Evolution of heat transfer in MHD nanofluid flow over a porous plate: Insights into the influences of slip and variable viscosity

Temperature-dependent viscosity finds application in various industries such as oil and gas, polymer processing, and food manufacturing. Understanding how viscosity changes with temperature is critical for optimizing processes like drilling operations, polymer molding, and food product consistency. Additionally, it plays a vital role in controlling flow behavior, ensuring efficient heat transfer, and maintaining product quality across different temperature conditions. The exploration of temperature-dependent viscosity in Powell-Eyring nanofluid models represents a novel and unexplored avenue in the field. The study's novelty is underscored by its comprehensive investigation into a range of factors, such as surface suction, thermal radiation, slip velocity effects, and nanoparticle concentration slip, all integrated within the Powell-Eyring nanofluid model. Moreover, the adoption of bvp4c as a numerical tool further emphasizes the research's unique contributions. The curves of temperature, concentration, and velocity as a consequence of changes in physical parameters are discussed. Increasing the value of the suction parameter promotes heat transfer but slows the velocity of the nanofluid. The injection of a magnetic field is responsible for compensating for the suction rate. An improvement in the concentration of nanoparticles and temperature is observed as a result of an increase in the slip rate. It is evident that both nanoparticle concentration and temperature rise significantly when Bi, the Biot number, is increased. In the boundary layer, a decrease in velocity is observed as a consequence of an increase in velocity slip, porosity, and magnetic field parameters.