The present study analyses the phenomena of entropy generation of magneto third-grade fluid flow through the microchannel. The significance of Joule heating, viscous heating and internal heat source is also scrutinised. The non-dimensional forms of the corresponding governing equations of the physical phenomenon with the associated boundary conditions for third-grade fluid flow and heat transfer has been solved using finite element method. The impact of various parameters on the flow and heat transfer behaviour, entropy generation and Bejan number is explained using graphs. The obtained results are examined through the plots. The results showed that an increase in the fluid parameter reduces the activity of the fluid flow and, as a result, the temperature is diminished. An enhancement in fluid motion and temperature is obtained by increasing the viscosity index. We noted that the effect of Hartmann number on the rate of local entropy generation and Bejan number is sinusoidal in nature.