Numerical Methods for Chemical Engg

8/2/2019 Numerical Methods for Chemical Engg

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ecoud Mid-Term (V - ernester) Examinat ion, 201 1-12Th ;rd V ear B . Tec h ( Ch em ic cl P ..~ g ineering )

ub.: umet:ic al M eth od in C hem ical Eng ineering (CI-1305)M a urnurn Marks-3 0 T ime-One Hour

An wer all th e questionsI . olve th e differen tial equation u ing finite d iffe re nc e m eth odd~)' dy--+-= \Idx' dx '-

with th e boundar onditions: yeO) = 0 and y(l) = IAs tim e. h = 0.252 . C onsider th e reac tion

Date of Exam : 04.10.2011

(10)

A~ B ~ Cc arried out in a batc h reac tor. Th e differential equations desc ribing th e rim e dependence ofconcentrations for th e c omponents A . B and C are.arad omdCc =k- CIf 1 HTh e conc entration at tim e t = 0 are. C A = 1 k 1 1 1 0 1 / m 3 . C B = 0 k mol/m ", C c = 0 k mollm ' Th erate c onstants are: kl = I 5. an d k2 = 0 .1 5. Using th e fourth order Rung e-Kuna rn th od.determ ine th e c on ntrations of A , B and C after 0 .3 ee. A lime a tep size equal to 0.1 ec.W rite al l th e steps and sh ow your c al u la tio ns . (20)

---------------- -- ------------ ----- - - ---- - ---- ---- ----- - ---- - -- --- ---- -_-- - --- -- - -- -------- ----- ----- -------- --------


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Fin t'-.lid-T errn E xam ination. -0 11 -_0 12. Th ird B . Tec .h (C hem ical. V-, e rn e te l')

Numerical lethods 11 1 h em ic al E ng ineering (C H3 05 )Maximum lark -_0 Time-One Hour

Answer a ll th e q ue stio nI.The tim e (I) and conc en tr at ion (P) f produc t data in a reac tor is obtained a follow :

I(h r ) 0 .1 0 .3 0 .5 0 .7 0 .9C ncentration ~ . 2 : 2 99 3 .2611 3 .2_82 ~ . 1 2 6 6 2.97'9o f P ro du t. P.in g mol cm'F ind a fo rm ula. u ing lea t square meth od. of th e form: P = a + bl + c r \ hich w il l fitth e above data. (8)

Evaluate a real root of-I O x ~- 32x 3+ :r :~ x 2+8x+9= 0correct to th ree dec imal places using ewton-Raph son meth od. (n3. The feed to a distillation column consists of benzene ( I ) . toluene ( 2 ) . p-xylene (3 ) and 0-xylene (4). Feed analysis data is as follows:Benzene: \092 Ibm/min

