Temperature solid

Control of trav and compartment equipment is usually maintained by control of the circulating-air temperature (and humidiy) and rarely by solids temperature. On vacuum units, control of the absolute pressure and heating-medium temperature is utihzed. In direct dryers, cycle controllers are frequently employed to vary the air temper-... 

Use of the term mean-bulk temperature is to define the model from which temperatures are computed. In shock-compression modeling, especially in porous solids, temperatures computed are model dependent and are without definition unless specification of assumptions used in the calculations is given. The term mean-bulk temperature describes a model calculation in which the compressional energy is uniformly distributed throughout the sample without an attempt to specify local effects. In the energy localization case, it is well known that the computed temperatures can vary by an order of magnitude depending on the assumptions used in the calculation. 

The basic scheme for the numerical solution is the same as that used for the 1 -D model, except that in this case the solid temperature field used to solve the DAE system for each monolith channel must be calculated from the three-dimensional solid-phase energy balance equation. The three-dimensional energy balance equation can be solved by a nonlinear finite element solver (such as ABAQUS) for the solid-phase temperature field while a nonlinear finite difference solver for the DAE system calculates the gas-phase temperature and... 

Effectively, Eqs. (86) and (87) describe two interpenetrating continua which are thermally coupled. The value of the heat transfer coefficient a depends on the specific shape of the channels considered suitable correlations have been determined for circular or for rectangular channels [100]. In general, the temperature fields obtained from Eqs. (86) and (87) for the solid and the fluid phases are different, in contrast to the assumptions made in most other models for heat transfer in porous media [117]. Kim et al. [118] have used a model similar to that described here to compute the temperature distribution in a micro channel heat sink. They considered various values of the channel width (expressed in dimensionless form as the Darcy number) and various ratios of the solid and fluid thermal conductivity and determined the regimes where major deviations of the fluid temperature from the solid temperature are found. 

Assuming local thermal equilibrium, i.e. the equality of the averaged fluid and solid temperature, a transport equation for the average temperature results which still contains and integral over the fluctuating component. In order to close the equation, a relationship between the fluctuating component and the spatial derivatives of the average temperature of the form... 

Thus a single stage, NH= 1, corresponds to a solids temperature rise (or drop) equal to the average gas-solids temperature difference, as shown in the lower left-hand side of Fig. 10. On this basis, it is convenient to define equipment efficiency in terms of a unitary heat transfer stage ... 

Solids temperature was measured at various heights by intercepting receptacles, each of which contains a bare thermocouple which follows the solids temperature when turned upright to collect the solids, and measures the gas temperature when the solids are dumped by simply turning the receptacles 180°. 

The radiative heat transfer across the vapor layer is neglected under the condition that the solid temperature is lower than 700 °C (Harvie and Fletcher, 2001 a,b). On the liquid-vapor interface, the energy-balance equation is... 

The amount of heat actually taken up by the particles was an important quantity, as tubes operate under heat transfer limited conditions near the tube inlet. Fig. 30 shows a plot of Q against r, where Q was the total energy flow into the solid particles, for the entire segment. For inlet conditions, Q varied strongly at lower r, but was almost constant at higher values. As rcut/rp decreased from 0.95 to 0.0 and the effectiveness factor increased from nearly zero to one, the active solid volume increased by a factor of 7. If the solid temperature had remained the same, the heat sink would also have had to increase sevenfold. This could not be sustained by the heat transfer rate to the particles, so the particle temperature had to decrease. This reduced the heat sink and increased the driving force for heat transfer until a balance was found, which is represented by the curve for the inlet in Fig. 30. 

Almost all of the models assume local thermal equilibrium between the various phases. The exceptions are the models of Beming et al., ° who use a heat-transfer coefficient to relate the gas temperature to the solid temperature. While this approach may be slightly more accurate, assuming a valid heat-transfer coefficient is known, it is not necessarily needed. Because of the intimate contact between the gas, liquid, and solid phases within the small pores of the various fuel-cell sandwich layers, assuming that all of the phases have the same temperature as each other at each point in the fuel cell is valid. Doing this eliminates the phase dependences in the above equations and allows for a single thermal energy equation to be written. 

Figure 5 shows the axial gas and solid temperature profiles during start-up operation. Notice that the hot spot in the reactor moves down the bed as the heat of reaction increases the temperature of the catalyst particles. Also note the significant temperature difference between the catalyst and gas in the early part of the reactor, where conversion is rapid due to the heat of reaction being generated on the catalyst surface. These differences are even more pronounced (over 20 K) near the center of the bed and near the outer wall.11... 

In our original system of partial differential equations, to obtain a pseudohomogeneous model the two energy balances can be combined by eliminating the term (Usg/Vb)(Ts — Tg), that describes the heat transfer between the solid and the gas. If the gas and solid temperatures are assumed to be equal (Ts = Tg)19 and the homogeneous gas/solid temperature is defined as T, the combined energy balance for the gas and solid becomes... 

Another procedure often used with less stringent assumptions than the equality of the gas and solid temperatures is the pseudohomogeneous analysis proposed by Vortmeyer and Schaefer (1974). This procedure has proved to be quite effective for simple adiabatic packed bed analyses and involves reducing the energy balances for the gas and catalyst to a single equation using the... 

Transient simulations using the full, nonlinear model show that under the conditions studied concentration profiles reach a quasi steady state quite rapidly (often within 3 to 5 sec), whereas the thermal response of the reactor bed is much slower22 due to the large heat capacity of the reactor bed and thermal well. An example of this phenomenon is shown in Fig. 18, where the transient responses of the solid temperatures, thermal well temperatures, and concentrations are shown for a major step change in the inlet gas temperature and inlet CO concentration. In this example, the effect of the step change is nearly immediate on the concentration profiles, with the major effect being within the first 10 sec. However, Fig. 18a shows that the thermal well temperatures and the catalyst temperatures take up to 10 times as long as the... 

If the liquid is subcooled, the highest solid temperature which will allow nucleate boiling is the same as if the liquid were at its boiling point. The AT between the solid and the bulk liquid is of far less significance than the temperature of the solid minus the liquid boiling point. The critical value expressed this latter way should be exactly the same as for a liquid actually at its boiling point. 

Consideration should be given to whether the solid particles are small enough to be in thermal equilibrium with the liquid. If this will be the case, then an average heat capacity should be used. If the solid temperature is expected to lag behind that of the liquid, then a safe assumption is that the solid has zero heat capacity, i.e. 

Hydrogen sulfide Total dissolved solids Temperature Iron... 

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