Mass single-phase

HEM for Two-Phase Pipe Discharge With a pipe present, the backpressure experienced by the orifice is no longer qg, but rather an intermediate pressure ratio qi. Thus qi replaces T o iri ihe orifice solution for mass flux G. ri Eq. (26-95). Correspondingly, the momentum balance is integrated between qi and T o lo give the pipe flow solution for G,p. The solutions for orifice and pipe now must be solved simultaneously to make G. ri = G,p and to find qi and T o- This can be done explicitly for the simple case of incompressible single-phase (hquid) inclined or horizontal pipe flow The solution is implicit for compressible regimes. 

Pathway temperatures must be strictly controlled (especially in single-phase systems) to create a balance between low-temperature oxide dissolution and high-temperature mass transfer limitations. 

The theoretical treatment which has been developed in Sections 10.2-10.4 relates to mass transfer within a single phase in which no discontinuities exist. In many important applications of mass transfer, however, material is transferred across a phase boundary. Thus, in distillation a vapour and liquid are brought into contact in the fractionating column and the more volatile material is transferred from the liquid to the vapour while the less volatile constituent is transferred in the opposite direction this is an example of equimolecular counterdiffusion. In gas absorption, the soluble gas diffuses to the surface, dissolves in the liquid, and then passes into the bulk of the liquid, and the carrier gas is not transferred. In both of these examples, one phase is a liquid and the other a gas. In liquid -liquid extraction however, a solute is transferred from one liquid solvent to another across a phase boundary, and in the dissolution of a crystal the solute is transferred from a solid to a liquid. 

Acikalin T, Wait S, Garimella S, Raman A (2004) Experimental investigation of the thermal performance of piezoelectric fans. Heat Transfer Eng 25 4-14 Adams TM, Abdel-Khalik SI, Jeter SM, Qureshi ZH (1998) An experimental investigation of single-phase forced convection in micro-channels. Int J Heat Mass Transfer 41 851-857 Adams TM, Dowling ME, Abdel-Khalik SI, Jeter SM (1999) Applicability of traditional turbulent single phase forced convection correlations to non-circular micro-channels. Int J Heat Mass Transfer 42 4411 415... 

Calame JP, Myers RE, Binari SC, Wood FN, Garven M (2007) Experimental investigation of micro-channel coolers for the high heat flux thermal management of GaN-on-SiC semiconductor devices. Int J Heat Mass Transfer 50 4767-4779 Celata GP, Cumo M, Zummo G (2004) Thermal-hydraulic characteristics of single- phase flow in capillary pipes. Exp Thermal Fluid Sci 28 87-95 Celata GP (2004). Heat transfer and fluid flow in micro-channels. Begell House, N.Y. 

Guo ZY, Li ZX (2003) Size effect on single-phase channel flow and heat transfer at microscale. Int J Heat Mass Transfer 24 284-298... 

Qu W, Mudawar 1 (2002a) Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink. Int J Heat Mass Transfer 45 2549-2565 Qu W, Mudawar 1 (2004) Measurement and correlation of critical heat flux in two-phase micro-channel heat sinks. Int J Heat Mass Transfer 47 2045-2059 Qu W, Mudawar 1 (2002b) Prediction and measurement of incipient boiUng heat flux in micro-channel heat sinks. Int J Heat Mass Transfer 45 3933-3945... 

Adams TM, Abdel-Khalik SI, Jeter SM, Qureshi ZH (1998) An experimental investigation of single-phase forced convection in micro-channels. Int J Heat Mass Transfer 41 851-857... 

Celata GP, Cumo M, Marcom V, McPhail SJ, Zummo Z (2006) Micro-tube liquid single phase heat transfer in laminar flow. Int. J. Heat Mass Transfer 49 3538-3546... 

Lelea D, Nishio S, Takano K (2004) The experimental research on micro-tube heat transfer and fluid flow of distilled water. Int J Heat Mass Transfer 47 2817-2830 Li J, Peterson GP, Cheng P (2004) Three-dimensional analysis of heat transfer in a micro-heat sink with single phase flow. Int J Heat Mass Transfer 47 4215-4231 Lin TY, Yang CY (2007) An experimental investigation by method of fluid crystal thermography. Int. J. Heat Mass Transfer 50(23-24) 4736-4742... 

Bo = q/Gh] Q, where t is the period between successive events, U is the mean velocity of single-phase flow in the micro-channel, Jh is the hydraulic diameter of the channel, q is heat flux, m is mass flux, /zlg is the latent heat of vaporization). The dependence t on Bo can be approximated, with a standard deviation of 16%, by... 

Section 1.5 described one basic problem of scaling batch reactors namely, it is impossible to maintain a constant mixing time if the scaleup ratio is large. However, this is a problem for fed-batch reactors and does not pose a limitation if the reactants are premixed. A single-phase, isothermal (or adiabatic) reaction in batch can be scaled indefinitely if the reactants are premixed and preheated before being charged. The restriction to single-phase systems avoids mass... 

Section 5.3 discusses a variety of techniques for avoiding scaleup problems. The above paragraphs describe the simplest of these techniques. Mixing, mass transfer, and heat transfer aU become more difficult as size increases. To avoid limitations, avoid these steps. Use premixed feed with enough inerts so that the reaction stays single phase and the reactor can be operated adiabatically. This simplistic approach is occasionally possible and even economical. 

In general, a multitude of different phenomena of flow, heat and mass transfer occur during a liquid/liquid or gas/liquid reaction. Rather than discussing all relevant effects, which would be a tremendous task, the focus of this section is solely on flow phenomena in either single-phase aqueous systems or air/water systems. 

Despite affecting conversion, mass transfer is known to impact enantio- and regioselectivity for many reactions [63]. For this reason, conventional micro-titration apparatus, typically employed in combinatorial chemistry of single-phase reactions, also often suffer from insufficient mixing when dealing with multi-phases [63, 66]. 

In the simplest cases, the solvent may consist of one specified component, although in fact in a steady-state cyclic process it is highly unlikely that the solvent will ever come back to the initial composition at time zero. Rather, perhaps, one can say that make-up will entail addition of one material only. Again, clearly this need not be a pure compound, but its composition should be consistent. The single solvent offers limited scope for manipulating the system since it alone must meet all process and operational requirements. In other words, it must satisfy all aspects that will lead to an overall viable system. These aspects include selectivity, capacity, solubility, mass transfer, phase separation, costs, among others. The solvent is, therefore, a mixture components. The solvent components are extractant, (ii) diluent, (iii) modifier, and (iv) synergist. 

Flow through orifices For the liquid or vapor phase flow alone passing through the orifice, expressions similar to a single-phase incompressible flow case can be written for the mass flow rates of both phases ... 

The phenomenon of critical flow is well known for the case of single-phase compressible flow through nozzles or orifices. When the differential pressure over the restriction is increased beyond a certain critical value, the mass flow rate ceases to increase. At that point it has reached its maximum possible value, called the critical flow rate, and the flow is characterized by the attainment of the critical state of the fluid at the throat of the restriction. This state is readily calculable for an isen-tropic expansion from gas dynamics. Since a two-phase gas-liquid mixture is a compressible fluid, a similar phenomenon may be expected to occur for such flows. In fact, two-phase critical flows have been observed, but they are more complicated than single-phase flows because of the liquid flashing as the pressure decreases along the flow path. The phase change may cause the flow pattern transition, and departure from phase equilibrium can be anticipated when the expansion is rapid. Interest in critical two-phase flow arises from the importance of predicting dis-... 

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