Scrutiny of MHD impact on Carreau Yasuda (CY) fluid flow over a heated wall of the uniform micro-channel

The Carreau-Yasuda model is a useful rheological tool for describing complex fluid flow behavior, especially those involving non-Newtonian fluids. This is significant because it allows for a more accurate depiction of fluids with non-linear connections between shear stress and shear rate. This research aimed to examine the effects of slip on the peristaltic transport of a magnetized Carreau–Yasuda (CY) fluid in a uniform channel where the fluid characteristics change at a heated wall. Non-dimensionalization of the governing equations was achieved by assuming a large wavelength and a low Reynolds number and then solving the resulting coupled equations with appropriate boundary conditions and mathematical "ND Solve" methods. This research looked into the two extremes of shear rate-dependent fluid behavior: shear-thinning (a decrease in viscosity with increasing shear rate) and shear-thickening (an increase in viscosity with increasing shear rate). The model can also predict Newtonian and Carreau fluid behaviors. Critical parameters such as velocity, temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number were displayed visually and tabulated in the study's results. In addition, the study used the stream function method to investigate the peristaltic motion of the bolus, uncovering that magnetic effects can decrease bolus size due to their substantial influence on apparent viscosity, with shear-thinning behavior proving more influential than shear-thickening behavior. The study further clarifies the dynamic fluctuations in fluid viscosity in response to increasing shear stress, which sheds light on the viscoelastic nature of shear-dependent behavior in a uniform microchannel using the Carreau–Yasuda fluid.