Browsing by Author "Muhammad Bilal Riaz"

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    Analytic solutions of oldyrod-b fluid with fractional derivatives in a circular duct that applies a constant couple
    (Alexendria Engineering Journal, Elsevier, 2016) Muhammad Bilal Riaz; Muhammad Imran Asjad
    The aim of this article was to analyze the rotational flow of an Oldroyd-B fluid with fractional derivatives, induced by an infinite circular cylinder that applies a constant couple to the fluid. Such kind of problem in the settings of fractional derivatives has not been found in the literature. The solutions are based on an important remark regarding the governing equation for the nontrivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions and can easily be reduced to the similar solutions corresponding to ordinary Oldroyd-B, fractional/ordinary Maxwell, fractional/ordinary second-grade, and Newtonian fluids performing the same motion. The obtained results are expressed in terms of Newtonian and non-Newtonian contributions. Finally, the influence of fractional parameters on the velocity, shear stress and a comparison between generalized and ordinary fluids is graphically underlined.
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    Analytical solutions for different motions of differential and rate type fluids with fractional derivatives.
    (UMT Lahore, 2018-10-24) Muhammad Bilal Riaz
    In this dissertation, we present the analytical studies of some fluid flow models. We analyze the fractional models for the flow of non-Newtonian fluids via classical computational techniques to obtain analytical solutions. This study includes the investigation of the unsteady natural convection flow of Maxwell fluid with fractional derivative over an exponentially accelerated infinite vertical plate. Slip condition, chemical reaction, transverse magnetic field and Newtonian heating effects are also considered using a modern definition of fractional derivative. Moreover, the unsteady flow of Maxwell fluid with non-integer order derivatives through a circular cylinder of infinite length in a rotating frame is studied. The motion of Maxwell fluid is generated by a time dependent torsion applied to the surface of the cylinder. As novelty, the dimensionless governing equation related to the non-trivial shear stress is used and the first exact solution analogous to a ramped shear stress on the surface is obtained. The rotational flow of an Oldroyd-B fluid with fractional derivative induced by an infinite circular cylinder that applies a constant couple stress to the fluid is investigated. It is worth mentioning that the considered problem of Oldroyd-B fluid in the settings of fractional derivatives has not been found in the literature. Some unsteady Couette flows of an Oldroyd-B fluid with non-integer derivative in an annular region of two infinite co-axial circular cylinders are investigated. Flows are due to the motion of the outer cylinder, that rotates about its axis with an arbitrary time dependent velocity while the inner cylinder is held fixed. Finally, the analysis of the second grade fluid with fractional derivative is made. The fluid fills the annulus region between two coaxial cylinders in which one cylinder is at rest while the other experiences time dependent shear stress. In all the flow models, we obtained the exact or semi analytical solutions for the motions with technical relevance. These solutions correspond to some flows in which either velocity or the shear stress is given on the boundary are established for different kinds of rate and differential type fluids. The obtained solutions presented in all the fluid flow models satisfy the imposed initial and boundary conditions. Further, the flow properties and comparison of models with respect to derivative (fractional or ordinary) are highlighted by graphical illustrations.