Analysis of tiny inflexible suspended particles and solar thermal radiation aspects during the wavy flows of magneto-Cross nanofluid

Abstract

The periodic wavy motion of the generalized materials in the presence of spinning tiny inflexible suspended particles has a wide range of practical applications, i.e., the typical motion of lubricants, paints, blood, anisotropic fluids polymeric, etc. These fluids are the main examples of micro-polar materials. However, this work is a constructive approach for maximizing the heat transfer rate during the periodic motion of Cross liquid in combination with micropolar fluid. Furthermore, the same practical problem is formulated with solar thermal radiation, Brownian motion, thermophoretic force, Lorentz force, and gravity force. All the leading factors are examined for their significant inclusion while observing the novel behavior of the materials. The mathematical equations are then modeled in terms of dimensionless ordinary differential equations (ODEs). In particular, the material's speed, temperature, resistive forces, concentrations as well as flow of heat and mass transfer rates are graphically visualized. Vertical velocity components are uplifted for higher variations in the vortex viscosity factor as well as an opposite trend is noticed in the behavior of horizontal components of velocity. The findings highlight that higher vortex viscosity increases the vertical velocity components while reducing horizontal velocity, indicating directional flow influences. Thermal radiation and Brownian motion both elevate the temperature of the material during motion. Additionally, a higher vortex viscosity enhances resistive forces in the wavy flow, while an increase in the Weissenberg number reduces these forces. Brownian motion reduces the heat transfer rate, whereas the nanoparticle volume fraction shows the opposite behavior. The accuracy and authenticity of the approximated results are validated by providing a good agreement with the previous works and with the results obtained in the Richardson extrapolation.