Temperature distributions

The temperature distribution in ceramic materials heated by microwave energy can be obtained by solving the continuity equation for heat (equation 

By substituting P using equation 24 and noting any functional relationship between and T, various solutions of T a function of y (considering only one dimension) and t can be obtained. 

A key feature of the model vas the assumption that the loss tangent of the lower density regions was approximately equal to that of the higher 

Whilst the exact nature of the relationship between loss tangent and density is uncertain, by allowing that tan 6p tan we find  

Microwave sintering of strontium titanate and a-alumina was used to experimentally verify the importance of porosity level and distribution by comparing heating rates for samples of varying porosity. The results clearly indicated that the model is essentially correct the fastest heating rate (ie the maximum power absorbtion) being obtained for samples with approximately 50% porosity. Power absorbtion fell sharply for samples with lower or higher 

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A simple algorithm can be developed (see App. E) to target the minimum total number of shells (as a real, i.e., noninteger number) for a stream set based on the temperature distribution of the composite curves. The algorithm starts by dividing the composite... 

With this technology even boreholes, up to 2mm underneath the surface, can be identified, A remarkable borehole is represented in illustration 10, For the elucidation of the temperature contrast, a three-dimensional temperature distribution of the entire blade is shown beside the infrared picture (the similarity of the temperature distribution with the actual blade airfoil is purely coincidental). 

For IR defectoscopy of cement kilns one can use the data about temperature distribution over an operating cement kiln surface, obtained with scanning units of thermal monitoring [1],... 

Fig.3 shows comparison of calculated temperature distribution along the coordinate Z of a kiln cylindrical body with an experimental one. 

Figure 5.15 (a) The predicted temperature distribution eorresponding to the no-slip... 

For simplicity, we further assume h = 1. Let some initial temperature distribution be given ... 

Whereas the OVD, PCVD, and MCVD processes build a refractive index profile layer by layer, the VAD process uses gaseous constituents in the flame to control the shape and temperature distribution across the face of the growing soot boule. 

After exiting the economizer, the feedwater is directed iato the boilet s cylindrical steam dmm via a common header pipe that penetrates the dmm s wall and distributes the water evenly within the dmm through holes drilled ia the upper side of the distribution pipe. Because the distribution pipe is located axially below the waterline ia the lower section of the steam dmm, the incoming feedwater mixes thoroughly with the water ia the dmm and prevents any significantly uneven temperature distributions within the dmm. 

Dry-heat sterilization is generally conducted at 160—170°C for >2 h. Specific exposures are dictated by the bioburden concentration and the temperature tolerance of the products under sterilization. At considerably higher temperatures, the required exposure times are much shorter. The effectiveness of any cycle type must be tested. For dry-heat sterilization, forced-air-type ovens are usually specified for better temperature distribution. Temperature-recording devices are recommended. 

The sterilizers or retorts used to process canned or prepackaged foods must be designed in such a way as to assure uniform temperature distribution throughout. Adequate venting permits complete air removal. The air vent is located at the opposite end from the steam inlet (24). The retorts may be horizontal or vertical in design. 

Deposits sometimes block fuel nozzles and distort fuel spray patterns, lea ding to skewed temperature distribution with the possibiUty of burnout of turbiae parts by a "hot streak" exhaust. These deposits are sometimes associated with metal-containing particulates, but ia geaeral are another manifestation of fuel iastabiUty. 

Steady state pi oblems. In such problems the configuration of the system is to be determined. This solution does not change with time but continues indefinitely in the same pattern, hence the name steady state. Typical chemical engineering examples include steady temperature distributions in heat conduction, equilibrium in chemical reactions, and steady diffusion problems. 

Various numerical and graphical methods are used for unsteady-state conduction problems, in particular the Schmidt graphical method (Foppls Festschrift, Springer-Verlag, Berhn, 1924). These methods are very useful because any form of initial temperature distribution may be used. 

I0-38Z ) is solved to give the temperature distribution from which the heat-transfer coefficient may be determined. The major difficulties in solving Eq. (5-38Z ) are in accurately defining the thickness of the various flow layers (laminar sublayer and buffer layer) and in obtaining a suitable relationship for prediction of the eddy diffusivities. For assistance in predicting eddy diffusivities, see Reichardt (NACA Tech. Memo 1408, 1957) and Strunk and Chao [Am. ln.st. Chem. Eng. J., 10, 269(1964)]. 

Dukler Theory The preceding expressions for condensation are based on the classical Nusselt theoiy. It is generally known and conceded that the film coefficients for steam and organic vapors calculated by the Nusselt theory are conservatively low. Dukler [Chem. Eng. Prog., 55, 62 (1959)] developed equations for velocity and temperature distribution in thin films on vertical walls based on expressions of Deissler (NACA Tech. Notes 2129, 1950 2138, 1952 3145, 1959) for the eddy viscosity and thermal conductivity near the solid boundaiy. According to the Dukler theoiy, three fixed factors must be known to estabhsh the value of the average film coefficient the terminal Reynolds number, the Prandtl number of the condensed phase, and a dimensionless group defined as follows ... 

Thermal-expansion and -contraction loads occur when a piping system is prevented from free thermal expansion or contraction as a result of anchors and restraints or undergoes large, rapid temperature changes or unequal temperature distribution because of an injection of cold liquid striking the wall of a pipe cariying hot gas. 

Estimate temperature distribution in the evaporator, taking into account boiling-point elevations. If all heating surfaces are to be equal, the temperature drop across each effect will be approximately inversely proportional to the heat-transfer coefficient in that effect. 

Values of enthalpy constants for approximate equations are not tabulated here but are also computed for each stage based on the initial temperature distribution. 

A factor in addition to the RTD and temperature distribution that affects the molecular weight distribution (MWD) is the nature of the chemical reaciion. If the period during which the molecule is growing is short compared with the residence time in the reactor, the MWD in a batch reactor is broader than in a CSTR. This situation holds for many free radical and ionic polymerization processes where the reaction intermediates are very short hved. In cases where the growth period is the same as the residence time in the reactor, the MWD is narrower in batch than in CSTR. Polymerizations that have no termination step—for instance, polycondensations—are of this type. This topic is treated by Denbigh (J. Applied Chem., 1, 227 [1951]). 

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