A Thermodynamic Theory for Radiating Heat Transfer

Abstract

Splitting up the heat flow into severa[ parts and applying the basic ideas of Gyarmati's wave approach of thermodynamics, a systematic thermodynamical ana[ysis is given for radiating heat transfer. The possible transformations make clear that the above splitting can be done so that the different parts of the radiating heat transfer ate independealt of eacah other. The cliffere~t paxts of the heat flow are dynamic state variabtes and the whole treatment based on variables with a priori physical meaning is a bit more complicated than that based on abstract dynamic variables while the result is the same [1].

A Thermodynamic Theory for Heat Radiation Through the Atmosphere

“…The first equation is the usual one for heat exchange between two media and the other coincides with the equation derived in [1] for radiating heat transfer. The physical meaning of the coefficients k and ë and their connection to the radiating properties of the material will be discussed next.…”

“…As it was derived in [1], the radiating energy density and the heat flow obey the equations --+ divf= e -acu r , (7.1) at 1 df c ITC* = -a*"**"" (7 ' 2) J.Non-EquiUb. Thermodyn., Vol.…”

“…In a recent paper [1] we have shown that the heat propagation in a medium, the thermodynamic properties of which are given as functions of the internal energy and n dynamic state variables of jß-type vectors, can be split into n + 1 parts, one of which is obeying Fourier's equation while the others are described by Cattaneo-Vernotte type constitutive equations. If insisting on the finite velocity of signal propagations, one can not avoid the conclusion that the heat conductivity in Fourier's equation vanishes, and in this case the heat propagation is purely radiation in the semi-transparent medium.…”

Entropy Production In Thermodynamic Climate Models

“…We have used this fluxes as independent variables, developing a generalized Gibbs equation following the Extended Irreversible Thermodynamics (EIT) theory [24] that has been successfully applied in many systems. We have taken into account a Maxwell-Cattaneo type equation for the phenomenological laws of the heat and the radiative fluxes, that in the later case can be related to the radiative transfer equation [33,[36][37]. A generalized expression for the rate of entropy production outside equilibrium has been obtained with the addition of a new term related with the radiative part.…”

“…Going back to (10) and following Ciancio and Verh s [36][37], we obtain for a very anisotropic radiation field with c being the velocity of light, σ Α the absorption coefficient and U R the internal radiative energy per unit volume of the atmosphere, that can be expressed as…”