Engineering Mathematics |
Linear Algebra | Matrices and Determinants, Systems of linear equations, Eigen values, and Eigen vectors. |
Calculus | Limit, Continuity and Differentiability; Partial derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series |
Vector Calculus | Gradient; Divergence and Curl; Line, Surface and volume integrals; Stokes, Gauss and Green’s theorems |
Differential Equations | Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations; Laplace transforms; PDEs –Laplace, one dimensional heat and wave equations |
Probability and Statistics | Definitions of probability and sampling theorems, conditional probability, Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Analysis of experimental data; linear least squares method |
Numerical Methods | Solutions of linear and non-linear (Bisection, Secant, Newton- Raphson methods) algebraic equations; integration by trapezoidal and Simpson’s rule; single and multi-step methods for differential equations |
Metallurgical Thermodynamics |
Laws of Thermodynamics | First law – energy conservation, Second law - entropy; Enthalpy, Gibbs and Helmholtz free energy; Maxwell’s relations; Chemical potential; Applications to metallurgical systems, solutions, ideal and regular solutions; Gibbs phase rule, phase equilibria, binary phase diagram and lever rule, free-energy vs. composition diagrams; Equilibrium constant, Activity, Ellingham and phase stability diagrams; Thermodynamics of point defects, surfaces and interfaces, adsorption and segregation phenomena |
Electrochemistry | Single electrode potential, Electrochemical cells, Nernst equation, Potential-pH diagrams |
Transport Phenomena and Rate Processes |
Momentum Transfer | Concept of viscosity, shell balances, Bernoulli’s equation, mechanical energy balance equation, flow past plane surfaces and through pipes |
Heat Transfer | Conduction, Fourier’s Law, 1-D steady state conduction |
Convection | Heat transfer coefficient relations for forced convection |
Radiation | Black body radiation, Stefan-Boltzman Law, Kirchhoff’s Law |
Mass Transfer | Diffusion and Fick’s laws, Mass transfer coefficients |
Dimensional Analysis | Buckingham Pi theorem, Significance of dimensionless numbers |
Basic Laws of Chemical Kinetics | First order reactions, reaction rate constant, Arrhenius relation, heterogeneous reactions, oxidation kinetics |
Electrochemical Kinetics | Polarization |
Mineral Processing and Extractive Metallurgy |
Iron and Steel Making | Material and heat balance in blast furnace; Structure and properties of slags and molten salts – basicity of slags - sulphide and phosphate capacity of slags; Production of metallurgical coke. Other methods of iron making (COREX, MIDRE) |
Primary Steel Making | Basic oxygen furnace, process dynamics, oxidation reactions, electric arc furnace |
Secondary Steel Making | Ladle process – deoxidation, argon stirring, desulphurization, inclusion shape control, principles of degassing methods; Basics of stainless steel manufacturing |
Continuous Casting | Fluid flow in the tundish and mould, heat transfer in the mould, segregation, inclusion control. |
Physical Metallurgy |
Chemical Bonding | Ionic, covalent, metallic, and secondary bonding in materials, Crystal structure of solids – metals and alloys, ionic and covalent solids, and polymers |
Crystal Imperfections | Point, line and surface defects; Coherent, semi-coherent and incoherent interfaces |
Diffusion in Solids | Diffusion equation, steady state and error function solutions; Examples Homogenization and carburization; Kirkendall effect; Uphill diffusion; Atomic models for interstitial and substitutional diffusion; Pipe diffusion and grain boundary diffusion |
Phase Transformation | Driving force, Homogeneous and heterogeneous nucleation, growth Kinetics Solidification in isomorphous, eutectic and peritectic systems, cast structures and macrosegregation, dendritic solidification and constitutional supercooling, coring and microsegregation |
Solid State Transformations | Precipitation, spinoidal decomposition, ordering, massive transformation, discontinuous precipitation, eutectoid transformation, diffusionless transformations; Precipitate coarsening, Gibbs-Thomson effect. Principles of heat treatment of steels, TTT and CCT diagrams; Surface hardening treatments; Recovery, recrystallization and grain growth; Heat treatment of cast iron and aluminium alloys. Electronic, magnetic and optical properties of materials. Basic forms of corrosion and its prevention |
Mechanical Metallurgy |
Dislocation Theory | Edge, screw and mixed dislocations, source and multiplication of dislocations, stress fields around dislocations; Partial dislocations, dislocation interactions and reactions |
Strengthening Mechanisms | Work/strain hardening, strengthening due to grain boundaries, solid solution, precipitation and dispersion. Fracture behaviour, Griffith theory, linear elastic fracture mechanics, fracture toughness, fractography, ductile to brittle transition |
Fatigue | Cyclic stress-strain behaviour - low and high cycle fatigue, crack growth. Mechanisms of high-temperature deformation and failure; creep and stress rupture, stress exponent and activation energy |
Manufacturing Processes |
Metal Casting | Mould design involving feeding, gating and rising, casting practices, casting defects |
Hot, Warm and Cold Working of Metals | Metal forming – fundamentals of metal forming processes of rolling, forging, extrusion, wire drawing and sheet metal forming, defects in forming |
Metal Joining | Principles of soldering, brazing and welding, welding metallurgy, defects in welded joints in steels and aluminium alloys |
Powder Metallurgy | Production of powders, compaction and sintering |
Non-destructive Testing (NDT) | Dye-penetrant, ultrasonic, radiography, eddy current, acoustic emission and magnetic particle inspection methods |
