This work presents a numerical investigation of viscous nanofluid flow over a curved stretching surface. Single-walled carbon nanotubes were taken as a solid constituent of the nanofluids. Dynamic viscosity was assumed to be an inverse function of fluid temperature. The problem is modeled with the help of a generalized theory of Eringen Micropolar fluid in a curvilinear coordinates system. The governing systems of non-linear partial differential equations consist of mass flux equation, linear momentum equations, angular momentum equation, and energy equation. The transformed ordinary differential equations for linear and angular momentum along with energy were solved numerically with the help of the Keller box method. Numerical and graphical results were obtained to analyze the flow characteristic. It is perceived that by keeping the dynamic viscosity temperature dependent, the velocity of the fluid away from the surface rose in magnitude with the values of the magnetic parameter, while the couple stress coefficient decreased with rising values of the magnetic parameter.