Unsteady flow of a ternary hybrid nanofluid over an inclined flat plate when Ohmic heating and quadratic thermal radiation are significant: couple stress model with shape factor analysis

The investigation of the flow of pair stress fluid over an inclined flat plate has garnered considerable interest in recent times owing to its extensive applicability in diverse domains such as engineering, fluid mechanics, and heat transfer. This work theoretically investigates the steady and dissipative flow of a ternary hybrid nanofluid (composed of Ethylene Glycol, Copper (II) oxide, Titanium dioxide, and Silica) over a tilted flat plate. The analysis takes into account quadratic thermal radiation, Ohmic heating, and irreversibility. We transformed the problem’s equations into a set of ordinary differential equations and solved them using the bvp4c solver. The results are shown for two instances of shape factors, namely cylindrical and brick. The results pertaining to the engineering factors of interest are elucidated through the utilisation of multiple linear regression. An increase in the couple stress parameter ( \(Cs\) $\mathit{Cs}$ ) is shown to result in an elevation in fluid velocity and entropy formation. Observations indicate that for values of \(0.5 \le Cs \le 3\) $0.5\le Cs\le 3$ , the friction factor increases at a rate of 0.04584044 (for the cylindrical shape) and 0.04583592 (for the brick shape). It has been observed that when the Eckert number ( \({\text{Eck}}\) $\text{Eck}$ ) increases, the temperature of the fluid becomes more intense. Additionally, for values of \(0 \le {\text{Eck}} \le 0.5\) $0\le \text{Eck}\le 0.5$ , the rate of heat transmission decreases by 0.291088899 for the cylindrical shape and 0.284062962 for the Brick shape. Furthermore, it has been observed that the Bejan number decreases when the couple stress parameter and Brinkman number increase.