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

M Ferdows,Faris Alzahrani,Shuyu Sun,M Z I Bangalee,Amran Hossan

doi:10.1038/s41598-020-72545-y

Abstract

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 (s = frac{{U_{w} }}{{U_{infty } }}). Living microorganisms’ cell are mixed into the nanofluid to neglect the unstable condition of nano type particles. The governing equations are transformed to non-linear ordinary differential equations with respect to pertinent boundary conditions by using similarity transformation. The significant differential equations are solved using build in function bvp4c in MATLAB. It is seen that the solution is not unique for vertical stretching sheet. This research is reached to excellent argument when found results are compared with available result. It is noticed that dual results are obtained demanding on critical value (s_{c}), the meanings are indicated at these critical values both solutions are connected and behind these critical value boundary layer separates thus the solution are not stable.

Highlights

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
It is noticed that dual results are obtained demanding on critical value, the meanings are indicated at these critical values both solutions are connected and behind these critical value boundary layer separates the solution are not stable
The momentum and heat transfer of electro-magneto hydrodynamics boundary layer flow are incorporated in Bilal et al.[4] over stretching sheet with slip

Summary

Sb θ Dn

This works, we showed that for the certain range of parameter s the multiple solutions are possible and we analyzed whether the solution is stable or not. For this reason we take new dimensionless variable δ , where δ cause to begin an initial value problem and consistent. The unsteady problem arises for stability analysis from our considered steady formula:

Pe χ

Numerical method

Results

Conclusions

Additional information