Me 501 Advanced Engineering Mathematics (4 0 0 8)




НазваниеMe 501 Advanced Engineering Mathematics (4 0 0 8)
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Detail Syllabi:


SEMESTER-I


Specialisation: Fluids and Thermal Engineering


ME 501 Advanced Engineering Mathematics (4 0 0 8)


Vector and Tensor Analysis (Cartesian and Curvilinear): Orthogonal coordinate systems, Transformation of coordinate systems. Review of ODEs; Laplace & Fourier methods, series solutions, and orthogonal polynomials. Sturm-Liouville problem, Review of 1st and 2nd order PDEs. Similarity transformations for converting PDEs to ODEs. Linear systems of algebraic equations, Gauss elimination, LU decomposition etc., Gram-Schmidt orthogonalization. Matrix inversion, ill-conditioned systems. Numerical eigen solution techniques (Power, Jacobi, Given, Householder, and QR methods). Numerical solution of systems of nonlinear algebraic equations; Newton-Raphson method. Numerical integration: Newton-Cotes methods, error estimates, Gaussian quadrature, Numerical integration of ODEs: Euler, Adams, Runge-Kutta methods, and predictor-corrector procedures; stability of solutions; solution of stiff equations. Solution of PDEs: finite difference techniques. Functions of Complex Variable: analytic functions and mapping. Probability and Statistics – Probability Distribution, Bays Theorem, Random numbers, Parameter Estimation, Testing of Hypothesis, Goodness of Fit.


Texts/References:


  1. I.N. Sneddon, Elements of Partial Differential Equations, McGraw-Hill, 1957.

  2. F.B. Hilderbrand, Introduction to Numerical Analysis, Tata McGraw-Hill, 1974.

  3. W.E. Boyce and R.C. Diprima, Elementary Differential Equations and Boundary Value Problems, Wilet, 1977.

  4. E. Kreyzig, Advanced Engineering Mathematics, New Age International, 1996.

  5. M.K. Jain, S.R.K. Iyenger and R.K. Jain, Computational Methods for Partial Differential Equations, New Age International, 1994.

  6. R. Courant and D. Hilbert, Methods of Mathematical Physics, Wiley, 1989.

  7. Louis A. Pipes and Lawrence R. Harvill, Applied Mathematics for Engineers and Physicists, McGraw-Hill International Edition, 1970.

  8. M. K. Jain, S. R. K. Iyengar, and R. K. Jain, 'Numerical Methods for Scientific and Engineering Computation', 3rd edition, 1993, New Age International.

  9. D. S. Watkins, 'Fundamentals of Matrix Computations', 1992, John Wiley.

  10. A. J. McConell 'Applications of Tensor Analysis', 1957, Dover.



ME 520 Fluid Mechanics (3 0 0 6)


Fluid kinematics; Integral and differential forms of governing equations; Mass, momentum, and energy conservation equations; Navier-Stokes equations and its applications; Potential flow; Laminar boundary-layer; Free-shear flows: jet, wake, and mixing layer; Instability and transition; Turbulent flow; Compressible flow: Isentropic flow; flow with area change; flow with heat transfer; flow with friction.


Texts:


  1. B.R.Munson, D.F.Young and T.H.Okiishi., Fundamental of Fluid Mechanics, John Wiley and Sons., 1994.

  2. P.M.Gerhar, R.J.Gross and J.I.Hochstein., Fundamentals of Fluid Mechanics, Addison-Wesley Publishing Co., 1993

  3. H.Schlichting, Boundary Layer Theory, McGraw-Hill Series in Mechanical Engineering, 1979

  4. F.M.White, Fluid Mechanics, McGraw-Hill international editions., 1994.

  5. F.M.White, Viscous Fluid Flow, McGraw-Hill international editions., 1991



ME 521 Experimental Methods (2 0 2 6)


Theory and Experimentation in Engineering: Problem solving approaches, Types of engineering experiments, computer simulation and physical experimentation; Generalized measuring system, types of inputs, analog and digital signals, standards, calibration and uncertainty, Measurement System: Performance characteristics, static performance characteristics-static calibration-linearity, static sensitivity, repeatability, hysteresis- threshold- resolution, readability and span; Analysis of Experimental Data : Causes and types of experimental error, un-certainty analysis, statistical analysis of data, probability distributions and curve fitting; Dynamic performance characteristics; Input types; Instrument types- zero order instrument, first order instrument, second order instrument; Experiment Plans: Model building; Measurement Methods and Applications : Measurement of force and torque; Measurement of strain and stress; Measurement of pressure; Flow measurement and flow visualization; measurement of temperature; optical methods of measurements; Data Acquisition and Processing : Types and configurations of DAS, signal conditioning, A/D, D/A conversion; Design, Planning, Execution and Analysis of experimental projects.


Texts:


1. Beckwith, Buck, and Marangoni, Mechanical Measurements, Narosa Publishing House, 1995.

2. Doeblin, Measurement Systems - Application and Design, 4e, McGraw-Hill, 1990.

3. Holman, Experimental Methods for Engineers, 6e, McGraw-Hill, 1994.

4. Doeblin, Engineering Experimentation, McGraw-Hill, 1995.


SEMESTER-II


ME 522 Convective Heat and Mass Transfer (3 0 0 6)


Conservation equations and boundary conditions; One-dimensional solutions; Heat transfer in laminar developed and developing duct flows; Laminar boundary layers: Similarity and integral solutions; Turbulence fundamentals and modeling; Heat tranfer in turbulent boundary layers and turbulent duct flows; Laminar and turbulent free convection; Fundamentals of boiling and condensation; Numerical methods.


Texts:


1. W. M. Kays and E. M. Crawford, Convective Heat and Mass Transfer, Mc Graw Hill,1993.

2. Louis C Burmeister, Convective Heat Transfer, John Wiley and Sons, 1993.

3. Adrian Bejan, Convective Heat Transfer, John Wiley and Sons, 1995.


ME 523 Advanced Engineering Thermodynamics (3 0 0 6)


Review of fist and second law of thermodynamics, Maxwell equations, Joule-Thompson experiment, irreversibility and availability, exergy analysis, phase transition, types of equilibrium and stability, multi-component and multi-phase systems, equations of state, chemical thermodynamics, combustion. Third law of thermodynamics

Kinetic theory of gases- introduction, basic assumption, molecular flux, equation of state for an ideal gas, collisions with a moving wall, principle of equipartition of energy, classical theory of specific heat capacity.

Transport phenomena-intermolecular forces, The Van der Waals equation of state, collision cross section, mean free path

Statistical thermodynamics- introduction, energy states and energy levels, macro and microscales, thermodynamic probability, B-E, F-D, M-D statistics, distribution function, partition energy, statistical interpretation of entropy, application of statistics to gases-mono-atomic ideal gas, distribution of molecular velocity, ideal gas in a gravitational field.


References:


1. F.W.Sears and G.L.Salinger, Thermodynamics, Kinetic Theory And Statistical Thermodynamics, Narosa Publishing House, New Delhi.

2. Wylen and Sontag, Fundamentals of Classical Thermodynamics, Wiley Eastern Limited, New Delhi.

3. M.J.Moran and H.N.Shapiro, Fundamentals Of Engineering Thermodynamics, John Wiley and Sons.

4. Zemansky, Engineering Thermodynamics, Mc Graw Hill.

5. Bejan, Advanced Engineering Thermodynamics, John Wiley and sons.


SEMESTER-I

Specialisation: Machine Design
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