Abstract

Heat flow δQ of the First Law of Thermodynamics is expressed in terms of the entropy flow δ( Q/ T) δQ  δ[ T( Q/ T)] = Tδ( Q/ T)+( Q/ T) dT where Tδ( 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 = Q K + 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 П x ~ (1+q x R/q x K)Nu x 2 and П s ~ (1+q R/q K)Pe −2 where q R and q K are the one-dimensional fluxes associated with Q R and Q K , Nu x 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, ∂Pe/ ∂T b = 0, customarily used in the evaluation of minimum quench distance without any physical justification, is shown to correspond to an extremum in entropy production.

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