Radiative entropy production--lost heat into entropy

Abstract

Heat flow [delta]Q of the First Law of Thermodynamics is expressed in terms of the entropy flow [delta](Q/T)[delta]Q [triple bond] [delta][T(Q/T)] = T[delta](Q/T)+(Q/T)dT where T[delta](Q/T) denotes the energy equivalent of the entropy flow, and (Q/T)dT introduces the concept of lost heat into entropy production. Here Q = QK + QR where superscripts K and R indicate conduction and radiation, respectively. In terms of the lost heat, dimensionless entropy productions on the wall of a thermal boundary layer and in a quenched laminar flame are respectively shown to be Px ~ (1+qxR/qxK)Nux2 and Ps ~ (1+qR/qK)Pe-2 where qR and qK are the one-dimensional fluxes associated with QR and QK, Nux is a local Nusselt number, and Pe is a Peclet number based on the laminar flame speed at the adiabatic flame temperature. The tangency condition, [part]Pe/[part]Tb = 0, customarily used in the evaluation of minimum quench distance without any physical justification, is shown to correspond to an extremum in entropy production.