Coupling radiative heat transfer in participating media with other heat transfer modes

Abstract

transfer modes are minimized or eliminated as in Dewar flasks and cryogenic storage systems. In this review, we discuss the common and not-so-common methods for treating radiation heat transfer in participating (absorbing/emitting and scattering) media, and how these methods are coupled with the overall energy equation for treating thermal transfer problems.Because radiation is almost inevitably coupled with other heat transfer modes, an overall thermal analysis requires solution of the energy equation, which is actually a balance of energy rates. Here, we follow the development in Howell et al. [1].The general form for the energy equation for a compressible fluid is where D/Dt is the substantial derivative, the left-hand side accounts for changes in stored energy within the medium, and the terms on the right-hand side account for changes in pressure work, contributions by conduction and radiation, internal sources (chemical, electrical, nuclear, etc.,), and viscous dissipation. In most practical thermal analysis problems, the pressure work and viscous dissipation terms can be neglected.Of greatest interest here is the evaluation of the local divergence of radiative flux, −∇ · q r . This is the difference in the local absorbed radiative energy minus the local emitted radiation, 4π ∞ =0 κ I b d , where κ λ is the local spectral absorptivity of the medium and I λb is the blackbody intensity given by the Planck distribution. In an absorbing-emitting-scattering medium, the absorbed radiative energy is found by first finding the local radiative intensity I λ (Ω), which is defined as the spectral energy propagating in a given direction Ω per unit solid angle, per unit area AbstractThe common methods for finding the local radiative flux divergence in participating media through solution of the radiative transfer equation are outlined. The pros and cons of each method are discussed in terms of their speed, ability to handle spectral properties and scattering phenomena, as well as their accuracy in different ranges of media transport properties. The suitability of each method for inclusion in the energy equation to efficiently solve multi-mode thermal transfer problems is discussed. Finally, remaining topics needing research are outlined.