Thermal Gradient Calculation

Thermal Gradients may be measured or calculated by means of heat flow formulas, etc. After they are established it is likely to be found from the formula that for most cyclic heating conditions the tolerable temperature gradient is exceeded. This means that some plastic flow will result (for a ductile alloy) or that fracture will occur. Fortunately, most engineering alloys have some ductility. However, if the cycles are repeated and flow occurs on each cycle, the ductility can become exhausted and cracking will then result. At this point it should be recognized that conventional room temperature tensile properties may have little or no relation to the properties that control behavior at the higher temperatures. 

R. W. H. Sargent The maximum concentration of CO2 in the fixed-bed tests was 1000 ppm and there was no measurable rise in gas temperature along the bed. We are currently doing tests with much higher CO2 concentrations and have extended the model to deal with thermal effects. Calculations with this model for the original tests confirm that temperature gradients are negligible, both in the gas phase and in the interior of the pellets. 

Blocks are normally 9" x 6" and supplied in thicknesses of l", V/", 2" and 2V2" to meet the requirements of a variety of applications. The thickness of the block for a particular application is determined by the hot face temperature or operating temperature. The thermal gradient is calculated to ensure that the membrane or substrate does not experience temperatures beyond its recommended limit. 

The in-depth model of the deposition process is another important aspect of gaining a deep understanding of an LI-CVI process as well as a TG-CVI process. Under a strong thermal gradient the relationship between the deposition rate on a fibre (udep) and the densification rate inside the preform (u/ront) can be calculated by using the one-dimensional model [42],... 

The use of a systems analog to improve the performance of a DTA apparatus and also to study the thermal effects in the DTA curve was investigated by Wilburn et al. (29,30). A finite-difference procedure was used to relate the thermal gradients within the samples and to generate or absorb heat according to a known equation. The influence of such physical properties on the shape and peak temperature of a typical DTA curve was calculated on an ICT Model 1909 computer. 

Thermopower calculations show results opposite to that of the Hall coefficient electron-llke for in-plane thermal gradients and a change of sign (or nearly so, depending on the energy dependence of the scattering) for a 90 rotation of VT. These rather unusual... 

The factors in Table 17.2, which have detrimental effects on DTA curves, have minimal effects on DSC curves. In particular, measurements obtained from the total area under the curve (calculation of A// and sample mass) are not affected. However, these factors still have an effect on the rate of reaction, particularly if large thermal gradients are allowed to develop in the sample or reference, that have a severe effect upon the apparent rate of reaction and any values calculated from these rates. 

Thermal gradients can be logarithmic or linear across a vessel wall. Given a steady heat input inside or outside a tube the heat distribution will be logarithmic if there is a temperature difference between tlie inside and outside of the tube. This effect is significant for thick-walled vessels. A linear temperature distribution occurs if the wall is thin. Stress calculations are much simpler for linear distribution. 

Incorporating Thermal Gradients into the Model Calculations... 

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