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transfer media,

Index

HEDH
A B C D E F G H I J K L M N O P Q R S
Saddle supports, for heat exchangers, Safety factors, Safety, of heat exchangers: Salicyl aldehyde: Salts, heat transfer, as heat transfer media, Sand roughness, equivalent, Santotherm, heat transfer media, Sastri and Rao correlation for surface tension, Saturated boiling: Saturated density: Saturated fluids, tables of physical properties, Saturation pressure, Saturation temperature, Saunders, E A D Sauer, H J Jr, Scale formation in heat exchangers, Scaling approximations, in nonisothermal gas radiation, Scattering bed models, for radiative heat transfer from surfaces, Scattering, interaction phenomena with, Scattering coefficient, Schack wide-band model, for gas radiation properties, Schick and Prausnitz method, for critical volume of mixtures, Schlunder, E U Schmidt, F W Schmidt correlation, for heat transfer in in-line banks of high fin tubes, Schmidt number, Schneider, G E, Schrock and Grossman correlations, for forced convective heat transfer in two-phase flow, Schunk, M Schwier, K, Scraped surfaces: Scaling devices, in shell-and-tube heat exchangers, Seawater physical properties, Seider-Tate equation, for heat transfer in heat exchangers, Selection of heat transfer equipment: Semiconductors, thermal conductivity, Separated flow model: Separation, exergy analysis for, Separators, for use in association with evaporators, Series solutions, for one-dimensional transient conduction, Serrated fins, in plate fin heat exchangers, Shah correlation for boiling, Shah correlation, for boiling in horizontal tubes, Shape factor, in radiative heat transfer between diffuse surfaces, Shear flow, of non-Newtonian fluids, Shear free flow, of non-Newtonian fluids, Shear rate, in fluid, Shear stress: Sheffield, J W, Shelf dryer, Shell-and-tube heat exchanger: Shell-to-baffle clearance, in shell-and-tube heat exchangers, Shells, for shell-and-tube heat exchangers: Sherwood number Shipes, K V, Short-tube vertical evaporator, Sigma phase embrittlement, of stainless steels, Silicate scales, in heat exchangers, Silicone oils, as heat transfer media, physical properties of, Silver method, for calculation of multicomponent condensation, Similarity theory, Simonis, V, Single-phase fluid flow: Single stage flash evaporation (SSF): Singularities, two-phase gas-liquid pressure drop across, Sink, in radiation: Skid-mounted units, specification of, Skin friction coefficient, Skrinska, A, Slab: Sleeves, internal, for expansion bellows, Slot: Slug flow: Slugging, in fluidized beds, Smith, A A, Smith, R, Smith, R A Smith, O, Snell's law, in radiation, Software, for code design, Solar absorber, Solar reflector, Soldered fins, in double pipe exchangers, Solid fuels, properties of, Solids circulation, in fluidized beds, Solid-gas flow: Solid-liquid flow: Solidification: Solids: Solids circulation, in fluidized beds, Soot blowing, Sound velocity: Source, in radiation: Spacers, in shell-and-tube heat exchangers, Spalding, D B, Sparging: Specific enthalpy, Specific entropy: Specific heat capacity, Specific internal energy, Specific volume: Specification of heat exchangers, Spectral absorptivity: Spectral emissivity, in gases, Specular surface, Specular-walled passages, radiative heat transfer in, Spheres: Spherical coordinates, for finite difference equations for conduction, Spherical shells: Spheroids (oblate and prolate), free convective heat transfer from, Spine fins: Spiral heat exchanger: Spirally fluted tubes: Sponge rubber balls, in fouling mitigation, Spray dryers, Sprays, in heat exchangers, Square ducts: Stable equilibrium, of vapor and liquid, Staggered tube banks: Stainless steels, Stanton number Startup: State diagram, for fluidized beds, Static mixers, in heat exchangers, Statically stable foams, Steam, dropwise condensation of, Steam tables, Steam turbine exhaust condensers, Steels, as material of construction, Stefan-Boltzmann constant, Stefan's law, for blackbody radiation, Stegmaier, W, Steiner and Taborek correlation, for forced convective boiling, Stephan and Korner correlation, for boiling of binary mixtures, Stiffeners, PD5500 code guidelines for, Stiffeners, against external pressure, EN13445 guidance on, Stirred beds, heat transfer to, Stirred reactor model, for furnaces, Stone's strongly implicit method, Straight fins (longitudinal fins): Stratified gas-liquid flow: Stratified liquid-liquid-gas flow: Steam analysis methods, for shell-side heat transfer and pressure drop in shell-and-tube heat exchangers, Stress, compressive, in heat exchanger tubes, Stress corrosion cracking, of stainless steels, Stress equation models, for turbulent boundary layers, Stress-strain curve, for solids, Stress tensor: Stresses: Strip baffles, in tube bundles with longitudinal flow, Strouhal number, Subchannel analysis, for critical heat flux in rod bundles, Subcooled boiling: Subcooling: Sublayer, viscous, Submerged combustion, Successive over-under relaxation method for solution of implicit equations, Suction: Suction line exchangers in refrigeration, Sulfur: Sulfur compounds (organic): Sulfur dioxide: Sulfur hexafluoride: Sulfur trioxide: Supercritical fluids: Superficial velocity, in multiphase flow, Superheated gases: Superheated liquid, in metastable state, Superheated vapor, condensation of, on vertical surface, Supersaturation, as cause of fogging in condensers: Suppression of nucleate boiling, Surface catalysis, in augmentation of heat transfer, Surface condensers, Surface finish: Surface, hydraulically smooth, Surface material, effect on fouling, Surface models, in radiative heat transfer, Surface modification for drag reduction, Surface temperature, effect on fouling, Surface tension: Surfactants, in drag reduction, Suspension, radiation interaction phenomena in, Sutherland formula, for viscosity variation with temperature, Sutterby fluid (non-Newtonian), free convective heat transfer to, Swirling flow, in augmentation of heat transfer, Synthetic heat transfer media, Synthetic mixture heat transfer media,
T U V W X Y Z

