Section 1: Engineering Mathematics | Linear Algebra | Matrices and Determinants, Systems of linear equations, Eigenvalues and Eigenvectors. |
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. |
Section 2: 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. |
Section 3: 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. |
Section 4: Mineral Processing and Extractive Metallurgy | Comminution Techniques | Size classification, Flotation, Gravity and other methods of mineral beneficiation; Agglomeration: sintering, pelletizing and briquetting. |
Material and Energy Balances | Material and Energy balances in metallurgical processes. |
Extraction of Non-Ferrous Metals | Principles and processes for the extraction of non-ferrous metals – Aluminium, Copper and Titanium. |
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. |
Section 5: 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. |
X-ray Diffraction | Bragg’s law, Optical metallography, Principles of SEM imaging. |
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, Spinodal 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. |
Material Properties | Electronic, magnetic and optical properties of materials. |
Corrosion | Basic forms of corrosion and its prevention. |
Section 6: Mechanical Metallurgy | Stress and Strain Analysis | Strain tensor and stress tensor, Representation by Mohr’s circle, Elasticity, Stiffness and compliance tensor, Yield criteria, Plastic deformation by slip and twinning. |
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. |
High Temperature Deformation and Failure | Mechanisms of high temperature deformation and failure; Creep and stress rupture, Stress exponent and activation energy. |
Section 7: Manufacturing Processes | Metal Casting | Mould design involving feeding, gating and risering, Casting practices, Casting defects. |
Metal Forming | 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 aluminum 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. |
