Response surface methodology for the optimisation of heat transfer rate for concatenated non-Newtonian fluid flow over a curved stretching sheet

The current article unveils the repercussions obtained from analysing the Casson–Williamson nanofluid flow across a curved stretched surface using the Darcy–Forchheimer model. The modelling is contemplated with homogeneous–heterogeneous chemical reactions. The impact of nonlinear thermal radiation, exponential heat source and magnetic field is considered. Further, response surface methodology is a statistical technique used to understand the association of parametric factors under consideration on the response which is the Nusselt number in the present context. The prime aim of this modelling is to give optimal conditions for producing the highest heat transfer rate to build an efficient model with the aid of sensitivity analysis. In addition, entropy propagated in the media is provided to enhance the importance of this investigation. Runge–Kutta–Fehlberg 4–5th order technique has been used to obtain the numerical output. The analysis reveals that the first-order slip component has a negative effect on velocity distribution, whereas the second-order slip factor has the opposite effect. The Nusselt number decreases as the unsteadiness parameter reaches its maximum value and when the sheet is susceptible to intense radiation. Graphical representations of streamlines and isotherms are provided to illustrate the flow and heat distribution. The sensitivity analysis emphasises that the Brownian motion parameter has positive sensitivity, whereas thermophoresis and an exponential heat source have negative sensitivity on the Nusselt number.