Temperature field analysis

Qualitative observations of the TLC color play are possible with the naked eye. But for precise temperature field analysis, an optical-electronic calibration process is required where the TLC color play has to be analyzed at a series of different temperatures. This procedure should be carried out by slow heating of the system, to ensure a homogeneous temperature distribution inside the FOV. At various temperature levels single pictures are recorded and saved in coimection with the actual temperature recorded by thermocouples, for example. 

Qu et al. (2000) carried out experiments on heat transfer for water flow at 100 < Re < 1,450 in trapezoidal silicon micro-channels, with the hydraulic diameter ranging from 62.3 to 168.9pm. The dimensions are presented in Table 4.5. A numerical analysis was also carried out by solving a conjugate heat transfer problem involving simultaneous determination of the temperature field in both the solid and fluid regions. It was found that the experimentally determined Nusselt number in micro-channels is lower than that predicted by numerical analysis. A roughness-viscosity model was applied to interpret the experimental results. 

Heat transfer in micro-channels occurs under superposition of hydrodynamic and thermal effects, determining the main characteristics of this process. Experimental study of the heat transfer in micro-channels is problematic because of their small size, which makes a direct diagnostics of temperature field in the fluid and the wall difficult. Certain information on mechanisms of this phenomenon can be obtained by analysis of the experimental data, in particular, by comparison of measurements with predictions that are based on several models of heat transfer in circular, rectangular and trapezoidal micro-channels. This approach makes it possible to estimate the applicability of the conventional theory, and the correctness of several hypotheses related to the mechanism of heat transfer. It is possible to reveal the effects of the Reynolds number, axial conduction, energy dissipation, heat losses to the environment, etc., on the heat transfer. 

In this description the temperature field has been taken to be linear in the coordinate y and to be independent of the shape of the melt/crystal interface. This is a good assumption for systems with equal thermal conductivities in melt and crystal and negligible convective heat transport and latent heat release. Extensions of the model that include determination of the temperature field are discussed in the original analysis of Mullins and Sekerka (17) and in other papers (18,19). 

In the laboratory, soil water content is measured by drying in the oven and with a pressure plate apparatus. Drying soil can change the form and species of components present, and for this reason, most soils are air dried carefully or at temperatures only slightly above room temperature before analysis. A number of different field measuring methods are used mostly to determine the amount of water available for plant use. 

I. Chromathermography. The term coined by Zhukhovitskii et al(Ref 41) for a chromatographic analysis in which a stream of air is applied while the firnace(which heats consecutive sections of the adsorbing column, and causes desorption) is moved down the column. The air stream thus distributes the components at different spots of the temperature field, and keeps them separated. The method, first proposed in 1951, was discontinuous(Ref 41 45), but later(Ref 46), the continuous modification, called "thermal dynamic method was devised (Compare with "programmed temperature gas chromatography listed unde r item D)... 

Several issues must be addressed. First, the heat-transfer environment must yield a well-controlled temperature field in the crystal and melt near the melt-crystal interface so that the crystallization rate, the shape of the solidification interface, and the thermoelastic stresses in the crystal can be controlled. Low dislocation and defect densities occur when the temperature gradients in the crystal are low. This point will become an underlying theme of this chapter and has manifestations in the analysis of many of the transport processes described here. 

Convection in the crystal growth systems discussed earlier cannot be characterized by analysis with either perfectly aligned vertical temperature gradients or slender cavities, because these systems have spatially varying temperature fields and nearly unit aspect ratios. Even when only one driving force is present, such as buoyancy-driven convection, the flow structure can be quite complex, and little insight into the nonlinear structure of the flow has been gained by asymptotic analysis. 

Billig (98) realized this point and used a one-dimensional heat-transfer analysis for the crystal with assumptions about the temperature field in the melt to derive the the following relationship that has been used heavily in qualitative discussions of crystal growth dynamics ... 

Kobayashi (143) presented the first computer simulations that considered the determination of the crystal radius as part of the analysis but avoided the capillary problem by considering a flat melt-ambient surface, which is consistent with <)>o = 99°. Calculations were performed for a fixed crystal radius, and then the growth rate was adjusted to balance the heat flux into the crystal. Crowley (148) was the first to present numerical calculations of a conduction-dominated heat-transfer model for the simultaneous determination of the temperature fields in crystal and melt and of the shapes of the melt-crystal and melt-ambient surfaces for an idealized system with a melt pool so large that no interactions with the crucible are considered. She used a time-dependent formulation of the thermal-capillary model and computed the shape of an evolving crystal from a short initial configuration. 

In a series of papers, Derby and Brown (144, 149-152) developed a detailed TCM that included the calculation of the temperature field in the melt, crystal, and crucible the location of the melt-crystal and melt-ambient surfaces and the crystal shape. The analysis is based on a finite-ele-ment-Newton method, which has been described in detail (152). The heat-transfer model included conduction in each of the phases and an idealized model for radiation from the crystal, melt, and crucible surfaces without a systematic calculation of view factors and difiuse-gray radiative exchange (153). 

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