Seifedine Kadry

This paper focuses on the study of Blasius–Rayleigh–Stokes nanofluid dusty flow with generalized Fourier and Fick laws under the influence of a transitive magnetic field. The Blasius–Rayleigh–Stokes nanofluid dusty flow has significant applications in various fields, including the design of heat exchangers, microfluidic devices and industrial processes involving the transportation of suspended particles in fluids. This paper considers the impact of melting heat transfer at the surface boundary. By employing relevant transformations, the mathematical model is transformed into a system of self-similar equations. The solution to this set of highly nonlinear equations is obtained using the bvp4c numerical method in combination with the response surface methodology (RSM) statistical approach. The results are presented through graphical illustrations and numerically calculated tabulated values. It is observed that the fitted model for the skin friction coefficient [Formula: see text] optimal. Moreover, the model parameters [Formula: see text], Q, [Formula: see text], M and L are linearly and quadratically significant in explaining the variation presented for skin friction coefficient [Formula: see text]. This indicates the response skin friction coefficient [Formula: see text] is minimized to 0.005 at [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] and is maximized to 1.387 at [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].