Ahlam Mahmoud Al-Jabali creator author. text theses my 2021 monographic eng xv, 135 pages : illustrations (some color) ; 30 cm. + 1 CD-ROM Advancement in the study of fluid mechanics has gained worldwide attention owing to its prominence applications in industry and engineering, those related to chemicals industries, thermal oil recovery, food and slurry transportation, polymer and food processing. Keeping views of its rheological features, numerous researchers have concentrated on the flows dealing with these versatile nature fluids. Studies have found that conventional equations such as Navier-Stokes are unable to reliably explain the rheological behavior of some fluids, as investigations on actual applications is expensive and risky at times. Therefore, this study focused on the subfamily undernon-Newtonian fluid models, namely Eyring Powell fluid to overcome these limitations. In line with this, a studyon mathematical model of a convective boundary layer under temperature-dependent viscosity on single-phase and two-phase flow over a vertical stretching sheet with Newtonian heating (NH) boundary conditions for Eyring Powell fluid was carried out. The key contributions of this thesis include filling the research gap on mathematical models of Eyring Powell fluid under single-phase and two-phase flow. Three main analyses were conducted; the first and second analysis focused on the study of forced and mixed convection of single-phase flow, while the third analysis studied the mixed convection under two-phase flow. The governing non-linear equations for each problem converted into ordinary differential equation using suitable set of similarity transformation before numerically solved by using the implicit finite difference scheme known asthe Kellerbox method (KBM). The numerical models were computed usingthe MATLAB software and the results present the behavior of fluid flow characteristics involving non-dimensional velocity and temperature distribution as well as skin friction and heat transfer of fluid for various nondimensional parameters namely, fluid parameters, Prandtl number, mixed convection parameter, fluid-particle interaction, specific heat ratio of mixture, mass concentration of particle phase and viscosity parameter. The numerical solutions obtained were illustrated through graphs and tables. From the obtained results, it was observed that the investigated parameters affect of both fluid and dust fluid characteristics, specifically skin friction, heat transfer and the fluid’s velocity and temperature. Under single-phase and two-phase flow,it clearly indicates that the fluid profiles are asymptotically approached to zero, farther from the plate, which matches the boundary condition appropriately. It is anticipated that the results in this study will lead to a deeper understanding of the characteristics of single-phase and twophase fluid flow as well as the solutions to its flow problems. specialized Ahlam Mahmoud Al-Jabali Centre for Mathematical Sciences Thesis (Master of Science (Mathematics) -- Universiti Malaysia Pahang – 2021 Includes bibliographical references Centre for Mathematical Sciences Dissertations Universities and colleges Dissertations Theses THE0009155(Local) UMP 220314 20251125105951.0 eng