Radiative entropy production-cost heat into entropy

Heat flow SQ of the First Law of Thermodynamics is expressed in terms of the entropy flow &Q/T) SQ = SIT(QIT)I = ~~(Q/~+(Q~~d~ where T&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 f Q R 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 l-I, (1 +qF/q$)Nu,’ and IIs (1 +qR/qK) Pe-* where gR and q” are the one-dimensional fluxes associated with QR and QK, Nu, 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, aPe/aTb = 0, customarily used in the evaluation of minimum quench distance without any physical justification, is shown to correspond to an extremum in entropy production.