| dc.description.abstract | This thesis deals with elegant application of certain
known mathematical methods and with certain numerical procedures
devised to obtain solutions of the differential equations arising
in the flow and heat transfer problems of viscous and visco-elastic
fluids. The techniques devised here replace the usual expansion
methods in terms of small parameters. These methods are applied
to physical problems to shov/ their applicability and efficiency.
Satisfactory solutions have been obtained either in the closed
forms or in terras of simple quadratures or without using the
brute-force trial and error method specially when the two-point
boundary value and eigen-value problems are involved. Thus the
solutions of the physical problems as well as the methods
developed here are of interest.
The thesis consists of seven chapters. Chapter I gives
a general introduction to the matter discussed in the succeeding
chapters. Here we have stated in brief and in general teims the
main types of problems that we have investigated in the thesis.
We have also recorded here the constitutive equations of the fluidj
and the equations of motion relating to some of the geometries
that we have employed in our studies. Each of the subsequent
chapters deals exclusively with one particular type of problem.
- 1 -
Each of these chapters starts with a short introduction to the
problem followed by the author's contribution*
Every care has been taken to present the contribution in
a connected manner to avoid repetition as far as possible.
Wherever necessary a chapter is split up into different parts to
present the related work. All the equations and formulae etc.
of chapter I have been numbered separately. Each of the other
chapters has its own section numbers and the numbers of the
equations etc.
Chapter II deals with time-dependent heat transfer in the
presence of a heat source in a Newtonian fluid adopting the
Laplace Transform technique and is based on the following papers:
(i) A note on the temperature distribution in a channel
bounded by two co-axial cylinders (in collaboration
with Prof.P.L.Bhatnagar), Proc.Gamb.Phil,Soc62,
(1966), 301-302.
(ii) Heat transfer in a flow of viscous incompressible
fluid in a cylinder and cylindrical anrailus,
Jour.Ind.Inst.Sci., 49, (1967), 1-9.
Chapter III deals with the steady laminar flow and heat
transfer in Noll fluid for which formal solutions have been
obtained and is based on the following paper :
Laminar flow of elastico-viscous fluid inside a
cylinder, Ind.Jour.Pure and Appl.Phys., 5, (196 7),
246-247.
Chapter IV deals with the steady laminar flow and heat
transfer in Rivlin-Ericksen fluid between two infinite parallel
plates - one stationary and other rotating - and with an
iterative procedure of solving two-point boundary value problems
associated with coupled nonlinear ordinary differential equations.
These investigations are reported for the first time in this thesis.
Chapter V deals with steady laminar flows and heat
transfer with suction and injection for which the solutions of
two-point boundary value problems associated with ordinary
differential equations are obtained without trial and error.
This chapter is based on the following papers :
(i) Plane Gouette flow with suction or injection
and heat transfer for Rivlin-Sricksen fluid,
Jour.Ind.Inst.Sci., 50, (1968), 244-257.
(ii) Steady laminar flow with suction or injection
and heat transfer through porous pipe
"to appear in Proc .Ind.Acad.Sci .
Chapter VI deals with a new numerical procedure for
initial value problem associated with second order non-linear
ordinary differential equation: and is based on the following
paper :
Numerical procedure for second order nonlinear
ordinary differential equations and application
to heat transfer problem (in collaboration with
Miss Swarnalata Prabhii) [to appear in Proc.Ind.
Acad .Sci.]
Chapter VII deals with the application of Galerkin’s
method to the study of stability of laminar flow of a Maxwell
fluid inside a circular cylinder. This study is reported for
the first time in this thesis. | |
