174:
561:
Hirschfelder, J. O., & Curtiss, C. F. (1948, January). Theory of propagation of flames. Part I: General equations. In
Symposium on Combustion and Flame, and Explosion Phenomena (Vol. 3, No. 1, pp. 121-127).
509:
31:) is the ratio of mass-flux of a particular chemical species to the total mass flux of a gaseous mixture. It includes both the convectional mass flux and the diffusional mass flux. It was introduced by
409:
228:
57:
334:
540:
359:
282:
437:
306:
253:
618:
415:
similar to the mass fraction, but the mass-flux fraction can take both positive and negative values. This variable is used in steady, one-dimensional
445:
580:
von Karman, T., & Penner, S. S. (1954). The thermal theory of constant-pressure deflagration for first-order global reactions.
613:
231:
40:
371:
185:
32:
169:{\displaystyle \epsilon _{i}={\frac {\rho _{i}(v+V_{i})}{\rho v}}=Y_{i}\left(1+{\frac {V_{i}}{v}}\right)}
36:
623:
312:
571:
von Karman, T., & Penner, S. S. (1954). Fundamental approach to laminar flame propagation.
518:
344:
260:
439:
direction) steady flows, the conservation equation for the mass-flux fraction reduces to
422:
291:
238:
607:
598:
Penner, S. S. (1957). Chemistry problems in jet propulsion (Vol. 1). Pergamon Press.
416:
44:
504:{\displaystyle {\frac {d\epsilon _{i}}{dx}}={\frac {w_{i}}{\rho v}}}
419:
problems in place of the mass fraction. For one-dimensional (
16:
Ratio of mass-flux of chemical species to total mass flux
589:
Williams, F. A. (2018). Combustion theory. CRC Press.
521:
448:
425:
374:
347:
315:
294:
263:
241:
188:
60:
255:
is the mass average velocity of the gaseous mixture
534:
503:
431:
403:
353:
328:
300:
276:
247:
222:
168:
284:is the average velocity with which the species
47:in 1954. The mass-flux fraction of a species
8:
526:
520:
485:
479:
459:
449:
447:
424:
389:
379:
373:
346:
320:
314:
293:
268:
262:
240:
212:
206:
193:
187:
150:
144:
127:
100:
81:
74:
65:
59:
404:{\displaystyle \sum _{i}\epsilon _{i}=1}
554:
542:is the mass production rate of species
223:{\displaystyle Y_{i}=\rho _{i}/\rho }
7:
619:Dimensionless numbers of chemistry
14:
106:
87:
1:
25:Hirschfelder-Curtiss variable
640:
365:It satisfies the identity
336:is the density of species
329:{\displaystyle \rho _{i}}
536:
505:
433:
405:
355:
330:
302:
278:
249:
224:
170:
33:Joseph O. Hirschfelder
29:Kármán-Penner variable
537:
535:{\displaystyle w_{i}}
506:
434:
406:
356:
354:{\displaystyle \rho }
331:
303:
279:
277:{\displaystyle V_{i}}
250:
225:
171:
39:in 1948 and later by
519:
446:
423:
372:
345:
313:
292:
288:diffuse relative to
261:
239:
186:
58:
614:Chemical properties
361:is the gas density.
41:Theodore von Kármán
532:
501:
429:
401:
384:
351:
326:
298:
274:
245:
220:
166:
37:Charles F. Curtiss
21:mass-flux fraction
499:
474:
432:{\displaystyle x}
375:
301:{\displaystyle v}
248:{\displaystyle v}
159:
118:
631:
599:
596:
590:
587:
581:
578:
572:
569:
563:
559:
541:
539:
538:
533:
531:
530:
510:
508:
507:
502:
500:
498:
490:
489:
480:
475:
473:
465:
464:
463:
450:
438:
436:
435:
430:
410:
408:
407:
402:
394:
393:
383:
360:
358:
357:
352:
335:
333:
332:
327:
325:
324:
307:
305:
304:
299:
283:
281:
280:
275:
273:
272:
254:
252:
251:
246:
229:
227:
226:
221:
216:
211:
210:
198:
197:
175:
173:
172:
167:
165:
161:
160:
155:
154:
145:
132:
131:
119:
117:
109:
105:
104:
86:
85:
75:
70:
69:
639:
638:
634:
633:
632:
630:
629:
628:
604:
603:
602:
597:
593:
588:
584:
579:
575:
570:
566:
560:
556:
552:
522:
517:
516:
491:
481:
466:
455:
451:
444:
443:
421:
420:
385:
370:
369:
343:
342:
316:
311:
310:
290:
289:
264:
259:
258:
237:
236:
202:
189:
184:
183:
146:
137:
133:
123:
110:
96:
77:
76:
61:
56:
55:
17:
12:
11:
5:
637:
635:
627:
626:
621:
616:
606:
605:
601:
600:
591:
582:
573:
564:
553:
551:
548:
529:
525:
513:
512:
497:
494:
488:
484:
478:
472:
469:
462:
458:
454:
428:
413:
412:
400:
397:
392:
388:
382:
378:
363:
362:
350:
340:
323:
319:
308:
297:
271:
267:
256:
244:
234:
219:
215:
209:
205:
201:
196:
192:
177:
176:
164:
158:
153:
149:
143:
140:
136:
130:
126:
122:
116:
113:
108:
103:
99:
95:
92:
89:
84:
80:
73:
68:
64:
51:is defined as
15:
13:
10:
9:
6:
4:
3:
2:
636:
625:
622:
620:
617:
615:
612:
611:
609:
595:
592:
586:
583:
577:
574:
568:
565:
558:
555:
549:
547:
545:
527:
523:
495:
492:
486:
482:
476:
470:
467:
460:
456:
452:
442:
441:
440:
426:
418:
398:
395:
390:
386:
380:
376:
368:
367:
366:
348:
341:
339:
321:
317:
309:
295:
287:
269:
265:
257:
242:
235:
233:
232:mass fraction
217:
213:
207:
203:
199:
194:
190:
182:
181:
180:
162:
156:
151:
147:
141:
138:
134:
128:
124:
120:
114:
111:
101:
97:
93:
90:
82:
78:
71:
66:
62:
54:
53:
52:
50:
46:
42:
38:
34:
30:
26:
22:
594:
585:
576:
567:
557:
543:
514:
414:
364:
337:
285:
178:
48:
28:
24:
20:
18:
624:Combustion
608:Categories
550:References
417:combustion
45:Sol Penner
562:Elsevier.
493:ρ
457:ϵ
387:ϵ
377:∑
349:ρ
318:ρ
218:ρ
204:ρ
112:ρ
79:ρ
63:ϵ
230:is the
515:where
179:where
43:and
35:and
23:(or
19:The
27:or
610::
546:.
544:i
528:i
524:w
511:,
496:v
487:i
483:w
477:=
471:x
468:d
461:i
453:d
427:x
411:,
399:1
396:=
391:i
381:i
338:i
322:i
296:v
286:i
270:i
266:V
243:v
214:/
208:i
200:=
195:i
191:Y
163:)
157:v
152:i
148:V
142:+
139:1
135:(
129:i
125:Y
121:=
115:v
107:)
102:i
98:V
94:+
91:v
88:(
83:i
72:=
67:i
49:i
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