Stability theory of nano-fluid over an exponentially stretching cylindrical surface containing microorganisms.

This research is emphasized to describe the stability analysis in the form of dual solution of the flow and heat analysis on nanofluid over an exponential stretching cylindrical surface containing microorganisms. The research is also implemented to manifest the dual profiles of velocity, temperature and nanoparticle concentration in the effect of velocity ratio parameter ([Formula: see text]). Living microorganisms' cell are mixed into the nanofluid to neglect the unstable condition of nano type particles.