THAPAR UNIVERSITY Computational Methods in Chemical Engineering,MARCH 2015 PAPER Notes | EduRev

: THAPAR UNIVERSITY Computational Methods in Chemical Engineering,MARCH 2015 PAPER Notes | EduRev

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Roll Number: 
Thapar University Patiala 
Department of Chemical Engineering 
M. Tech- Chemical Engineering 	 PCH2O3: Computational Methods in 
MST, March 2015 	 Chemical Engineering 
Time: 02 Hours; MM: 30 	 Name of Faculty: Dr.V. K. Sangal 
Note: Attempt all questions and assume any missing data suitably. 
The optimum recycle ratio for an autocatalytic reaction is given by the solution of the following 
differential equation: 
In[(1+ 0.01R)/ 0.0111] = [(R+1)/ (1 + 0.0IR)R} 
Solve this equation by Newton-Raphson method. 
The reaction rate constant for the decomposition of a substituted dibasic acid has been determined 
at various temperatures as given in the following table. Use the method of least squares to 
determine the activation energy E in the equation. 
K = A &El" , Where T is measured in Kelvin. 	 (6) 
Temperature (°C) K X 104  (If' ) 
50 1.08 
70.1 7.34 
89.4 45.4 
101 138 
An insulated rod (insulated around its outer circumference) is 0.20 m long and is of uniform cross 
section. It has its right end held at a temperature of 373 K while its left end loses heat to the 
surroundings, which are at 293 K. The rod has a thermal conductivity K of 0.52 Cal/(sec* cm * 
C), and the heat transfer coefficient is 0.073 Cal/(sec/cm 2/°C). Solve for steady state 
temperatures using the finite difference method with eight equal subintervals. 
(Solve the linear 
equations by Tri-diagonal matrices method) 	 (10) 
4. A thermocouple at equilibrium with ambient air at 10 °C is plunged into a warm water bath at time 
equal to zero. The warm water acts as an infinite heat source at 20°C since its mass is many times 
that of the thermocouple. Calculate the response curve of the thermocouple. The governing 
differential equation is Newton's law of heating or cooling and is 
Cp dT/dt = U A (Tp -T) 
Time constant of the thermocouple (Cp/ UA) = 0.4 min'' 	 (5) 
5. Solve the set of equations for the time 0.1 sec. 	 (5) 
da/dt = 1195 a - 1995 b, 	 a(0) = 2, 
db/dt = 1197 a — 1997 b, 	 b(0) = -2, 
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