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Rabas and Taborek correlation, for heat transfer in banks of low fin tubes, Rackett equation (modified) for liquid density Radiation: Radiation shields, in radiation heat transfer, Radiation source analysis, Radiative heat transfer: Radiators, automotive, construction, Radiometers, application in gas radiation property measurement, Radiosity, Stephan's law for,
Introduction
Radiosity-irradiation formulations in radiative heat transfer, Rankine cycle in refrigeration, Rao, B K Raoult's law for partial pressure, Rating of heat exchangers, Rayleigh instability, in free convection, Rayleigh number Reay, D Reboilers: Reciprocal mode integrating sphere, for reflection and transmission measurements in radiation, Rectangles: Rectangular ducts: Rectangular enclosures, free convective heat transfer in: Rectangular fins, for plate fin exchangers Reduced pressure, correlations for pool boiling using, Reference temperature: Refinery processes, fouling in, Reflection, of thermal radiation, from solid surfaces: Reflectivity, of solid surfaces, Reflectometer, heated cavity, Reflux condensers, Refractories, density of, Refractory surfaces, Refrigerants: Refrigerant 11 (Trichlorofluoromethane): Refrigerant 12 (Dichlorodifluoromethane): Refrigerant 13 (Chlorotrifluoromethane): Refrigerant 21 (Dichlorofluoromethane): Refrigerant 22 (Chlorodifluoromethane): Refrigerant 116: Refrigerant plant, entropy generation in, Refrigeration, heat transfer in, Regenerators and thermal energy storage, Regimes of heat transfer, in ducts, single phase flow, Reidel method, for predicting enthalpy of vaporisation, Reinforcing rings, for expansion bellows, Relaminarization, of turbulent flow, Reichenberg method, for effect of pressure on gas viscosity, Relief system design for shell-and-tube heat exchangers with tube side failure, Removal of fouling deposits: Renewable fuels, properties of, Renotherm, heat transfer medium, Repair, of expansion bellows, Residence times, in dryers: Resistance network analysis, Resistance (thermal) due to fouling: Reversible (minimum) work, in Reynolds number, Reynolds stress models, for turbulence, Rheologically complex materials, properties of: Rheological properties of drag reducing agents Rheology, shear flow experiments used in, Rhine, J M, Ribatski, G, Riblets for drag reduction, Richardson number, Richie, J M, Ring cells, in free convection, RODbaffles, in tube bundles with longitudinal flow, Rod bundles: Rohsenow correlation, for nucleate boiling, Roll cells, in free convection, Roller expansion, of tubes into tube sheets, Rose, J W, Rossby number, Rotary dryer, Rotating drums, heat transfer to particle bed in, Rotating surface, in an annular duct Rotation, as device for heat transfer augmentation, Roughness, surface: Rough walled passages, radiative heat transfer down, Rubber (sponge) balls, in fouling mitigation, Ryznar index for water quality,

