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In this study of the nanofluid flow in a channel, the power of the magnetic field has been introduced to the momentum and energy equations as an innovative development. The impact of heat transfer due to free convection has also been considered. Nanofluid modeling has made use of Buongiorno's model. The similarity solution was used to transform the governing equations of the problem into ordinary differential equations, which were then solved using the finite element method (FEM). Investigations have been done into how several factors, such as the Hartmann number, Eckert number, Brownian number, Thermophoresis, and Lewis number, affect the profile of velocity, temperature, and concentration. Results indicate that the reduction in the dimensionless maximum velocity increases by 10.7% from Ha = 0 to Ha = 5, 23.5% from Ha = 5 to Ha = 10, and 48.4% from Ha = 10 to Ha = 20. Also, the Joule heating effect is prominent, as evidenced by a significant increase in the dimensionless maximum temperature from Ha = 0 to Ha = 20, reaching a rise of 540.3%.