Profile solid temperature

It is useful for illustrative purposes to consider a laser beam with a Gaussian spatial profile and a square pulse time profile. If the laser has a Gaussian spatial beam profile the temperature at the surface of the Irradiated solid (z=0) at a time t after the laser pulse is started is given by(4) ... 

Figure 5-20 Closure age and closure temperature at every point along the profile (solid curves), and the bulk mineral closure age and closure temperature (dashed lines). Same input parameters as Figure 5-18.

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... 

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... 

Figure 8. I-V discharge profile (solid symbols) and power density (open symbols) of the porous electrolyte SC-SOFC. Data collected at a set temperature of 606°C [4]...

The two main advantages are the good solids mixing and uniform solids temperature profile in the fluidized bed. These two advantages produce the finest grade char of any of the pyrolysis processes. 

Figure 8.3 Storage modulus (G ) profiles (solid lines) of 15% (w/w) starch suspensions as a function of time during a heating and a cooling cycle (dotted lines) (a) potato starch (b) wheat starch. The maximum heating temperature is indicated in each curve.153...

Figure 3. Two-dimensional solid temperature profile in a (3.3 cm x 3.3 cm) structure (see text for conditions).

The objective was to develop a model for continuous emulsion polymerization of styrene in tubular reactors which predicts the radial and axial profiles of temperature and concentration, and to verify the model using a 240 ft. long, 1/2 in. OD Stainless Steel Tubular reactor. The mathematical model (solved by numerical techniques on a digital computer and based on Smith-Ewart kinetics) accurately predicts the experimental conversion, except at low conversions. Hiqh soap level (1.0%) and low temperature (less than 70°C) permitted the reactor to perform without plugging, giving a uniform latex of 30% solids and up to 90% conversion, with a particle size of about 1000 K and a molecular weight of about 2 X 10 . 

The CL intensity-temperature-time (ITt) profiles of resin coupons aged for various periods of time, temperature, humidity, and tensile stress were measured. ITt profiles of resin coupons were measured immediately after removal from the fabrication mold and after selected aging. In the plots and all ITt profiles, the temperature (T) of the sample during CL measurement is shown by a dashed line (the temperature scale is the left ordinate), the CL intensity by the solid line (intensity flux is the right ordinate), and, on the abscissa, the time (t) after the mesurement commenced. A ITt profile of a resin coupon measured immediately after removal from the fabrication mold is shown in Figure 2. 

The numerical solution to the system of equations (12) - (17) parallels that of the one-phase model almost exactly, with longer computation times due to the increased size of the collocation matrix and its bandwidth. Typical computation times to produce fluid and solid temperature profiles at each of five bed-depths were 3-4 seconds. 

The difference between these is shown most clearly in the gas and solids temperature profiles along the dryer. For cross-flow dryers, all solids particles are exposed to the same gas temperature, and the solids temperature approaches the gas temperature near the end of... 

Viskanta and Gore [2] studied a two-section burner which was substantially thinner than the current study and was constructed with different materials. In agreement with their results, the temperature profiles (not shown) for different heat-transfer coefficients indicated that for higher values of h, the peak solid temperature increased due to more effective gas-to-solid heat transfer. This then promoted higher radiative flux from the high-temperature zone. The maximum gas temperature was not, however, significantly affected. 

LAMINAR AND TURBULENT FLOW IN BOUNDARY LAYERS. The fluid velocity at the solid-fluid interface is zero, and the velocities close to the solid surface are, of necessity, small. Flow in this part of the boundary layer very near the surface therefore is essentially laminar. Actually it is laminar most of the time, but occasionally eddies from the main portion of the flow or the outer region of the boundary layer move very close to the wall, temporarily disrupting the velocity profile. These eddies may have little effect on the average velocity profile near the wall, but they can have a large effect on the profiles of temperature or concentration when heat or mass is being transferred to or from the wall. This effect is most pronounced for mass transfer in liquids. 

Fig. 60. Reduction of NO with CO over Rh/Ce ) 6Zro 402 reaction profile vs. temperature obtained after an initial period of 60 min at 300 K (reaction conditions NO(l%) and CO(3%) in He, heating/cooling rate 1 Kmin W/ F= 1 x 10 3 gcil,il ysl ml"1 min). Selectivity in N20 formation (squares) and CO conversion (triangles) measured on a freshly reduced catalyst NO conversion measured in run-up experiment on a freshly reduced catalyst (solid circles) and run-down experiment on an aged catalyst (open circles). (Fomasiero et al. 1998.)...

Figure 4 Phase diagram for CO2 including typical ocean temperature profile (solid line). Reprinted from Brewer PG, Peltzer E, Aya I, et al. (2004) Small scale field study of an ocean CO2 plume. Journal of Oceanography 60(4) 751.

Figure II.8.b-I One-dimensional heterogeneous model with interfacial gradients. Start up of reactor, transient temperature profiles. AT = temperature increase of gas phase above feed value AT = increase of solid temperature above initial value.

FIGURE 3.14 Solution of a model of drying for a shrinking solid. Gelatin plate 3 mm thick, initial moisture content 6.55 kg/kg. Shrinkage coefficient 5 = 1.36. Main plot shows dimensionless moisture content O, dimensionless thickness 5 = R/Rq, solid temperature t. Insert shows evolution of the internal profiles of O. 

FIGURE 3.22 Simulation of deep bed drying of cereal grains (a) moisture content profiles (solid lines) and gas humidity profiles (broken lines) (b) material temperature (solid lines) and air temperature (broken lines). Initial solid temperature 20°C and gas inlet temperature 70°C. Profiles are calculated at 0.33,1.67,3.33, 6.67, and 11.67 min of elapsed time. is equilibrium moisture content and is wet-bulb temperature. 

In addition to temperature differences between fluid and solid catalysts, temperature profiles within the porous catalyst may occur. However, because of the higher thermal conductivity of the solid, temperature differences are normally small and exceed rarely several degrees. 

Optohydrodynamics Fluid Actuation by Light, Fig. 2 Variation of the interface bending for increasing beam power P (a) upward and (b) downward continuous Ar" laser beam (wavelength in vacuum io = 514 nm) of beam waist coo- The theoretical profiles (solid lines) are calculated from Eq. 7. Experiments are performed in a phase-separated near-critical binary liquid mixture in order to drastically reduce the interfacial tension when approaching in temperature the critical temperature Tc-... 

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