Introduction and Fundamentals

DOI 10.1615/hedhme.a.000153

2.3.1 Introduction and fundamentals

A. Classification of multiphase flows

Surveys carried out on industrial heat exchanger systems have indicated that more than half of these involve multiphase flow in one form or another. Multiphase flow’s are ubiquitous in the power generation and process industries and have a very wide range of applications. Such flows are often extremely complex in nature and it should be stated at the outset that many of the relationships used for multiphase flows are of an essentially empirical nature, are of limited applicability, and reflect the poor physical understanding of many two-phase flow phenomena.

This part of the handbook deals with a variety of multiphase flows in which the phases passing through the system may be solid (denoted by the subscript s), liquid (denoted by  ), or gas 1 (denoted by g ). Some of the characteristic features associated with the behavior of each of these phases in multiphase flows are as follows:

  1. Solids: Normally, the solid phase is in the form of lumps or particles. To all intents and purposes, the solid phase can be regarded as incompressible and to have a nondeformable interface with the fluid phase or phases with which it is flowing. The flow characteristics are strongly dependent on the size of the individual solid elements and on the motions of the associated fluids. Very small particles follow the fluid motions whereas larger particles are less responsive to turbulent eddies in the fluid. Normally, the size is nonuniform and a knowledge of the particle size distribution is of great significance in studying such flows. More often than not, the solid is denser than the associated fluid phases and, in horizontal flow systems, this can give rise to gravitational separation or stratification. Solid particles may adhere to channel walls as permanent fouling layers, and these layers can often be very significant resistances to heat transfer. Examples here would be the deposition of magnetite particles on the tubes of a boiler or deposition of crystalline solids in a cooler crystallizer.

  2. Liquid: In multiphase flows containing a liquid phase, the liquid can be the continuous phase, containing dispersed elements of solids (particles), gases (bubbles), or other liquids (drops). The liquid phase can also be discontinuous, for example, in the form of drops suspended in a gas phase or in another liquid phase. With the exception of some special kinds of non-Newtonian liquids, liquids differ greatly from solids in their response to deforming forces. In solids, provided the force is not too high, a small reversible deformation (elastic) occurs, allowing an equal and opposite force to be transmitted through the solid to balance the imposed force, if the solid is to remain at rest. As a fluid, a liquid does not have this property and a balancing force can only exist if the liquid is in motion. A liquid also differs from a solid insofar as its interface with other fluids (gases or other liquids) is readily deformable. The existence of interfacial tension (which may be regarded as the energy required to form a unit area of interface) tends to limit the deformation. For example, there is a tendency to form spherical droplets when the liquid is the discontinuous phase, such droplets representing the minimum interfacial energy per unit volume of the liquid.
    Another important property of liquid phases relates to wetting. When a liquid phase is in contact with a solid phase (such as the channel wall) and is adjacent to another phase which is also in contact with the wall, there exists at the wall a triple interface, and the angle subtended at this interface

  3. Gas: As a fluid, a gas lias the same properties as a liquid in its response to forces. However, it has the important additional property of being (in comparison to liquids and solids) highly compressible. Notwithstanding this property, many multiphase flows containing gases can be treated as essentially incompressible, particularly if the pressure is reasonably high and the Mach number with respect to the gas phase is low (e.g., < 0.2).

Having made some general statements about the properties of the various phases that make up multiphase flows, the common forms of multiphase flow will now be considered and examples given of their applications.

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