## Saturday, October 20, 2012

### MA 9215 APPLIED MATHEMATICS FOR THERMAL ENGINEERS SYLLABUS | ANNA UNIVERSITY ME INTERNAL COMBUSTION ENGINEERING 1ST SEM SYLLABUS REGULATION 2009 2011 2012-2013

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MA 9215 APPLIED MATHEMATICS FOR THERMAL ENGINEERS SYLLABUS | ANNA UNIVERSITY ME INTERNAL COMBUSTION ENGINEERING 1ST SEM SYLLABUS REGULATION 2009 2011 2012-2013 BELOW IS THE ANNA UNIVERSITY FIRST SEMESTER ME INTERNAL COMBUSTION ENGINEERING DEPARTMENT SYLLABUS, TEXTBOOKS, REFERENCE BOOKS,EXAM PORTIONS,QUESTION BANK,PREVIOUS YEAR QUESTION PAPERS,MODEL QUESTION PAPERS, CLASS NOTES, IMPORTANT 2 MARKS, 8 MARKS, 16 MARKS TOPICS. IT IS APPLICABLE FOR ALL STUDENTS ADMITTED IN THE YEAR 2011 2012-2013 (ANNA UNIVERSITY CHENNAI,TRICHY,MADURAI,TIRUNELVELI,COIMBATORE), 2009 REGULATION OF ANNA UNIVERSITY CHENNAI AND STUDENTS ADMITTED IN ANNA UNIVERSITY CHENNAI DURING 2009

MA 9215 APPLIED MATHEMATICS FOR THERMAL ENGINEERS L T P C
3 1 0 4
AIM: This course is mainly focused on understanding the concepts and techniques
for solving, analytically and numerically, the governing partial differential
equations that arise in the field of thermal engineering.
OBJECTIVE:
 To explain the use of Fourier transformation and to obtain solutions for time
dependent and steady state heat conduction problems.
 To familiarize the students with the concepts of Calculus of Variations to
obtain exact and approximation solutions for energy functional, which are
needed in branches of thermal engineering.
 To make the students knowledgeable in the area of conformal mapping and
Schwarz-Christoffel transformation, so that students will be familiar with the
uses of these transformations in grid generation and solution techniques for
fluid and heat flow problems.
 To acquaint the students with the concepts of grid based numerical methods,
in particularly the finite difference schemes, for time dependent heat
conduction problems in both one space and two space variable(s). The
stability of these numerical schemes will also be discussed.
 To introduce similar finite difference schemes for steady state heat
conduction problems on rectangular and circular domains with prescribed /
derivative/ mixed boundary conditions.
UNIT I APPLICATIONS OF FOURIER TRANSFORM 9
Fourier Transform methods – one dimensional heat conduction problems in infinite
and semi-infinite rod – Laplace Equation – Poisson Equation.
UNIT II CALCULUS OF VARIATIONS 9
Concept of variation and its properties – Euler’s equation – Functionals dependant on
first and higher order derivatives – Functionals dependant on functions of several
independent variables – Variational problems with moving boundaries – Direct
methods – Ritz and Kantorovich methods.
UNIT III CONFORMAL MAPPING AND APPLICATIONS 9
The Schwarz-Christoffel transformation – Transformation of boundaries in parametric
form – Physical applications: Fluid flow and heat flow problems.
UNITIV FINITE DIFFERENCE METHODS FOR PARABOLIC EQUATIONS 9
One dimensional parabolic equation – Explicit and Crank-Nicolson Schemes –
Thomas Algorithm – Weighted average approximation – Dirichlet and Neumann
conditions – Two dimensional parabolic equations – ADI method.
UNIT V FINITE DIFFERENCE METHODS FOR ELLIPTIC EQUATIONS 9
Solutions of Laplace and Poisson equations in a rectangular region – Finite
difference in polar coordinates – Formulae for derivatives near a curved boundary
while using a square mesh.
L +T: 45+15, TOTAL: 60 PERIODS
3
REFERENCE BOOKS:
1. Mitchell A.R. and Griffith D.F., The Finite difference method in partial differential
equations, John Wiley and sons, New York (1980).
2. Sankara Rao, K., Introduction to Partial Differential Equations, Prentice Hall of
India Pvt. Ltd., New Delhi (1997).
3. Gupta, A.S., Calculus of Variations with Applications, Prentice Hall of India Pvt.
Ltd., New Delhi (1997).
4. Spiegel, M.R., Theory and Problems of Complex Variables and its Application
(Schaum’s Outline Series), McGraw Hill Book Co., Singapore (1981).
5. Andrews, L.C. and Shivamoggi, B.K., Integral Transforms for Engineers, Prentice
Hall of India Pvt. Ltd., New Delhi (2003).
6. Elsgolts, L., Differential Equations and the Calculus of Variations, MIR Publishers,
Moscow (1973).
7. Mathews, J.H. and Howell, R.W., Complex Analysis for Mathematics and
Engineering, Narosa Publishing House, New Delhi (1997).
8. Morton, K.W. and Mayers, D.F. Numerical solution of partial differential
equations, Cambridge University press, Cambridge (2002).
9. Jain, M. K., Iyengar, S. R. K. and Jain, R. K. “ Computational Methods for Partial
Differential Equations”, New Age International (P) Ltd., 2003.