HW4SolnME525SP2011

HW4SolnME525SP2011 - 1 ME 525 Homework #4 Due Thur sday,...

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1. Turn Given: P reacti m h ME ns, 6.8. Plug flow rea ions with giv x h(x) E 525 Hom Prof. Luch actor in a co ven global ra x+ x m mework #4 ht (E-mail a nstant area d ate coefficie m h(x+ x) 1 Due Thur address: Lu duct. Adiaba nt. rsday, Mar [email protected] atic flow, sin ch 10, 2011 ue.edu) ngle-step, th ree species
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2 : SOLUTION : write First law Q W  0 , , 0 : 0 0 0 , 0 p xx x ii i i i i if i p i i pi i ip i i c dh mh h s om dx dh Since h Y h or dx dh dY dh d Yh Y h dx dx dx dx Apply calorific equation of state h h c dT dh dT c dx dx dh dT Thus Yc Y dx dx             ,, '' : 0 0, : 0 i ix ix x i i i i i i To eliminate dY dx we write the species conservation eqn mm m Divide by A x take limit x recognize derivative dm m where m m Y and m MW dx Since        '' ' : exp / 1 , i i i i Fa u FF F Ox F Pr F m constant dY dY m MW o r I I dx dx m m To relate to Y s we apply the given kinetics AE R T F O x mM W M W We can express F    ,: ; Fo x mix mix x uF uo x Ox in terms of Y Y PMW FY O xY RTMW
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3   2 ; ;; exp / ; 1 , Fo xP r uuu F au F O x u ox FP r F ox F pF o x Since MWs all equal PPP FY O x Y P rY RT Thus dY MW P AE R T Y YI I I dx m R T dY dY dY dY IV dx dx dx dx Returning to Eqn I dY dY dT ch h dx dx          2 1 11 1 0 exp / , : 10 0 0 pr pr u p F F ox ox F ox pr F ox F c pr e f o x e f pr p ref dY hV dx dx MW P Let Z A E R T then V becomes mR T dT c h ZYY h ZYY h dx w h e r e h h cTT h cTT hc T T substituting the above yie         1 o x p r e f lds dT cZ Y Y c T T dx  0 1 1 2 0 Aexp / x c o x c pa u F o x c u h or dT Y Y h dx dT P mc MW E RTY YY h dx R T Comment : we can interpret our final result that the rate-of -change of sensible enthalpy with distance is the "heat - r   elease" associated with combustion.
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This note was uploaded on 04/17/2011 for the course ME 525 taught by Professor Lucth during the Spring '11 term at Purdue.

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HW4SolnME525SP2011 - 1 ME 525 Homework #4 Due Thur sday,...

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