Volume-averaged temperature

Following the line of arguments developed by CarboneU and Whitaker [188] and Nozad et al. [189], a volume-averaged temperature is introduced as... 

The volume averaged temperature equation is then given by ... 

With this assumed negligible local temperature difference between the phases, we assume that within the local representative elementary volume V= Vf+ V the solid and fluid phases are in local thermal equilibrium. This is stated using the phase (or intrinsic) and both-phases volume averaged temperatures as... 

Closure constitutive equations are developed similar to those used when the existence of the local thermal equilibrium was assumed. This requires relating the disturbances in the temperature fields to the gradients of the volume-averaged temperatures and to the difference between the phase volume-averaged temperatures. 

Fw,ave is the surface-averaged temperature at the fluid-solid interface of area Ai t, Tf ave is the volume-averaged temperature of the fluid field, and ki is the thermal conductivity of the pure... 

Code modifications being made by the INL to allow volume average temperature selection for wall boundary conditions... 

An assumption is made that the reactivity feedback for the reactor is divided evenly between the fuel Doppler effect and feedback from the core structural materials. Doppler temperature feedback is a function of the square root of the volume average temperature of the volume to which the feedback is being applied. The overall temperature feedback is divided between two heat structures the fuel pin structure for Doppler feedback and the core block structure for geometric feedback. Axial feedback coefficients are based on power squared weighting of the Doppler term calculated from the tabular input, and a geometric coefficient assumed to be half of the total temperature feedback. The... 

To extend the applicability of the characterization factor to the complex mixtures of hydrocarbons found in petroleum fractions, it was necessary to introduce the concept of a mean average boiling point temperature to a petroleum cut. This is calculated from the distillation curves, either ASTM or TBP. The volume average boiling point (VABP) is derived from the cut point temperatures for 10, 20, 50, 80 or 90% for the sample in question. In the above formula, VABP replaces the boiling point for the pure component. 

All packing materials produced at PSS are tested for all relevant properties. This includes physical tests (e.g., pressure stability, temperature stability, permeability, particle size distribution, porosity) as well as chromatographic tests using packed columns (plate count, resolution, peak symmetry, calibration curves). PSS uses inverse SEC methodology (26,27) to determine chromatographic-active sorbent properties such as surface area, pore volume, average pore size, and pore size distribution. Table 9.10 shows details on inverse SEC tests on PSS SDV sorbent as an example. Pig. 9.10 shows the dependence... 

The q(T) can be independently measured by a viscometer and the value of y is determined by the PCS measurement at a certain temperature (typically 21 22 °C). Under the condition that the hydrodynamic diameter of the probe molecule is constant in the temperature range examined, we can obtain the temperature of the confocal area. It is worth noting that the present method estimates average temperature inside the confocal volume of the microscopic system because ECS provides the average value of the translational diffusion velocity over multiple fluorescent molecules passing through the sampling area. 

Because of the dilution that results from the mixing of entering fluid elements with the reactor contents, the average reaction rate in a stirred tank reactor will usually be less than it would be in a tubular reactor of equal volume and temperature supplied with an identical feed stream. Consequently, in order to achieve the same production capacity and conversion level, a continuous flow stirred tank reactor or even a battery of several stirred tank reactors must be much larger than a tubular reactor. In many cases, however, the greater volume requirement is a relatively unimportant economic factor, particularly when one operates at ambient pres-... 

Table-. BET surface area, total pore volume, micro-pore volume, ignition temperature Tio% reduction temperature TR and average particle diameter of the Pd-ZSM-5 catalysts. ...

Following the steps for formulation of a CFD model introduced earlier, we begin by determining the set of state variables needed to describe the flow. Because the density is constant and we are only interested in the mixing properties of the flow, we can replace the chemical species and temperature by a single inert scalar field (x, t), known as the mixture fraction (Fox, 2003). If we take = 0 everywhere in the reactor at time t — 0 and set / = 1 in the first inlet stream, then the value of (x, t) tells us what fraction of the fluid located at point x at time t originated at the first inlet stream. If we denote the inlet volumetric flow rates by qi and q2, respectively, for the two inlets, at steady state the volume-average mixture fraction in the reactor will be... 

The average temperature of the compartment gases, Tg (average "fire" temperature), °K, averaged over the compartment volume and temporaily over the period of full development. 

The previous section is concerned mostly with an isolated molecule and its properties. When we have an ensemble of molecules in equilibrium with a particular volume and temperature, we find that the molecules are distributed among different energies and we are interested mostly in their average properties, which is the concern of statistical mechanics. 

Here, (A) represents the ensemble average of A, and p is the probability density of the state represented by p, r ). Under conditions of constant number of particles, volume and temperature, the probability density is the Boltzmann distribution... 

It is extremely difficult to model macroscopic transport of mass, energy, and momentum in porous media commonly encountered in various fields of science and engineering based on microscopic transport models that account for variation of velocity and temperature as well as other quantities of interest past individual solid particles. The basic idea of porous media theory, therefore, is to volume average the quantities of interest and develop field equations based on these average quantities. 

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