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 ΔC_sT ⁴ is high, where C_s is the Stefan-Boltzmann constant, 5.6697 × 10^–8 W/m² K⁴. When ΔT is small compared to the absolute temperature level, ΔC_sT ⁴ can be written 4C_sT_m³ΔT, where T_m is the mean temperature level. At 300 K, the value for 4C_sT_m³ is slightly over 6 W/m² K, on the same order as a natural-convection heat transfer coefficient. At T_m = 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