242 34 2 thermodynamics of combustion the above

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Unformatted text preview: in Eq. 2.38 represents i the difference of sensible enthalpy between TR and T0 (25 C) for the reactant mixture. With the assumption that the sensible enthalpy can be approximated by ˆ ˆ ˆ hsi,P(TP) % cpi (TP À T0) with cpi % constant, we have ðTP À T0 Þ X ^ ^ Ni;P cpi  cp ðTP À T0 Þ X i Ni;P ¼ ÀQ0 ;p þ rxn X i ^ Ni;R hsi;R ðTR Þ (2.40) i Rearranging the equation one finds TP as P ^ ÀQ0 ;p þ Ni;R hsi;R ðTR Þ rxn i P TP ¼ T0 þ ^ Ni;P cpi i ÀQ0 ;p rxn % TR þ P ^ Ni;P cpi (2.41) i LHV Á Nfuel Á Mfuel P ¼ TR þ ; ^ Ni;P cpi i where the following approximation has been applied4 P i ^ Ni;R hsi;R ðTR Þ P ¼ ^ Ni;P cpi P i i ^ Ni;R cp i;R ðTR À T0 Þ P % TR À T0 ^ Ni;P cpi i When reactants enter the combustor at the standard conditions, the above equation reduces to (as sensible enthalpies of reactants are zero at T0) TP ¼ T0 þ LHV Á Nfuel Á Mfuel P : ^ Ni;P cpi i 4 P i ^ Ni;R cp i;R and P i ^ Ni;p cpi are assumed to be approximately equal. (2.42) 34 2 Thermodynamics of Combustion The above procedure is general and can be applied to any mixture. Note that the specific heat is a function of temperature, so the accuracy of this approach ˆ depends on the value selected for the specific heat cp. If the heating value of a fuel is given, a mass-based analysis for the same control volume can be conducted. The initial mixture consists of fuel and air with mf and ma, respectively. By mass conservation, the products have a total mass of mf + ma. The  sensible enthalpy of the products is approximated by Hs,P ¼ (ma + mf )Á cp;P Á (TP – T0),  where cp;P is an average value of specific heat evaluated at the average temperature of    the reactants and products, i.e., cp;P ¼ cp ðT Þ; where T ¼ ðTp þ TR Þ=2. Similarly, the  sensible enthalpy of the reactants is estimated by Hs,R ¼ (ma + mf )Á cp;R Á (TR – T0),  where cp;R is an average value of specific heat evaluated at the average temperature of    reactants and the standa...
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