OCR Text |
Show - 24 - APPENDIX. THE EFFECT OF THE BOUNDARY LAYER TEMPERATURE The discrepancies in the calculated result of different investigations for the particle temperatures and for the combustion times are often due to the definition o f the boundary layer temperature. The gas properties, the density, the diffusivity and the heat conductivity depend on the temperature. The heat conductivity has a great effect on the particle temperature and on the devolatilization rate. The diffusivity has a significant effect on the combustion of the char. The calculations in this paper are made by using the boundary layer temperature Tb = O.S(Tparticle+ Tgas) . The effect of the temperature distribution in the boundary layer will be analysed. The heat transfer, neglecting the Stefan flow, around a spherical combusting fuel particle in the quasi-steady state can be described by the equation ~{>dT ) 2dTg} 2R dr g r dr = 0 (An Fig.A1. A combusting fuel particle GAS The integration twice gives surrounded by an ~(Tg' Tg A (Tg) dTg f = Co (R1 - ]r- ) (A2) infinite gas volume. T9 Ts Tg(r"·' • Too The integration constant Co can be found from the boundary condition far from the particle (Fig.A1). The solution is G(Tg) - G(Ts ) G(Tee ) - G(Ts ) 1 - R/r (A3) for the dependence between the gas temperature and the distance r. The function G(Tg) is (A4) The heat transfer coefficient h is defined by the equation dT AS(drg)r=R (AS) Th e d er i va t e (ddTr g) r=R can b e solved from the temperature distribtion (A3). The result is dT (drg ) r=R G(Tee ) - G(Ts ) G' (Ts) R (A6) where G' (Ts) = As· The heat transfer coefficient h is obtained from the formulas (AS) and (A6), h = 1 G(Tee) - G(Ts ) R Tee Ts (A7) We define the boundary layer temperature Tb, Tb=TS ... Tee , so that Nu = hd/Ab 2 with d=2R. We obtain for the gas heat conductivity at the boundary layer temperature Tb by applying the equation (A7) G(Tee ) - G(Ts ) A b = >. (Tb) = (AS) Tee - Ts We define the function F(Tg ) = G' (Tg) A(Tg ). The boundary layer temperature is obtained from the relation (AS), which gives |