In this paper, we study coupled flow and heat transfer of power-law nanofluids on a non-isothermal rough rotating disk subject to a magnetic field. The problem is formulated in terms of specified curvilinear orthogonal coordinate system. An improved BVP4C algorithm is proposed and numerical solutions are obtained. The influence of volume fraction, types and shapes of nanoparticles, magnetic field and power-law index on the flow and heat transfer behavior are discussed.<br/>Results show that the power-law exponents (PLE), nanoparticle volume fraction (NVF) and magnetic field inclination angle (MFIA) are almost no effects on velocities in wave surface direction, but have small or significant effects on azimuth direction. NVF have remarkable influence on local Nusselt number (LNN) and friction coefficients (FC) in radial and azimuth directions (AD). LNN increases with NVF while FC in AD decrease. The types of nanoparticles, magnetic field strength and inclination have small effects on LNN, but they have remarkable effects on the friction coefficients with positively correlated while the inclination is negatively correlated with heat transfer rate. The size of the nanoparticle shape factor is positively correlated with LNN.