Index

HEDH
A B C D E F G H I J K L M N O P Q R
Rabas and Taborek correlation, for heat transfer in banks of low fin tubes, Rackett equation (modified) for liquid density Radiation: Radiation shields, in radiation heat transfer, Radiation source analysis, Radiative heat transfer: Radiators, automotive, construction, Radiometers, application in gas radiation property measurement, Radiosity, Stephan's law for,
Introduction
Radiosity-irradiation formulations in radiative heat transfer, Rankine cycle in refrigeration, Rao, B K Raoult's law for partial pressure, Rating of heat exchangers, Rayleigh instability, in free convection, Rayleigh number Reay, D Reboilers: Reciprocal mode integrating sphere, for reflection and transmission measurements in radiation, Rectangles: Rectangular ducts: Rectangular enclosures, free convective heat transfer in: Rectangular fins, for plate fin exchangers Reduced pressure, correlations for pool boiling using, Reference temperature: Refinery processes, fouling in, Reflection, of thermal radiation, from solid surfaces: Reflectivity, of solid surfaces, Reflectometer, heated cavity, Reflux condensers, Refractories, density of, Refractory surfaces, Refrigerants: Refrigerant 11 (Trichlorofluoromethane): Refrigerant 12 (Dichlorodifluoromethane): Refrigerant 13 (Chlorotrifluoromethane): Refrigerant 21 (Dichlorofluoromethane): Refrigerant 22 (Chlorodifluoromethane): Refrigerant 116: Refrigerant plant, entropy generation in, Refrigeration, heat transfer in, Regenerators and thermal energy storage, Regimes of heat transfer, in ducts, single phase flow, Reidel method, for predicting enthalpy of vaporisation, Reinforcing rings, for expansion bellows, Relaminarization, of turbulent flow, Reichenberg method, for effect of pressure on gas viscosity, Relief system design for shell-and-tube heat exchangers with tube side failure, Removal of fouling deposits: Renewable fuels, properties of, Renotherm, heat transfer medium, Repair, of expansion bellows, Residence times, in dryers: Resistance network analysis, Resistance (thermal) due to fouling: Reversible (minimum) work, in Reynolds number, Reynolds stress models, for turbulence, Rheologically complex materials, properties of: Rheological properties of drag reducing agents Rheology, shear flow experiments used in, Rhine, J M, Ribatski, G, Riblets for drag reduction, Richardson number, Richie, J M, Ring cells, in free convection, RODbaffles, in tube bundles with longitudinal flow, Rod bundles: Rohsenow correlation, for nucleate boiling, Roll cells, in free convection, Roller expansion, of tubes into tube sheets, Rose, J W, Rossby number, Rotary dryer, Rotating drums, heat transfer to particle bed in, Rotating surface, in an annular duct Rotation, as device for heat transfer augmentation, Roughness, surface: Rough walled passages, radiative heat transfer down, Rubber (sponge) balls, in fouling mitigation, Ryznar index for water quality,
S T U V W X Y Z
R Radiosity, Stephan's law for,
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Introduction

DOI 10.1615/hedhme.a.000204

2.9.1 Introduction

D. K. Edwards

A. Radiation heat transfer in thermal design

When does one consider radiation heat transfer, and when does one not? One does not consider radiation inside of a fluid that is highly opaque to the source spectrum. In a fluid such as water, the radiation is merely a contributor to what we know as thermal conductivity. Similarly, one docs not consider radiation inside a fluid that is perfectly transparent to the source spectrum. If there is no physical mechanism by which the fluid can absorb energy from radiation passing through it, then it follows from thermodynamics that it cannot emit radiation either, and it cannot be either heated or cooled by radiation. Such a fluid is said to be diathermanous. The walls surrounding such a fluid, however, may exchange heat radiation, but only if they are not isothermal. Thus one does not ordinarily consider radiation within the passages of a heat exchanger containing oil, water, or air. The first two are opaque. The last is diathermanous.

When two walls at different temperatures are in view of each other or one wall is in view of a participating medium (one neither opaque not diathermanous), the radiation heat flux (W/m2) tends to be high when ΔCsT 4 is high, where Cs is the Stefan-Boltzmann constant, 5.6697 × 10–8 W/m2 K4. When ΔT is small compared to the absolute temperature level, ΔCsT 4 can be written 4CsTm3ΔT, where Tm is the mean temperature level. At 300 K, the value for 4CsTm3 is slightly over 6 W/m2 K, on the same order as a natural-convection heat transfer coefficient. At Tm = 2,000 K, the value is nearly 300 times greater. From such a value, 1,800 W/m2 K, one can see why radiation contributes to film-boiling heat transfer. Radiation is important when temperatures are high, distances are large (because convective heat transfer coefficients go as passage size D as D–1/5 for turbulent flow or D–1 for laminar flow), or under vacuum conditions when convective heat transfer coefficients are low because of the low fluid density.

B. Thermodynamic surfaces and surface systems

The thermal designer needs to know surface heat fluxes adjacent to the interface between phases. When one phase is highly opaque and the other is not, the opaque surface system concept is used. Figure 1 depicts a surface system. The s surface lies just outside the highly opaque phase: the u surface lies just within it. The m surface lies sufficiently below the phase interface so that (1) no radiation crossing the s and u surfaces is transmitted to the m surface, and (2) the radiation flux crossing the m surface is given by the radiation-diffusion equation and is included with the conduction. For no flow through the surfaces and negligible transient heat storage in the mass between the m and u surfaces, one has

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