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.