Abstract The study of the inclined flow along with the heterogeneous/homogeneous reactions in the fluid has been widely used in many industrial and engineering applications, such as petrochemical, pharmaceutical, materials science, heat exchanger design, fluid flow through porous media, etc. The purpose of this study is to present an infinite shear rate viscosity model using the inclined Carreau fluid with nanoscale heat transport. The model considers the effect of inclined angle on the fluid’s viscosity and the transfer of heat at the nanoscale. The result shows that the viscosity of the fluid decreases by increasing the inclination angle and the coefficient of heat transfer also increases with the inclination. The model can be used to predict the viscosity and heat transfer fluid’s behavior in the inclined systems that is widely used in the industrial and engineering applications. The results provide a better understanding of the inclined flow behavior of fluids and the heat transfer at the nanoscale, which can be useful in heat exchanger design, fluid flow through porous media, etc. Greater Infinite shear rate viscosity parameter gives the higher magnitude of Carreau fluid velocity. Moreover, inclined magnetic field reduces the velocity due to Lorentz force. Two numerical schemes are used to solve the model, BVP4C and Shooting.