| Summary: | Due to its wide range of uses in numerous manufacturing, technological, and industrial processes, mineral oil (MO) is extremely significant. Mineral oil (MO) is used in the manufacture of PVC, polystyrene, as a lubricant and cutting fluid, thermoplastic rubber, glossing products, wood products, cleaning products, lamp oil, glues, toys, veterinary, cosmetic, food preparation, and other things. Due to the above applications, this article deals with the exact solution of unsteadiness naturally convective flowing of Maxwell nanofluid with radiation and uniform heat flux. Al2O3 nanoparticles are suspended in so-called mineral oil to make a homogeneous solution of nanofluid. The problem is demonstrated regarding coupled PDEs with initial and boundary conditions. Certain dimensionless factors are utilized to make the governing equation into a dimensionless structure. The solution for energy and momentum profiles is captured through the Laplace transform method. To predict heat transport and shear stress at the wall, the temperature and velocity gradient is also calculated. In the lack of the radiation factor, the relevant heat equation is simplified to the well-known solution in the literature. These solutions are greatly affected by the variety of different dimensionless variables like the thermal radiation parameter, volume fraction, and Grashof number. In a specific situation, the solutions relating to Newtonian fluids are retrieved, and a graphic juxtaposition of Newtonian and Maxwell fluids is displayed. Finally, the impact of pertinent parameters is shown by plotting graphs. The range of the pertinent parameters is 0.1≤λ≤0.4, Gr=5×K(K=1,2,3,4), 0.01≤χ≤0.04, Nr=5×K(K=1,2,3,4), t=1,3,5,7 while Pr=158 is fixed for mineral oil. The volume fraction declines the nanofluid's temperature while accelerating the velocity. The amplification in the Grashof number and radiation parameter improves the velocity. The increasing Maxwell fluid factor enhances the nanofluid's velocity. A decrease in the nanofluid's shear stress occurs, but after certain estimations of y, the nanofluid's shear stress goes up against the Maxwell fluid factor.
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