To Date : July 12, 2000

CHENNAI – 600 036, INDIA

To: Date: Sep 18, 2002

THE DEAN,

IC&SR, IIT Madras.

Dear Sir,
I would like to inform you that the tenure of the UGC sponsored project entitled “Inverse Problems in Boundary Layer Flows” is completed on 5-8-2002 and I was the principal investigator of the project. After the completion of the tenure, the following final documents are needed to submit to the sponsoring agency(UGC, New Delhi) as per their requirements:

1. 
   Audited utilization certificate in respect of the expenditure incurred on the project from 6-8-99 to 7-2-2002 from Government Auditor/chartered Accountant.
   
2. 
   Final item-wise statement of expenditure incurred on the project from 6-8-99 to 5-8-2002 in the prescribed format (copy enclosed).
   
3. 
   Month-wise details of the grant paid to the project fellow.
   
4. 
   Refund of unspent balance, if any, through demand draft in favour of the Secretary, University Grants Commission, New Delhi.
   

I request you to kindly take necessary action for making the above documents required by the sponsoring agency.

Thanking you, yours sincerely,

(SATYAJIT ROY)

To Date: 9^th September , 2003
Professor A. R. Balakrishnan,

Associate Editor, IJHMT.

Dear Sir,
Sub: Submission of a revised version of Manuscript No. MS# IND/B-03-016
I am sending a revised version of the manuscript No. MS# IND/B-03-016 of our paper entitled “Unsteady mixed convection from a rotating cone in a rotating fluid due to the combined effects of thermal and mass diffusion” by S. Roy and D. Anilkumar, for the consideration of it’s publication in “International Journal of Heat and Mass Transfer”.

A detailed response to the reviewers is also attached herewith.

Thanking you,
yours sincerely

(SATYAJIT ROY)

To: The Dean, Academic Research Date: October 20, 2003

I.I.T. Madras.

Through: The Head of the Department of Mathematics, I.I.T. Madras
Dear Sir,

Kindly refer my earlier letter dated 15-10-2003 (copy enclosed) for the conduct of the Viva-Voce examination of Ph.D. thesis of Mr. P. Saikrishnan. I would like to suggest a panel of examiners as follows:

1. 
   Prof. K. Ekambavanan Phone: [phone] (O)
   

Department of Mathematics 2440 5573 (R)

College of Engineering, Guindy E-Mail – [e-mail]

Anna University, Chennai – 600 025

2. 
   Prof. B.S. Dandapat
   

Applied Mathematics and Physics Unit

Indian Statistical Unit Calcutta Phone: [phone] (O)

203 B.T. Road 033- 25778921 (R)

KOLKATA – 700 035 E-Mail- [e-mail]

3. 
   Prof. P. Ganesan Phone: [phone] (O)
   

Department of Mathematics 2442 5137 (R)

College of Engineering, Guindy E-Mail – [e-mail]

Anna University, Chennai – 600 025

4. 
   Dr. S. krishnambal Phone: [phone] (O)
   

Department of Mathematics 2434 6352 (R)

College of Engineering, Guindy E-Mail – [e-mail]

Anna University, Chennai – 600 025

Further, I request you to kindly nominate an examiner to conduct the Viva-Voce examination for Ph.D. thesis of Mr. P. Saikrishnan.

Thanking you.

Yours sincerely

(SATYAJIT ROY)

Signature of DC members

1. 
   Prof. R. Usha ……………
   
2. 
   Dr. YVSS Sanyasiraju ……………
   
3. 
   Dr. R. Sarathi ……………
   
4. 
   Dr. Tanmay Basak ……………
   

Thanking you, Yours sincerely,

(SATYAJIT ROY)

UGC Refresher Course - Optimization : Algorithm and Applications

( 11-21 December, 2002)

Department of Mathematics, I.I.T. Madras
Dr. Satyajit Roy MATLAB ASSIGNMENT Date: 16 December, 2002
1. (Operations with Vectors) Let u =[1, 3, 2, 0] and v = [-2, 0, 1, 2] . What are the outputs of the following expressions? Use MATLAB and verify your results.

(i) u + v (ii) u – v (iii) [ u, v(3:4) ] (iv) u ._* v (v) u’_* v (vi) max(abs(u + i _*v )) (vii) v’_* u (viii) v. _* u

2. (Operations with vectors and matrices) Let A = [2, 1; 4, 3], a = zeros(1,4), B=zeros(2), c =ones(1,4), D=ones(2), E =eye(4). Workout the following MATLAB expressions and verify your results.

(i) a + c (ii) c’_* c (iii) A + D (iv) B _* D (v) A ._* D (vi) B ._* A (vii) E _* c’ (viii) a’_* c (ix) c_* c’ (x) D ._* A (xi) c _* E (xii) E(2, : ) + c (xiii) E(: , 3 )’ + c (xiv) any(E) + c (xv) any(E)’ _* c (xvi) any(E) ._* c (xvii) any(E) ._* a (xviii) any(E) + a (xix) [E E’] (xx) [E ; E’]

3. (Operations with complex numbers) Let u = 2 + i and v =3 + 2 _* j . Workout the following MATLAB expressions and verify your results.

