Page 1 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. 1. 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. (4) 2. 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 3. 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, BEST OF LUCKRead More

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