In this research article, the effect of rotating and second-grade fluid on an MHD Jeffery–Hamel flow (J–HF) has been investigated. Here, the MHD second-grade fluid theory has been used. The PDEs that represent this flow are transformed into ODEs, which are then solved using two separate methods: the 4th–5th-order Runge–Kutta Fehlberg technique with shooting methodology and the DTM technique. The impact of diverse physical factors, like rotational factor, Deborah, and Hartmann numbers, on the dimensionless rapidity \(F\) of the second-grade fluid and the wall frictional force factor is analyzed. Backflow is not detected in the lower part of the channel, according to the study. Additionally, the results show that the reverse flow disappears completely as the Hartmann number increases. Also, it is found that the Deborah quantity has less impact on the dimensionless velocity \(F\) of second-grade fluid nearby the down surface of the rotative diverging channel, but a significant increase in the thickener of the momentum boundary layer at the upper half of the channel is noticed with the rise in the magnitude of the Deborah number, hence signaling the beginning of the backflowing behavior. The current findings are contrasted to those of prior investigations and the HAM-built Mathematica package BVPh 2. The newly used analytical method shows high reliability, usefulness, and precision, as evidenced by the excellent agreement between DTM, HAM-BMP BVPh 2, and computational RKF45.
