Doctoral Thesis / Dissertation from the year 2022 in the subject Mathematics - Applied Mathematics, grade: 75.0%, Ladoke Akintola University of Technology, course: Applied Mathematics, language: English, abstract: This thesis aimed at studying the reacting system of boundary layer flow of CuO-Oil- based Nanofluid with heat generation through a vertical permeable surface. A boundary layer is formed whenever there is a relative motion between the boundary and the fluid. The details of flow within the boundary layer are very important for the understanding of many problems in aerodynamics, including the wind stall, the skin- drag on an object, heat transfers that occur in high speed flight and in naval architecture for the designs of ships and submarines. The concept of boundary layer was first introduced by Prandtl in 1904 and since then it has been applied to several fluid flowproblems. The science of fluid dynamics encompasses the movement of gases and liquids, interaction of fluid with solid and the study of forces related to these phenomena. It plays an important role in every aspect of our daily life for example from morning bath to evening coffee. It has potential applications in the field of science, engineering, manufacturing, transportation, environment, medicine, energy and others. Flows are important for the existence of natural and technical world. Properties of the fluid, forces acting on the fluid particles and boundaries of the flow domain determine the resultant flow pattern. Deformation of fluids occurs continuously under application of shear stress which makes them isotropic substances. Navier-Stokes equations are the fundamental equations of the fluid that portray the stream as either Newtonian or non-Newtonian Harlow and Amsden. There is a broad scope of heat transfer applications in numerous industrial processes involving mechanical, electrical and chemical industry. Achieving higher convective rate of heat transfer in thermal systems and processes has always been the challenges facing Scientists and Engineers. As a result, this process requires an immensity amount of vitality to manage the method of fluid heating/cooling and transport of heat. It is known that cooling is necessary for maintaining the preferred performance and steadfastness of an engine. Heat transfer fluids like water, oil, ethyl glycol and salt water collect and transport heat from the region with high temperature to the region with low temperature. In Automobiles, piston converts the heat generated as a result of the combustion of the fuel into mechanical work and drives the crankshaft in the course of the connecting rod. Continuous heating of the piston without proficient cooling can lead to elevated fuel and oil utilization, harmful exhaust emissions, reduction in engine power output or undeviating engine damage. Heat transfer fluids are expected to have high thermal conductivity, high volumetric heat capacity, and low viscosity. On the other hand, the heat carrier fluids have low thermal conductivity and affect the proper functioning of the system. In order to guarantee durability, reliability and extend lifespan of an engine, there is need for use of heat carriers’ fluid with improved heat transfer properties. The innovative conception of nanofluid was proposed as a solution to these challenges. Nanofluid, an improved heat transfer fluid, is a fluid-dispersed which contains nanoparticles of size range (1-100nm). The fluids such as oil, water and ethyl glycol are some of the fluids used in nanofluid. Materials commonly used as nanoparticles are chemically stable metals (copper, gold), metal oxides (CuO, Al O ) and Carbon in various forms (diamond, graphite, carbon nanotubes). The mixture of concentration of nanopaticles into the heat carrier fluids enhances the viscosity of nanofluids and other thermo-physical properties like thermal conductivity, specific heat capacity and density. Oil based nanofluids is used in the cooling of electronic equipment, nuclear reactors, power transformers and automobile engines. Oil in an engine cushions the bearings in opposition to the shocks of firing cylinders. It serves as lubricant to neutralize the corrosive elements during combustions and prevents the metal surfaces of an engine from rust. It also serves as coolant agent for parts of engine that are not exposed to the water-cooling system. Metal oxides are commonly used as thermal additives in Nanofluid due to their outstanding properties such as high thermal conductivity and excellent compatibility with base fluid. Al O , TiO , ZnO and CuO are the most popular metal oxides nanoparticles. Nanofluids containing metal oxides have exhibited special potentials in heat transfer applications. Among various metal oxides nanoparticles, CuO has higher thermal conductivity; it is a monoclinic crystal structure and has many attractive properties. CuO particles have spheroid shapes and most of the particles are under aggregate states. And to have an efficient Nanofluid, the particles should have spherical shape to have a higher critical dilute limit. Excessive concentration of nanoparticles in base fluid at low temperature leads to increase in the density of nanofluid, which is the compactness of nanoparticles, it results into very thick nanofluid and this leads to viscous nano-oil which provides stronger fluid film and the thicker the nanofluid film, the more resistant it will be rubbed from lubricated surfaces. Nanofluids’ viscosity is the measure of its thickness or struggle to flow. It is directly connected with how well oil based nanofluid lubricates and protects surfaces that it moves through. However, very thick nanofluid offers excessive resistance to flow at low temperatures and as a result may not flow quickly enough to those parts requiring lubrication. It is therefore crucial that for nanofluid to be effective, it must exhibit moderate concentration of nanoparticles and the right thermo-physical properties at both the highest and the lowest temperatures which are necessity for proper functional of the engine.