New similarity solutions of heat and mass transfer in flow of Carreau fluid over a rough sheet with nonlinear kinematics

This research introduces novel and generalized similarity solutions for heat and mass transfer in the flow of Carreau fluid across a rough, non-flat sheet characterized by nonlinear kinematics. Previous research presented space-dependent parameters, particularly Weissenberg numbers, within the transformed ordinary differential equation systems, which is against the spirit of the fundamental principle of similarity solutions. By creating a mathematically consistent transformation, we overcome this significant issues and produce a more comprehensive and precise modelling framework. MATLAB's bvp4c approach is used to numerically solve the governing equations. Important dimensionless factors are examined in relation to velocity, temperature, concentration, and skin friction, including the Weissenberg number, non-linear kinematics, power-law index, Prandtl number, Schmidt number, and surface roughness. Notably, we discover that while raising the Weissenberg number thickens the velocity boundary layer in shear-thickening fluids, surface roughness and sheet temperature greatly increase the mass transfer rate. These findings provide new perspectives for non-Newtonian thermal processing systems, coating processes, and biomedical transport applications.