 15.].

Then the vectors of the heating and cooling processes are obtained as shown in Fig. 3. It is seen that the vector of the heating process always appears on the first quadrant of the thermodynamic compass, whereas the cooling process on the third quadrant, giving rise to the following four cases. 

When the concept of the exergy increase A is applied, the process vector on the thermodynamic compass shown in Fig. 1 (b) may be decomposed into two vectors Q and W. The vector Q on the diagonal line is equivalent to the heat sink at the reference temperature To, of which direction factor is unity. On the other hand, the vector W on the abscissa is equivalent to the work sink and has the magnitude of the exergy increase of the process, A . 

The diffusion term on the right-hand side assumes that the flux of surfactant that is due to random Brownian motions is linear in the gradient of T and that the process is isotropic. In writing a complete mass balance for any species, it is necessary to include the possibility of a mean flux that is due to random molecular motion in the presence of a gradient in concentration - just as it was necessary to hypothesize a heat flux vector in the conservation of energy balance. The relationship... 

Here, c is the concentration and j is the flux of the species in question due to the diffusion process. The species flux vector j plays the same role in the diffusion problem as the heat flux vector q plays in the transfer of heat by conduction. In the classical diffusion problem,... 

Fig. 6.8. X-ray scattering profile along the equator as a function of the scattering vector at various temperatures during the heating process in oriented glassy states of PET annealed a1 Ta- Here, Ta = 125 C and the heating rate is lOK/min. The upper figure shows the results for temperatures between 50 and 120 C, and the lower one shows those for temperatures above Ta(= 125 C)...

Figure 8.9 Temperature dependence of G for a highly asymmetric SIS triblock copolymer specimen having a 0.18 weight fraction of PS block (Vector 4111, Dexco Polymers Company), which was annealed at 140 °C for 2 days prior to the isochronal dynamic temperature sweep experiments at an angular frequency of 0.01 rad/s in the heating process. (Reprinted from Sakamoto et al., Macromolecules 30 1621. Copyright 1997, with permission from the American Chemical Society.)...

Just as heat is the by-product of most spontaneous chemical reactions, so electricity is the by-product of the same reactions carried out in an electrogenerative way, such as that illustrated in Fig. 7.190. However, there is one big difference. Electricity can be used as a vector—and sent for hundreds of miles with little loss—and used at the other end. Could such processes become the basis of industrial processes that, as the rule and not the special case, make things electrogeneratively instead of thermally ... 

Here the momentum in the intermediate state is described by the unit vector h. Nq qi can be considered to represents a process in which a heat mode of wavevector q is annihilated and a thermal (heat) mode of wavevector q and a viscous mode of wavevector q q are created. 

The phase transition rate in the crystallization of polymeric materials is of the same order as the rates of the heat exchange processes accompanying crystallization. Consequently, the boundary between phases becomes spatially dispersed. This excludes the possibility of using methods based on the front transition model proposed for metals to calculate residual stresses in plastics.148 It is possible to split the general problem and to find the temperature-conversion field independently. Then, assuming that the evolution of temperature T(x,t) and degree of crystallinity a(x,t) in time t and in space (x is the radius vector of an arbitrary point in a body) is known, we can analyze the mechanical problem.143... 

However, A and T are scaler quantities, and because Lu is only a property of the medium, in an isotropic medium it must also be a scalar. Because there is no way to define a direction for the vector heat flow, Lu = 0 is required. There can be no coupling between vector and scalar irreversible flow processes in isotropic media.10,11 This is known as the Curie-Prigogine principle. 

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