(i) abs(u) (ii) angle(u) (iii) angle(u + v) (iv) real (v – u) (v) imag(u + v) (vi) u /v (vii) abs(v/u) (viii) abs( (u +1)³ ) (ix) u’ (x) [u, v]’

4. Use MATLAB to

(i) Find the zeros of the polynomial

3.65 X⁶ – 7 X⁵ + 5.6 X⁴ – 5.67 X³ + 2.45 X² – 1.35 X + 0.34

(ii) Find the polynomial whose roots are 1 , 0.34, 0.85, 3, and -7.

(iii) Plot a parabola passing through (-1, 0), (0, 2) and (1, 6).

(iv) Approximate a cubic polynomial passing through (-1, 0), (0, 2) and (1, 6).

22. 
    If 0.5 is a root of the bi-quadratic equation P₄ = 0 then obtain the cubic equation P₃ = 0 which has the same roots as P₄ = 0 except 0.5. Also find the roots of P₃ = 0 where P₄ = X⁴ – 12.9 X³ + 31 X² – 20.4 X + 4
    

(vi) Prove that the three points P(1, 5), Q(3, 11) and R(5, 17) are collinear.

5. Plot graphs using MATLAB

(i) Plot a graph of y = cos(x) against x for 0≤ x ≤ 2 with x- and y-labels.

(ii) Given that x = sin(2t) and y = sin(2t + /4) . Plot a graph of y against x.

(iii) Plot a 3D graph of the functions (a) f(x, y) = exp( - x ² – y² ) and (b) f(x, y) = Sin(x² – y²) where -3 ≤ x , y ≤ 3.

6. Find the three cube roots R₁ , R₂ , R₃ of 1 and show that R₁ . R₂ = R3 . Plot the three roots on the complex plane using MATLAB and show that they are the vertices of an equilateral triangle inscribed in the circle with radius 1.

7. The line representing the relationship between the Celsius and Fahrenheit scales passes through the points (0, 32) and (100, 212). Plot a graph using MATLAB that describes the relationship between Celsius and Fahrenheit scales between – 100F to 300F

8. Solve X’ = 3 X t² with X(0) = 1 for 0 ≤ t ≤ 1 using MATLAB by Euler method with t = 0.1 and by ode45 MATLAB in-built function . Compare these numerical results of X in a graph with the analytical results for 0 ≤ t ≤ 1.

ANNEXURE – 2


TO WHOM IT MAY CONCERN

I, hereby, accept to be the Co-guide of Mr. Prabal Dutta for his Ph.D. work on the topic ”Numerical studies of convective boundary layer flows”

(SATYAJIT ROY)

To Date: February 19^th, 2003

Professor B.S. Dandapat

Editorial Board Member, Int. Journal of A.M.E.

Dear Sir,

I am sending herewith three copies of the manuscript of our paper entitled “Steady laminar water boundary layer flow over a yawed cylinder” by S. Roy and P. Saikrishnan, for the consideration of it’s publication in “International Journal of Applied Mechanics and Engineering”. I have also enclosed herewith the original tracing sheets of the Figures 1- 6.
Thanking you, yours sincerely

(SATYAJIT ROY)

CERTIFICATE

This is to certify that Mr. P. Balraju participated in the National Symposium on Mathematical Methods and Applications held on 21^st December 2002 at I.I.T. Madras and presented the paper entitled “ MATLAB based simulation at two mixing tanks by state-space approach”.

(K.Subramanian, M.Muthusamy, P.Balraju & K.Suresh)

(SATYAJIT ROY)

SECRETARY, NSMMA-2002

To Date: November 17, 2004

Professor Ulrich GROSS

Editor, Int. J. Thermal Sciences

Dear Professor Gross,

Sub: Submission of Revised Manuscript (Paper No. UG 04-212)
I am sending herewith five copies of the Revised Manuscript of our paper entitled “Natural Convection inside a square cavity heated from below and symmetrically cooled at both sides: Effects of various Dirichlet boundary conditions at the bottom wall” by Tanmay Basak and S. Roy for the consideration of it’s publication in the journal “International Journal of Thermal Sciences”.

Thanking you,

yours sincerely

(SATYAJIT ROY)

To:

Professor Ulrich GROSS

Editor, Int. J. Thermal Sciences

Institut für Wärmetechnik und Thermodynamik

Technische Universität Bergakademie Freiberg,

09596 FREIBERG,

GERMANY

Registered AIR-MAIL

From:

Dr. SATYAJIT ROY,

Associate Professor,

Department of Mathematics,

Indian Institute of Technology Madras,