Abstract:
In this thesis some new results regarding non-Newtonian fluids with
fractional derivatives under different circumstances have been obtained.
The non-Newtonian fluids under discussion are fractional second grade
fluid, fractional Jeffrey fluid and fractional Oldroyd-B fluid. The similar
solutions for ordinary second grade fluid, ordinary Jeffrey fluid and ordi-
nary Oldroyd-B fluid are obtained as limiting cases of general solutions.
Governing equations are achieved by using approach of fractional calculus.
Laplace and Fourier sine transforms are used to obtain analytic solution for
velocity field and associated shear stress. The obtained solutions are ex-
pressed in series form using Fox H-function. Magnetohydrodynamic flow
of generalized second grade fluid induced by constant pressure gradient in
a porous medium is also discussed. The series solutions satisfy all the initial
and boundary conditions. The effects of different parameters on the flow are
analyzed graphically.
Some exact solutions are established for the magnetohydrodynamics flow
of generalized second grade fluid due to impulsive motion of a flat plate
passing through a porous space. Some new results are established corre-
sponding to generalized Jeffrey fluid produced by a flat plate between two
side walls perpendicular to the flat plate. The flow of generalized Jeffrey
fluid is set into motion by (i) impulsive motion of the plate, (ii) impulsive
accelerating plate, and (iii) non-uniformly accelerated plate. Unsteady mag-
netohydrodynamic flow of generalized Jeffrey fluid in a long porous rectan-
gular duct oscillating parallel to its length is also spotlighted. The volume
flux due to sine and cosine oscillations of the rectangular duct are achieved.
The oscillatory motion of magnetohydrodynamic flow of an incompress-
ible generalized Oldroyd-B fluid is studied. In particular, results regarding
Maxwell fluids are also obtained as limiting case of the general solutions.
