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This study gives unsteady radiative magneto hydrodynamic Carreau-Casson fluids in suspension of graphene particle with Cattaneo-Christov model. A simulation is performed by mixing of graphene nanoparticles into the base water. The arising set of governing partial differential equations (PDEs) are transformed into set of ordinary differential equations (ODEs) using similarity transformations and then solved numerically using shooting technique with Runge-Kutta (RK) method. The computational results for non-dimensional temperature and velocity profiles are presented through graphs and tables. We also presented the numerical values of physical quantities (friction factor and local numbers) for various physical parameters. We compared the present results with existing literature under some limited case. At the end of this analysis we concluded that, the temperature profiles are higher in Casson fluid when compared to Carreau fluid. Similarly, the friction between the particles is more in Casson fluid compare to Carreau fluid, and heat transfer rate is high in Carreau fluid compared to Casson fluid. This help us to conclude that the cooling treatment by using Casson fluid is useful compared to Carreau fluid over unsteady sheet.