Abstract:
Flow and Heat Transfer Over Stretching and Shrinking Surfaces
Finding the numerical solutions of ordinary and partial differential equations of nonlinear nature
has become somewhat possible, during the last few decades, due to the evolution of efficient
computing. However, the governing equations for fluid flow are difficult to address in terms of
finding analytical solutions. This difficulty lies in the highly nonlinear nature of these equations.
Thus, it has always been a challenging task for mathematicians and engineers to find possible
exact/approximate analytical and numerical solutions of these equations. The analytical results
have great advantage in the sense that; it helps to make comparison with exact numerical
solution ensuring the reliability of the two results and also helps to explain the underlying
physics of fluid. The analytical solutions are further useful to develop an insight for the
development of new analytical techniques and for the modeling of new exciting fluid flow
problems in both Newtonian and non-Newtonian fluids.
There has been a continuously increasing interest of the researchers to investigate the boundary
layer fluid flow problems over a stretching/shrinking surface. It is now known that surface shear
stress and heat transfer rate for both viscous and non-Newtonian fluid are different. These
stretching and shrinking velocities can be of various types such as liner, power law and
exponential. Thus our main objective in this thesis is to analyze some boundary layer flow
problems due to stretching/shrinking sheet with different types of velocities analytically. Both
transient and steady forced and mixed convection flows are considered. The present thesis is
mainly structured in two parts. Chapters 3 to 5 consist of transient and steady mixed convection
boundary layer flow of Newtonian and some classes of non-Newtonian fluids with linear
stretching and shrinking cases. Chapters 6 to 8 present the investigation of exponential stretching
case. The chapters of the thesis are arranged in the following fashion.
Chapter 1 dealt with the previous literature related to boundary layer stretched flows of viscous
and non- Newtonian fluids. Chapter 2 includes the basic equations of fluid flow and heat
transfer. Definitions of dimensionless physical parameters are also presented here. Chapter 3
explores unsteady mixed convection flow of a viscous fluid saturating porous medium adjacent
ixto a heated/cooled semi-infinite stretching vertical sheet. Analysis is presented in the presence of
a heat source. The unsteadiness in the flow is caused by continuous stretching of the sheet and
continuous increase in the surface temperature. Both analytical and numerical solutions of the
problem are given. The effects of emerging parameters on field quantities are examined and
discussed. The magnetohydrodynamic boundary layer flow of Casson fluid over a shrinking
sheet with heat transfer is investigated in Chapter 4. Interesting solution behavior is observed
with multiple solution branches for a certain range of magnetic field parameter. Laminar two-
dimensional unsteady flow and heat transfer of an upper convected, an incompressible Maxwell
fluid saturates the porous medium past a continuous stretching sheet is studied in Chapter 5. The
velocity and temperature distributions are assumed to vary according to a power-law form. The
governing boundary layer equations are reduced to local non-similarity equations. The resulting
equations are solved analytically using perturbation method. Steady state solutions of the
governing equations are obtained using the implicit finite difference method and by local non-
similarity method. A good agreement of the results computed by different methods has been
observed.
Chapter 6 addresses the steady mixed convection boundary layer flow near a two-dimensional
stagnation- point of a viscous fluid towards a vertical stretching sheet. Both cases of assisting
and opposing flows are considered. The governing nonlinear boundary layer equations are
transformed into ordinary differential equations by similarity transformation. Implicit finite
difference scheme is implemented for numerical simulation. The features of the flow and heat
transfer characteristics for different values of the governing parameters are analyzed and
discussed. Chapter 7 examines the boundary layer flow of a viscous fluid. The flow is due to
exponentially stretching of a surface. Unsteady mixed convection flow in the region of
stagnation point is considered. The resulting system of nonlinear partial differential equations is
reduced to local non-similar boundary layer equations using a new similarity transformation. A
comparison of the perturbation solutions for different time scales is made with the solution
obtained for all time through the implicit finite difference scheme (Keller-box method).
Attention is focused to investigate the effect of emerging parameters on the flow quantities.
Chapter 8 aims to investigate the boundary layer flow of nanofluids. The flow here is induced
by an exponentially stretching surface with constant temperature. The mathematical formulation
xof this problem involves the effects of Brownian motion and thermophoresis. Numerical solution
is presented by two independent methods namely nonlinear shooting method, and finite
difference method. The effects of embedded parameters on the flow fields are investigated.
Chapter 9 summaries the research material presented in this thesis.