OCR Text |
Show 2. Next, new values of '¥ 1+1 (t) are calculated in Eqn. 5, with J 1 and Jl obtained. 3. Finally, new values of S,+1(t) are computed in Eqn. 4 and boundary conduction. This procedure is repeated until the convergence criterion is satisfied. (iv) Calculation of the heat transfer in the preheat zone After the temperature distribution( S( t) ) in the preheat zone is derived, the dimensionless heat flux terms can be derived as below: Conduction Heat Flux Convection Heat Flux Radiation Heat Flux 'P rad = q~ = 2· Jt£l(t) - 2· J 2£1(to - t) n/2 +2 J~[(1 - C1l0)S4(t) + :o'¥(t)}E2(t -t)dt -2 J~O[(1 - C1lo)94(/) + :°'11(1)]£2(1 - t}dl (9) Total Heat Flux 'P 1010/ = 'P cond + '11 conv + 'P rod ( 1 0) 2.2 Wide-Band Model for Non-isothermal Gas [12][13][20]: Edwards( 1976) indicated the radiative properties of a molecular gas vary so strongly and rapidly across the spectrum that the assumption of a "gray" gas is almost never a good one. Quantum mechanics postulates that the energy levels for atomic or molecular electron orbit as well as the energy levels for molecular rotation and vibration are quantified~ i.e., electron orbit and rotational and vibrational frequencies can only change by certain discrete amouts. The orbit of an electron (0.01 - 1.5~) Vibrational energy level (1.5 - 20J.ll1l) Rotational energy level (> 20J.1ln) Changes in vibrational energy levels may be accompanied by rotational transitions, leading to closely spaced groups of spectral lines that, as a result of line broadening, may partly overlap and lead to so-called vibration-rotation bands in the infrared. The band strength parameter or band intensity a is defined by a == J~ lC'1drt = J~ (SIti)'1drt (11) lC'1 :the spectral absorption coefficients. In the preheat zone in the flame front, the gas temperature may steeply increase within a very short distance, which is characteristic of the gas in this zone. Based on the ideal gas, gas density distribution may change as below: T = T(s') Pa/(MI22.4 x 1000) = (27311)(P alP aim) 4 |