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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,
Radiation Interaction with Conduction and/or Convection
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
S Scattering, interaction phenomena with,
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Radiation Interaction with Conduction and/or Convection

DOI 10.1615/hedhme.a.000211

2.9 HEAT TRANSFER BY RADIATION
2.9.8 Radiation interaction with conduction and/or convection

K.T. Yang

A. Combined phenomena

In most heat transfer processes involving thermal radiation, radiation does not occur alone but acts together with other modes of heat transfer such as conduction and convection. In cases where the radiation process is only weakly coupled to the other mode of heat transfer, simple additions of separately calculated heat fluxes represent good approximations to the combined heat transfer. However, when the coupling is strong, radiation interaction with the other mode of heat transfer may lead to heat transfer and local temperature variations that are quite different from those based on either radiation or the other mode of heat transfer alone. When such is the case, it would be highly desirable to have well-grounded analyses and calculation procedures by which the radiation interactions can be determined. Furthermore, such analyses and procedures can be used to assess the validity of simpler analyses, including those by simple additions of the individual heat transfer process contributions, in specific instances.

Unfortunately, the calculation of radiation interaction with conduction or convection under strongly coupled conditions is in general very complicated. The difficulty lies in the difference in the basic mechanisms of heat transfer for radiation and for conduction and convection. Radiation essentially is linear in the blackbody emissive power or T 4, while conduction and convection are largely linear in T. Consequently, an interaction problem is inherently a nonlinear one. Furthermore, thermal radiation is an integral action-at-a-distance phenomenon, while conduction and convection represent a local field phenomenon. Thus, a combined phenomenon is governed it many instances by an integral-differential equation, which may present difficult in its solution. Additional complexities may include the necessity of dealing with complex geometries, the determination of radiation properties of participating media, and the evaluation of radiation fluxes.

On the other hand, despite these difficulties and complexities, relatively simple interaction analyses are still possible in certain instances. However, it is important to be able to identify such problems at the outset. This can be done by a classification of all the radiation interaction problems as follows. For conjugate interaction problems, in which radiation and conduction occur in separate regions sharing a common interface, the thermal resistance due to radiation is in series with that due to conduction. The interface temperatures are in general not known, but they may be determined by matching the interface heat fluxes. The analysis for these problems is relatively simple, even though closed-form solutions are not always possible due to the nonlinearity in the temperatures for radiation. Then there are the non-conjugate interaction problems, in which radiation takes place in the same region as conduction or convection. These problems can in turn be divided into active and passive interaction problems. In the latter case, the region contains a nonparticipating or transparent medium. If the surface temperatures are known or prescribed, then radiation and conduction or convection are entirely decoupled and hence can be analyzed separately. A simple addition gives the total heat transfer at the surface. If the surface temperatures are not known, the interaction takes place through the boundary condition in heat fluxes at the surface. In either case of passive interaction, the two thermal resistances of radiation and conduction or convection can be considered to be in parallel. For active interaction between radiation and conduction or convection, a participating medium must be present in the region. The radiation characteristics of such an emitting, absorbing, and scattering medium give rise to distributed energy sources, which must be accommodated in the conduction or convection analysis. The general complexity and difficulty in the analysis of radiation interaction with conduction or convection mentioned previously refer to active interaction problems. Closed-form solutions to these problems are extremely rare and therefore numerical solutions are almost always required. It is also important to realize that in actual applications the significance of active radiation interaction effects is not limited to high-temperature systems. Such effects may also become important even at moderate temperatures as long as the effect of thermal radiation is comparable to that of conduction or convection involved in the problem. A good example is the radiation interaction phenomenon with natural convection.

Many examples of radiation-interaction problems with conduction or convection can be cited, particularly in view of the recent advances in technology needed in new applications. The radiation-interaction phenomena and their analyses have become increasingly, more critical in the optimum design and performance of the relevant thermal devices and systems. For instance, in the more traditional areas of technology, radiation interaction plays dominant roles in the design of solar heating devices, radiating fins for spacecraft heat dissipation and evacuated insulation applications, and radiation-enhanced heating in boundary layers, internal duct flows, and heat exchangers, and cooling in materials processing such as wire drawing and certain extrusion processes. Also, because of the presence of high temperatures, radiation interaction analysis is particularly pertinent to large thermal devices and systems involving combustion and hot gases. Good examples included furnaces burning fossil fuels and molten liquid baths such as those for glass processing. Another area which has received great interest in recent times is the determination of the effects of radiation in fires. Radiation interaction had long been recognized as one of the critical phenomena underpinning the dynamics of fire in building-fire scenarios. Its analysis and simulation are needed to predict the generation and spread of fire and smoke and hot gases in rooms and buildings as a tool to determine the fire risks in building designs. Finally, it must be mentioned that radiation interaction has also been identified as the dominating phenomena in the energy transfer in semitransparent (nonopaque or translucent) materials such as plane or layered window panes, thin films, and coatings of such solids as glass, quartz, plastics, dielectrics, and semiconductors, including those associated with micro- and nano-structures. Of particular recent interest is the radiation-conduction phenomena in the processing of some materials by lasers under both steady and pulsed conditions, because of their direct relevance to the manufacture of optoelectronic and other advanced-material devices. It may also be mentioned that some liquids such as chlorine, water, and liquid oxygen are also semitransparent and offer unique radiation-interaction behaviours in specific applications.

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