Steady state temperature

A belt apparatus is capable of hoi ding pressures of 7 GPa (70 kbar) and temperatures of up to 3300 K for periods of hours. The maximum steady-state temperatures are limited by melting of the refractory near the reaction 2one (13). 

The LHS (heat generation) and RHS (heat removal) of Eq. (7-110) are plotted against T after x has been eliminated between the two balances the intersections identify the same steady state temperatures as the plot in Fig. 7-7a. 

Consider a first order, exothermic reaction (aA —> products) in a CFSTR having a constant supply of new reagents, and maintained at a steady state temperature T that is uniform throughout the system volume. Assuming perfect mixing and no density change, the material balance equation based on reactants is expressed as uC g = +... 

Steady-state temperatures along the length of a piston flow reactor are governed by an ordinary differential equation. Consider the differential reactor element shown in Figure 5.3. The energy balance is the same as Equation (5.14) except... 

The process gain (sensitivity) can be determined from steady-state values, and using these values can reduce the work required by the parameter estimation routines later. For narrow ranges of temperature, the following formulas for steady-state temperatures should be adequate ... 

Kll, K12, K21, K22 = process "gains", the proportional constants between a process input (the fraction of total of power going to the heaters in this extruder) and the steady state temperature of a node,... 

Here a steady-state formulation of heat transfer is considered (Pollard, 1978). A hot fluid flows with linear velocity v, through a tube of length L, and diameter D, such that heat is lost via the tube wall to the surrounding atmosphere. It is required to find the steady-state temperature profile along the tube length. 

Figure 5.80. The influence of jacket temperature (TJ = 650, 655, 657, and 658) is seen in these steady-state temperature profiles, for TEMP0=700.

If kinetic processes on catalytic surfaces in S02 oxidation are assumed to be at steady state, temperature and concentration fields in a radially symmetrical, adiabatic catalyst bed are described by the equations collected in Table IX for the reactor space 0 and time I > 0 (Matros, 1989 ... 

A radial temperature measurement consisted of establishing and recording a steady-state temperature profile for a combination of a specific bed length, Reynolds number, and angle of thermocouple cross. A total of four... 

For the identification of the onset temperature of the exotherm, the steady-state temperature difference may be plotted against the sample temperature. After calibration, the evolved heat can be estimated. A typical plot of an isoperibolic measurement is illustrated in Figure 2.16. The sample is heated by step-wise adjustment of the jacket (or oven) temperature. The actual sample temperature results from the heat accumulation as net difference between the heat generated by the chemical reaction and the heat transferred to the jacket (or oven). The resulting mean temperature difference is relatively small and not easy to detect accurately. Thus, a range of step changes in temperature is used to define a curve, which enables a more accurate determination of the start of the exothermic event and of To to be made. 

Critical steady-state temperature (CSST) the highest ambient temperature at which self-heating of a material as handled (in a package, container, tank, etc.) does not result in a runaway but remains in a stationary condition (see Self-Accelerating Decomposition Temperature). 

Transient Heating of Droplets When a cold liquid fuel droplet is injected into a hot stream or ignited by some other source, it must be heated to its steady-state temperature Ts derived in the last section. Since the heat-up time can influence the V/2 law, particularly for high-boiling-point fuels, it is of interest to examine the effect of the droplet heating mode on the main bulk combustion characteristic—the burning time. 

PSR A Fortran Program for Modeling Well-Stirred Reactors, Glarborg, P., Kee, R. J., Grcar, J. F. and Miller, J. A. Sandia National Laboratories, Livermore, CA, Sandia Report SAND86-8209, 1986. PSR is a Fortran computer program (psr.f) that predicts the steady-state temperature and species... 

Probe Time to Steady State, minutes Steady-State Temperature, °C... 

The HIPS resin was extruded at screw speeds of 30, 60, and 90 rpm at barrel temperatures of 200, 220, and 240 °C for Zones 1, 2, and 3, respectively. The screw temperatures in Zone 3 as a function of time at the screw speeds are shown in Fig. 10.20. Because the RTDs were positioned within 1 mm of the screw root surface, they were influenced by the temperature of the material flowing in the channels. Prior to the experiment, the screw was allowed to come to a steady-state temperature without rotation. Next, the screw speed was slowly increased to a speed of 30 rpm. The time for the screw to reach a steady state after changing the screw speed to 30 rpm was found to be about 10 minutes. The temperature of the T12 and T13 locations decreased with the introduction of the resin. This was caused by the flow of cooler solid resin that conducted energy out from the screw and into the solids. At sensor positions downstream from T13, the screw temperature increased at a screw speed of 30 rpm, indicating that the resin was mostly molten in these locations. These data suggest that the solid bed extended to somewhere between 15.3 and 16.5 diameters, that is, between T13 and T14. When the screw speed was increased to 60 rpm, the T12 and T13 sensors decreased in temperature, the T14 sensor was essentially constant, and the T15, T16, and T17 sensor temperatures increased. These data are consistent with solids moving further downstream with the increase in screw speed. For this case, the end of the solids bed was likely just upstream of the T14 sensor. If the solid bed were beyond this location, the T14 temperature would have decreased. Likewise, if the solid bed ended further upstream of the T14 sensor, the temperature would have increased. When the screw speed was increased to 90 rpm, the T12, T13, and T14 temperatures decreased while the T15, T16, and T17 temperatures increased. As before, the solids bed was conveyed further downstream with the increase in screw speed. At a screw speed of 90 rpm, the solid bed likely ended between the T14 and T15 sensor positions, that is, between 16.5 and 17.8 diameters. These RTDs were influenced by the cooler solid material because they were positioned within 1 mm of the screw root surface. 

The steady-state temperature of the fiberglass process line can be estimated with a lumped mass approach by iteratively solving Equation (5-22) for Tj. Assume the ambient and initial target temperature to be 20°C (293 K) and a nominal heat transfer coefficient of 0.015 kW/m K. 

Solving for yields an estimated steady-state temperature of 249°C (480°E). Because this temperature exceeds the first-order failure criterion for fiberglass of 150°C and the fire burns for 10 minutes, which is longer than the reported 2-6 minutes failure time for empty fiberglass pipes, the process line will be compromised. 

It was estimated that the system would operate for 183 days, and that 360 hr of heating would be required to achieve steady-state temperatures. This was estimated to be sufficient to raise the temperature of the soil from 25°F (ambient soil and air temperamre) to 90°F (D17162K, p. 12). 

Figure 3.30 Hybrid switch moduie steady-state temperature profiie at 810-W totai power dissipation. (From [31], 2003 Army Research Laboratory.)...

The details of the experimental apparatus and procedures are outlined in another paper (76). The reactor consisted of a quartz tube with an inside diameter of 18 mm which held the monolith or gauze pack. The reactor was operated at a steady state temperature which is a function of the heat generated by the exothermic reactions and... 

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