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Abstract: Abstract The primary goal of this article is to analyze the oscillating behavior of Maxwell Nano-fluid with regard to heat and mass transfer. Due to high thermal conductivity engine oil is taken as a base fluid and graphene Nano-particles are introduced in it. Coupled partial differential equations are used to model the governing equations. To evaluate the given differential equations, certain dimensionless factors and Laplace transformations are used. The analytical solution is obtained for temperature, concentration and velocity. The temperature and concentration gradient are also finds to analyze the rate of heat and mass transfer. As a special case, the solution for Newtonian fluid is discussed. Finally, the behaviors of various physical factors are studied graphically for both sine and cosine oscillation and give physical meanings to most of the parameters.