FRACTIONAL ORDER GENERALIZED FLUID FLOW MODELS: AN ANALYTICAL APPROACH

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.