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The recent work investigates the heat transfer attributes in the flow of engine oil which comprises of nano-particles such as Cu and TiO2. The performance of Copper and Titanium oxide is over looked in the flow of engine oil. The energy equation is amended by the features of thermal radiation, viscous dissipation, and heat generation. The mathematical model signifies the porosity, entropy generation and moving flat horizontal surface with the non-uniform stretching velocity. Quasi-linearization, which is a persuasive numerical technique to solve the complex coupled differential equations, is used to acquire the numerical solution of the problem. Flow and heat transfer aspects of Cu–TiO2 in the flow are examined against the preeminent parameters. The flow is significantly affected by the thermal jump conditions and porous media. It is observed here that the temperature as well as heat transport rate is reduced with the effect of involved preeminent parameters. However, such fluids must be used with caution in applications where a control on the heat transfer is required. We may conclude that the recent study will provide assistance in thermal cooling systems such as engine and generator cooling, nuclear system cooling, aircraft refrigeration system, and so forth. [ABSTRACT FROM AUTHOR]