Fractional modeling and analysis of heat and mass transfer in nanofluid via He–Laplace framework

The objective of this manuscript is to propose a fully fractional generalized model for heat and mass transfer in unsteady Carreau–Yasuda nanofluid between two stretching plates, taking into account the effects of magneto-hydrodynamics, porosity, thermophoresis, and Brownian motion. By proposing new similarity transformations, a fully fractional system of differential equations is recovered. For the solution and analysis of the developed model, the fractional extension of the He–Laplace algorithm is proposed and utilized. Error analysis is performed for validating the obtained solutions by finding system errors to ensure accuracy and reliability. Fractional-order momentum, temperature, and concentration profiles are analyzed in relation to key fluid parameters. In addition, physical quantities, such as skin friction, heat, and mass transfers, are analyzed through contour analysis. It is observed that heat and mass transfer in blood vessels are more strongly influenced by the Reynolds number than by the fractional parameter. This highlights the dominant role of flow inertia in transport processes at the fractional order. This paper highlights the significance of incorporating fractional derivatives into fluid flow phenomena to provide a more realistic and comprehensive approach. The results demonstrate that the fractional-order model is capable and compatible to capture complex fluid behaviors more accurately than traditional integer-order models.