Syllabus

Mathematical concepts; Introduction to solution techniques for ordinary differential equations,  Sturm-Liouville problems, Partial differential equations, Applications of PDE in heat transfer, mass transfer, diffusion, fluid flow, chemical reaction, transport process and process modeling-simulation, Boundary layer concept, balance equations for mass, momentum, energy; and estimation, Heat Transfer; Governing equations and boundary conditions; conduction, convection and radiation; Balance equations for mass transfer, Ideal reactors, Modeling of ideal reactors, solution techniques for models producing PDEs, models yielding ODEs, numerical solution methods, initial value problems, boundary value problems

Detailed version

Mathematical concepts:

Ordinary differential equations: Introduction to solution techniques for Ordinary differential equations, initial value problems, Sturm-Liouville problems, integral functions

Partial differential equations: Solution techniques for partial differential equations, separation of variables, combination of variables, Fourier integral method, Laplace transform methods

Numerical solution methods: Solution of non-linear algebraic equations, solution of linear algebraic equations, Initial value problems – Explicit integration method, Implicit integration method, Predictor corrector methods and Runge Kutta method, Boundary value problems- Linear boundary value and non-linear boundary value problems, Finite difference method for PDE

Fundamentals of transport process and process modeling: Basic laws of fluid mechanics- continuity equation, Bernoulli equation, Dimensional analysis, Principles of model development- Balance equations for mass, momentum, Energy transfer, Model development for turbulent core region, laminar sublayer region, Illustration of the Formulation Process, Combining Rate and Equilibrium Concepts, Boundary Conditions and Sign Conventions

Application of ODE/PDE: Applications of PDE in Heat Transfer, Mass Transfer, Comparison between Heat and Mass Transfer Results, Simultaneous Diffusion and Convection, Simultaneous Diffusion and Chemical Reaction, Simultaneous Diffusion, Convection, and Chemical Reaction, Heat transfer, Governing equations and boundary conditions for conduction; Transient conduction, Boundary layers, Laws of diffusion, Diffusion with and without chemical reaction, Ideal reactors: batch reactor, plug flow reactor and continuous stirred tank reactor, reactors in series; Modeling of ideal reactors and multiple reactors.