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The impact of thermal radiation on viscous dissipative boundary layer flow of heat absorbing magneto-nanofluid over a permeable exponentially stretching sheet with Navier's velocity and thermal slips has been analyzed. The prevailing mathematical equations are changed to nonlinear ordinary differential equations using the appropriate similarity variables and then the equations are numerically solved by Runge-Kutta scheme of fourth order together with the shooting technique. Three kinds of water based nanofluids having aluminum oxide, copper and titanium oxide as nanoparticles are considered for this investigation. The consequence of relevant flow parameters on nanofluid velocity, temperature distribution, wall velocity gradient and local Nusselt number are displayed by means of various graphs. In addition, analysis of quadratic regression estimation on the numerical data of coefficient of skin friction and local Nusselt number has been presented to verify the relationship among the controlling physical parameters and transfer rate parameters. Our result reveals that the velocity and temperature distribution profiles are lower for Cu-water nanofluid followed by Al2O3 and TiO2 water base nanofluids in the regime of boundary layer. The thermal radiation and viscous dissipation have tendency to augment the Cu-water temperature over the stretching sheet. [ABSTRACT FROM AUTHOR]