Thermal analysis of joule heating effect on micropolar nanofluid flow past a vertical stretching/Shrinking surface: Triple solutions

The combined usage of nanofluid and porous medium in various engineering and industrial processes provides great results in achieving the ultra-high cooling rate requirements of current industries. Further, the role of nanoliquid in the advancement of nanotechnology and electronic devices at the engineering and industrial level attracts researchers to explore this area of research. Furthermore, nonliquids are noteworthy in transportation, biomedical applications, as well as in thermal and mass transmission because of their high thermal conductivity characteristics in contrast with regular liquids. Taking this into account, the novel aspect of the current research is to explore thermal and mass transmission of micropolar nanoliquid flow through a non-linear vertical stretching/shrinking surface. Further chemical reactions and thermal radiation are utilized in energy and mass equations. Further suitable similarity transformations are introduced to convert the governing equations of micropolar nanofluid flow into non-linear ordinary differential equations. Then the resultant ODEs are solved by applying bvp4c in MATLAB software. Due to the existence of more than one solution, stability analysis is performed. It is observed that the first solution is stable and feasible. Moreover, the investigation portrays that the microrotation boundary layer thickness increases in all solutions with the growth in the material factor.