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• W3092349076 abstract "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 ( $$s = frac{{U_{w} }}{{U_{infty } }}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mfrac> <mml:msub> <mml:mi>U</mml:mi> <mml:mi>w</mml:mi> </mml:msub> <mml:msub> <mml:mi>U</mml:mi> <mml:mi>∞</mml:mi> </mml:msub> </mml:mfrac> </mml:mrow> </mml:math> ). 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 ( $$s_{c}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>s</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> ), 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." @default.
• W3092349076 created "2020-10-15" @default.
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• W3092349076 date "2020-10-12" @default.
• W3092349076 modified "2023-09-27" @default.
• W3092349076 title "Stability theory of nano-fluid over an exponentially stretching cylindrical surface containing microorganisms" @default.
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• W3092349076 doi "https://doi.org/10.1038/s41598-020-72545-y" @default.
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