- : x . . . , -; .. .0 . \4 1 , AV~O'),~~ ] . ' / ( ) ' 2 >

~~~{

"l.,-:: 0 .\. //l~Q"~~~'Y().~

' " " -4-; 'O'~--_ - - ------ - - --- -------- - - - - --------- - -- - - - -- - - - - - --- - --- - - - - -- - ------ - --- --- -- - - - - - - - -- - -- - ----- -\;---- - - - - - ------

\'1,.'l.7/ f l " " )"",) X'.i


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First Mid-Term Examination, 2009-2010Third B E (Chemical, V-Semester)

umerical Methods in Chemical Engineering (CH305)Maximum Marks-20 Time-One Hour

~ ~1 - r J.\ ; ., _ ';I ~". , . . ... i" i , J( - fh.,~~ ~'~-" ,

" -I-f r J # [ - J - iJAnswer all the questionsJ. Solve the set of following two equations by multivariable Newton-Raphson method"X ~ / 2.5x/+ 4~- 3.7=00.7XI2 ... 3xl-l.8~';' I = 0Assume the initial guesses for the two var iables ~ = < . . Q and "I = O.

Show the results for four iterations. ..-.Or,For solution of the linear system of equations

a"x + a,lY + anz = b,a21x+ az2j + anz = b zal,x + a3lY+ al3z = ~ - . ~D\,---:;.,-(6)by L U decomposition method, find tbe values of Un, Un,U33and 1 3 2 in terms of Il;j.If a,I=I,al2=l,a'3=-J, b,=1a~ = 1, an = 2, a23= -2 b z = 0a31= -2 , a32= 1 , a33= l.b, = IFind the values of x, y and z.

ua,tions using ~GaUi&-SeideLmetbod-3 ~ + I+1 . 5X2 + 1 .{l 3 x. - 4 .1 .3

X o + 4xI -X 2 -3. fJ X3= 0.33-2xo - 0.6x) -3.5 X2 +5.79 X3 = -)0.213~ + 0.5 x) -1.91x2 + 3.1 x, = 0.8646

(8)~ ~\ltart with X o = 0.0, X , = 0.0, X 2 = 0.0, x, =0.0. Carry out five iterations and show all theresults in a tabular form. ---3. Following are some experimental data for a Pitot tube traverse for the flow of water in a pipe of radius 3.06 in~;..

Position Distance from tube Local velocitycenter (r.inch) (u,ft/s)

I l ' 3 01 7.85 ~2 2.17 10.393 1'.43 ( 11.31II'" 4 0.72 '

11.665 0.0 /1 11.796 t ~ ~ ~ 11.707 11.47g 2.17 11.109 2.80 9.26

Plot these data and then use Simpson's rule for numerical integration to compute average velocity of flow. (6)


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First Mid-Term Examination. 2010-2011Third B E (Chemical, V-Semester)Subject: Numerical Methods in Chemical Engineering (OnoMaximum Marks-Xi Time-One Hour

. J Answer all tbe questions

1. During the operation of a batch reacto~, samples of product were withdrawn at different timeintervals and analyzed for the concentration of .reaefaflt A for the reaction: A+B-P.p o - t > c i vck PThe time-concentrat ion data are shown below: R + p -JQ

0.43.2516

Find an equation of the form: CA~ a+bt+ct, using the least square method which will fit theabove data. - (8)2. Find all the elements of lower (lJ and upper (uij) triangular matrices in terms ofp!! for solution ofthe linear system of equations:

PllX +PI Y+P13Z = q!>21X +t>nY+P23Z = rPlIX +Pl2)+P33Z = S

01 e the foll wing ~stem ~equations using:hU decomposition method; .com47x+y-5=83x+7y+4=10 (12)

~= YYH. -l - C .C : : g 71 = Y Y l . ~ A_Y1 -t C~ -~

J


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Mataviya Nationallnstituh! of Technology, Jaipur .First mid Term Exam

Semester _vth (Chemical Engineering) Time: 1:00 hr.Subject- Numerical Method in Chern. Engg. MM:20Note: Attempted all questions. Each carries equal marks.rolve these equations by iterative methods.

lOxl-2xl-Xl-X.=03- 2X , + - IOx1-X J - X 4 =15-X-X + lOX3 - 2X4 =27-X-X -2xJ + 10x4,=-9

;62. Solve th.e following system2x + y +- z = 103r+-2 +3.z=18 a

by Gauss Elimination method.

Find a real root of the equation Xl - 2 x -,5 =0, by Bisection method, with accuracyO.OOLDrive the formula for calculating' X and Y with the help of Newton Raphsonmethod.Use the method of false position to obtain a r o o t , correct to three decimal places,x3-x-1 =0.

., . (\


