## March 18, 2010

### ANDHRA UNIVERSITY DMCHE 401 Chemical Engineering Mathematics

ANDHRA UNIVERSITY DMCHE 401 Chemical Engineering Mathematics

UNIT-I
Mathematical formulation of the physical problems:(i) Application of the law of conservation of mass - Salt accumulation in stirred tank - Starting an equilibrium still - Solvent extraction in N stages- Diffusion with chemical reaction. (ii) Application of the law of conservation of energy - Radial heat transfer through a cylindrical conductor - Heating a closed kettle - Flow of heat from fin.

UNIT-II
Analytical (explicit) solution of ordinary differential equations encountered in Chemical Engineering problems:(i) First order differential equations-Method of separation of variables-Equations solved by integration factors-Certain examples involving mass and energy balances and reaction kinetics. (ii) Second order differential equations-Non-linear equations-Linear equations-Simultaneous diffusion and chemical reaction in a tubular reactor-Continuous hydrolysis of tallow in a spray column.

UNIT-III
Partial Differential equations:(i) Formulation of partial differential equations - Unsteady-state heat conduction in one dimension - Mass transfer with axial symmetry - Continuity equation.(ii) Boundary conditions : Function specified, derivative specified and mixed conditions.(iii) Particular solutions of partial differential equation: Compounding the independent variable into one variable, superposition of solutions, The method of Images and particular solution suggested by the boundary conditions.

UNIT-IV
Finite Differences:(i) The difference operator - Properties of the difference operator-Difference tables-other difference operators.(ii) Linear finite difference equations - complementary solution - particular solution - simultaneous linear difference equations(iii) Non-linear finite difference equations - analytical solutions. Solutions for the following type of problems by finite difference method:(a) Calculation of the number of plates required for an absorption column(b) Calculation of the number of theoretical plates required for distillation column(c) Calculation of number
of stages required for a counter current extraction and leaching operation.

UNIT-V
Application of Statistical Methods:(i) Propagation of errors of experimental data.(ii) Parameter estimation of algebric equations encountered in heat and mass transfer, kinetics and thermodynamics by(a) Method of averages(b) Linear least squares and (c) Weighted linear least squares methods(iii) Design of experiments: Factorial and Fractional factorial methods.

Text Books:1.Jenson V.G., & G.V Jeffreys, "Mathematical Methods in Chemical Engineering", Academic press, London and New York. Reference Books:1. Harold S. Mickley, Thomas S Sherwood and Charles E Reed, "Applied Mathematics in Chemical Engineering", Tata McGraw Hill Publication.
2. Volk, W., "Applied Statistics", 2nd edition, McGraw-Hill Chemical Engineering series.
3.Alkis Constantinides,S."Applied Numerical Methods with Personal Computers",MGH, Chemical Engineering series, 1987.