Viscous dissipation effects on hybrid nanofluid flow over a non-linearly shrinking sheet with power-law velocity

This research intends to investigate the effect of the nonlinearity of the surface velocity on the hybrid nanofluid flow behavior. Here, the total composition of Al₂O₃ (alumina) as well as Cu (copper) volume fractions, are implemented in a one-to-one ratio and then dispersed in water. The similarity equations are gained employing a similarity transformation, which is programmed in MATLAB software. The dual solutions are attainable for certain ranges with respect to the mass flux parameter $$ and the power-law index $$. Also, the turning point occurs in the region of $$ and $$. Besides, the rise of $$ led to reduce the skin friction as well as the heat transfer coefficients with 39.44 % and 11.71 % reduction, respectively. Moreover, 14.39 % reduction of the heat transfer rate is observed in the presence of viscous dissipation (Eckert number). It is found that only the first solution is stable as time progresses. Generally, this study gives scientists and engineers a starting point for predicting how to control the parameters to achieve the best results for relevant practical applications.