Abstract:
In this thesis, the mathematical model, for steady natural and mixed
convection boundary layer ows of incompressible uid, is developed.
The ows are induced over inclined horizontal surface, vertical surface
and horizontal circular disk. The important physical quantities such
as thermal radiation and magneto hydrodynamics are incorporated for
physical and experimental considerations. Some important physical
features like heat transfer and mass transfer are added for engineering
processes.
The fundamental governing equations and the theory of boundary
layer are discussed in detail in Chapter 2. This chapter contains the
elementary eld equations of uid mechanics as partial di erential
equations in terms of physically important unknown parameters such
as velocity, pressure and energy and concentration variables. The
boundary layer equations for momentum, thermal and mass transport
are nally developed for ready reference in physical models considered
subsequently.
In Chapter 3, investigation has been made on the natural convection
boundary layer ow of a viscous incompressible uid over a semi in -
nite at plate inclined at a small angle to the horizontal. The e ects
of internal heat generation and thermal radiation are taken into ac-
count. In both cases viscosity of the uid is taken as exponential
function of temperature. The e ect of important parameters are seen
on local skin friction coe cient and local Nusselt number. The veloc-
ity and temperature distributions are obtained at the separation point
and discussed physically. The dimensionless boundary layer equations
are transformed into the suitable nonlinear equations with the help
of stream function formulation (SFF) and primitive variable formula-
tion (PVF) which are respectively solved by using iterative schemes
namely; implicit nite di erence Keller-box method and implicit nite
di erence method along with Gaussian elimination method. Compar-
ison with the previously published results is made and an excellent
agreement has been found between the two.
Chapter 4 contains the study of MHD natural convection ow of an
electrically conducting and optically dense gray uid above a heated
vertical surface. Two cases of periodic and non periodic boundary
layer ows are considered together with the interaction of thermal ra-
diation. It is worth mentioning that the obtained results are for the
low Prandtl number uids known as liquid metals. Solutions of the
governing equations are obtained for the entire range of local Hart-
mann parameter. For the constant magnetic eld (non periodic case)
asymptotic solutions are also obtained for small and large values of
locally varying parameter ξ . The numerical values of skin friction co-
e cient, rate of heat transfer, velocity and temperature distributions
are discussed for various values of physical parameters.
Conjugate e ects of heat and mass transfer on the natural convection
ow of an electrically conducting uid along a semi-in nite vertical
at plate is examined in Chapter 5. It contains two case studies:
(a) When the e ects of uniform heat and mass ux are absent (b)
When both are present. The problem is particularly investigated un-
der the in uence of strong cross magnetic eld for liquid metals. For
entire range of local Hartmann parameter, ξ , the reduced governing
equations are integrated with the help of the implicit nite di er-
ence Keller-box scheme. However, for slightly small values of local
Hartmann parameter, ξ , problem is tackled with regular perturbation
method whereas asymptotic solutions are obtained for larger values of
ξ by using matched asymptotic technique. The discussion, for several
physically important parameters, has been carried out for the numeri-
cal results of shear stress, τw , heat transfer rate, Qw and mass transfer
rate, mw . The velocity, temperature and species concentration pro les
are plotted and critically analyzed in the presence of strong magnetic
eld.
In Chapter 6, the conduction-radiation interaction on the laminar
two-dimensional steady state mixed convection ow of a viscous in-
compressible uid over a semi-in nite vertical porous plate has been
studied. In this chapter the solution of the problem corresponds to the
situation where density of the uid varies exponentially with temper-
ature. Therefore, the underlying problem deals with the solutions for
high temperature di erence between the surface and the uid, which
in turn provide more accurate results. Taking into account primitive
variable formulation (PVF), the governing boundary layer equations
are reduced to parabolic equations, which are solved numerically using
implicit nite di erence method together with Gaussian elimination
method (see Appendix B). The numerical results are discussed for the
emerging parameters appearing in the analysis of the problem.
Chapter 7 contains the in uence of conduction-radiation on the nat-
ural convection ow over the horizontal circular disk. Two numerical
techniques are employed to solve the boundary layer problem, namely;
(i) implicit nite di erence Keller-box method (see Appendix A) and
(ii) implicit nite di erence scheme along with Gaussian elimination
technique (see Appendix B). The numerical results are compared
graphically showing a good compatibility between the two methods.
The results are presented for the whole range 0 < R < 1 of the radius
of the horizontal circular disk when the Prandtl number is consider-
ably small. Discussion has been carried out on the basis of numerical
results obtained in terms of local skin friction coe cient and local
Nusselt number.
Finally in Chapter 8, the important ndings of the physical models
investigated in this thesis are highlighted and the valid conclusions
are drawn.