Solidification transport

The pour point of a crude oil or product is the lowest temperature at which an oil is observed to flow under the conditions of the test. Pour point data indicates the amount of long-chain paraffins (petroleum wax) found in a crude oil. Paraffinic crudes usually have higher wax content than other crude types. Handling and transporting crude oils and heavy fuels is difficult at temperatures helow their pour points Often, chemical additives known as pour point depressants are used to improve the flow properties of the fuel. Long-chain n-paraffins ranging from 16-60 carhon atoms in particular, are responsible for near-ambient temperature precipitation. In middle distillates, less than 1% wax can be sufficient to cause solidification of the fuel. ... 

The presentation in this paper concentrates on the use of large-scale numerical simulation in unraveling these questions for models of two-dimensional directional solidification in an imposed temperature gradient. The simplest models for transport and interfacial physics in these processes are presented in Section 2 along with a summary of the analytical results for the onset of the cellular instability. The finite-element analyses used in the numerical calculations are described in Section 3. Steady-state and time-dependent results for shallow cell near the onset of the instability are presented in Section 4. The issue of the presence of a fundamental mechanism for wavelength selection for deep cells is discussed in Section 5 in the context of calculations with varying spatial wavelength. 

Applications of PCM cover many diverse fields. As mentioned before, the most important selection criterion is the phase change temperature. Only an appropriate selection ensures repeated melting and solidification. Connected to the melting and solidification process is the heat flux. The range of heat flux in different applications covers a wide range from several kW for space heating with water or air, domestic hot water and power plants to the order of several W for temperature protection and transport boxes (Figure 124). 

The liquid waste is stored for at least 6 y prior to solidification to reduce the decay heat (Fig. 16.8) by a factor of 10 or more. The first U.S. military fuel reprocessing wastes were stored as neutralized waste in mild steel tanks at the Hanford reservation in eastern Washington. These steel-lined, reinforced-concrete tanks were 500,000-1,000,000 gal in capacity with provisions for removal of waste heat and radiolysis products. Corrosion of several tanks occurred with the release of waste. Fortunately, the soil around these tanks retarded nuclide transport. A better (and more expensive) design for storage tanks was implemented at the Savannah River site in South Carolina consisting of a second steel tank inside of a Hanford-style tank. The storage of acid waste in these tanks has not encountered the corrosion problems seen with the Hanford tanks. 

The research race aiming at solidification of DSC by replacing the liquid electrolytes with solid state materials such as conductive polymers and novel hole transport materials is still on. Tennakone disclosed the use of CuBr as an exotic hole transport material for solidification of DSC.,02) Such success would open up the possibility of a low-cost printing process to fabricate solid-state DSC. 

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. 

When viewed from a reference frame that is stationary with respect to the solidification interface, the melt moves uniaxially toward the interface and the crystal moves away. Then solute transport in the melt is governed by the one-dimensional balance equation... 

When the alloy is nondilute, the melting temperature depends on the solute concentration adjacent to the interface through the shape of the liq-uidus curve. Then the transport of heat and solute and the location of the solidification interface do not decouple (23) Derby and Brown (24) presented a numerical algorithm for the analysis of this problem. 

Connection between Transport Processes and Solid Microstructure. The formation of cellular and dendritic patterns in the microstructure of binary crystals grown by directional solidification results from interactions of the temperature and concentration fields with the shape of the melt-crystal interface. Tiller et al. (21) first described the mechanism for constitutional supercooling or the microscale instability of a planar melt-crystal interface toward the formation of cells and dendrites. They described a simple system with a constant-temperature gradient G (in Kelvins per centimeter) and a melt that moves only to account for the solidification rate Vg. If the bulk composition of solute is c0 and the solidification is at steady state, then the exponential diffusion layer forms in front of the interface. The elevated concentration (assuming k < 1) in this layer corresponds to the melt that solidifies at a lower temperature, which is given by the phase diagram (Figure 5) as... 

Although equation 33 gives a physical description of the mechanism of the instability that leads to microstructure formation during solidification, it is not rigorous because it does not consider the effects of the rates of heat and species transport on the evolution of the disturbance. Because of this deficiency, equation 33 cannot be used as a basis for further analysis of microstructure formation. This deficiency is shown clearly by the inability of equation 33 to predict the spatial wavelength of the microstructure formed along the interface. 

Mullins and Sekerka (88, 89) analyzed the stability of a planar solidification interface to small disturbances by a rigorous solution of the equations for species and heat transport in melt and crystal and the constraint of equilibrium thermodynamics at the interface. For two-dimensional solidification samples in a constant-temperature gradient, the results predict the onset of a sinusoidal interfacial instability with a wavelength (X) corresponding to the disturbance that is just marginally stable as either G is decreased... 

The results of all the thermal-capillary models discussed so far have neglected the influence of convection in the melt in transporting heat to the solidification interface. The status of convection calculations that neglect the coupling to global heat transfer and capillary consideration is discussed later. The union of thermal-capillary analysis with detailed convection calculations is discussed in the subsection on melt flow. 

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