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End-Term Examiuariou, 2007~200Srhird B . T~ ~h (Chcmical. \'-S~'llleslt'r)umaicall\kllwtls ill Chemical Ellgilll' iring t".:ll 05)Maxinuuu Marks-J S Til ll lo '-Th rl 'C Ilour

Answer Q. \ . (3)


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< ; ( III(End-Term Examinati n. 2010-_011Third B. Tech Chemical. V- em,'. er

Ium rical Method ir: Chemi al Engin ring CH~O":)Ma. 'l:imUDl iark .-3,) Time- T H' H urs

An We! any three que .011. ~o.id particles having a diameter of O.1~ mm. hape factor < ;\ = and d~I'I, of 1010 k>?m"

are to fluidized wing air at 2.0 atn ;IT'd 25'~, Th Y idage t minimum t u.dizatie n is O . . ! ~Und r these n tirions nir rna, e a sumed as an ideal gil. and irs \ ,S,-'O. irv rn be r en as1.'45). 10" kg rn" ,I. .For calculation under minimum fluidization the following equation m ) be used:

Consider the re-action: .4 - -= - -+ B ~ C . carriedequations f r mponents A. B and are

d__ .i --kdl - I.~

ut in 8 batch reactor. The differenri I

1 . - - : - : L 'O-6 , ,1..:-0,l11-&. )[ " P.,+[ " ]l'(-\.1-6.,. p"- )"=0~Jdp e ,.J , E " , / ' , ~

F r calculati n by it ration, an initial value of)' .1 =0.1 ill' m3) be a ssurned.

(.--=k,Cdl -The initial concentrations of A.B and are A=1.0 krnc l rn', 8=0.0 kino! m. L,=0,(kmot'rrr'. \ 'alues of rate c nstants are 11=I SI nd ~= I SI. U sing th e R ung e- Uti fourth orderalgorithm find the cone ntrations of A. 8 and L at the- end of I' suming t equal to 1 s , lUl)

arad3. Solve the followin system o f equari liS h~ Gall' -Siedel method .

.wxl-20x.~-IOx, =390IO:\.I-60x1~2Ox3=-280IOxl-3G~+120xJ =-860Show all the iteration results in a tabuhr form.

(b) The following tabulated function repre ents a polynomial o r degree n.

Find the value of n.4. Solve the folio ing equation to find the temperature at the mesh po i ts for t - O.t.

~ 1 0 )


8/9

End-Term Examination, }011-_012Third B, Tech (Chemical. V- ernester)

umerical ethod in hernical Engineering ( 1-1305)fa: imurn farks-30 Time-Tv, Hours

~ J-('___.__ ML- f t ; : : A :_ ~ J....~J _ T~1fee ranks in eries are u ed to l:ea~ oil each fwhi~h is initiall~ filled with 1000 kgof 011 at 2 0 C. at mated steam at 2 :>0 C conden es within the coils immer ed in eachtank. Oil is fed into the first tank at a rate of 2 kg/s and overflows into the second andthird tank at the same flow rate. The temperature of the oil fed to the first tank i 20 .The tank are wel l mixed so that the temperature inside the tank i uniform and theoutlet stream temperature is same as that of the entire mixture within the tank. C p f il=2000 I/kg- K .. The rate of heat transfer to the. oil from the team is fiven by Q = (Ts-T), where A IS the outside area of the coil Jl1 each tank. A = 1 rn and the overall heattransfer coefficient is based on the outside area of the coil. U = 20 0 W/m2_ K. 0 (erminethe temperature in all the three tanks after 10 sec. Assume t = 5 sec. The followingenergy balance equations may be used if required.

dT . 'MC _ =mC,,(To-7;)+UA(T, -7;)~, "d r dT .AlC _ = mC,, (T. 1 - T,) +UA(T, - T2)" dt -MCp d ; 3 =mC,,(T2 -TJ+UA(T, -T)

J < F O I l Q W t n g ar e same xper imemal data fo r a Puot tube traver e for the flow of water ina ipe of rddius 3.06 ineb:Position Distance from tube Local velocity

center (r,inch) (u-FtJ )

1 2.80 7.852 2.17 1 0 . 3 93 1.43 1 1 . 3 14 0.72 11 .665 0.0 11 .796 0.72 11 .707 1.43 1 1 . 4 78 2.17 1 1 . 1 09 2.80 9,26

. . t comput av rag ePlot these data and then use Simpson's rule for Numericalll1tegratlon 0velocity of flow.3. Find Tza using Crank-Nicholson method for tbe following:

(8)

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T"'aV\k f JOU fo rsav iV \g trees ar.d.

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Numerical Methods for Chemical Engg