GATE Metallurgical Engineering Syllabus 2027 (Out) - Download PDF

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 and correlations; radiation; Stefan-Boltzmann Law; Kirchhoff’s Law.

Mass Transfer

Diffusion and Fick’s laws, Mass transfer coefficients and correlations

Dimensional Analysis

Significance of dimensionless numbers and their applications.

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

Ironmaking

Thermodynamics of blast furnace ironmaking; heat and material balance in blast furnace; production of sinter, pellets, metallurgical coke and testing, alternative routes of iron making (rotary kiln, MIDREX, COREX).

Primary Steel Making

Structure and properties of slags; thermodynamics and kinetics of steelmaking; basic oxygen furnace and electric arc furnace steel making.

Secondary Steel Making

Ladle process – deoxidation, degassing, argon stirring, desulphurization, inclusion shape control; basics of stainless steel manufacturing.

Continuous Casting

Basics of continuous casting, casting defects, thin slab casting.

Physical Metallurgy

Crystal Imperfections

Point, line and surface defects; coherent, semi-coherent and incoherent interfaces.

Diffusion in Solids

Atomic models for interstitial and substitutional diffusion; volume, surface and grain boundary diffusion, Kirkendall effect; uphill 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; eutectoid transformation, diffusionless transformations; precipitate coarsening, Gibbs-Thomson effect; glass transition in ceramics and polymers.

Mechanical Behaviour of Materials

Dislocation Theory

Edge, screw and mixed dislocations; sources 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.

Fatigue

Low and high cycle fatigue; crack growth.

Manufacturing Processes

Metal Casting

Mould design involving feeding, gating and risering, 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.

Y. Lakhtin