Analytical approach to unidirectional flow of non-Newtonian fluids of differential type - Abdulhameed, Mohammed (2015)
This thesis is regarding the development of mathematical models and analytical techniques for non-Newtonian fluids of differential types on a vertical plate, horizontal channel, vertical channel, capillary tube and horizontal cylinder. For a vertical plate, a mathematical model of the unsteady flow of second-grade fluid generated by an oscillating wall with transpiration, and the problem of magnetohydrodynamic (MHD) flow of third-grade fluid in a porous medium, have been developed. General solutions for the second-grade fluid are derived using Laplace transform, perturbation and variable separation techniques, while for the third-grade fluid are derived using symmetry reduction and new modified homotopy perturbation method (HPM). For a horizontal channel, a new analytical algorithm to solve transient flow of third-grade fluid generated by an oscillating upper wall has been proposed. A new approach of the optimal homotopy asymptotic method (OHAM) have been proposed to solve steady mixed convection flows of fourth-grade fluid in a vertical channel. The accuracy of the approximate solution is achieved through the residual function. For a capillary tube, two flow problems of the second-grade fluid were developed. Firstly, oscillating flow and heat transfer driven by a sinusoidal pressure waveform, and secondly, free convection flow driven due to the reactive nature of the viscoelastic fluid. The solutions for the first problem were derived using Bessel transform technique while for the second problem by using a new modified homotopy perturbation transform method. For a horizontal cylinder, an unsteady third-grade fluid in a wire coating process inside a cylindrical die is developed. A special case of the problem is obtained for magnetohydrodynamic flow with heat transfer for second-grade fluid. Both of these two problems are solved using a new modified homotopy perturbation transform method. Data, graph and solutions obtained are shown and were found in good agreement with previous studies.