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Thermophoresis and Brownian Motion Influenced Bioconvective Cylindrical Shaped Ag–CuO/H2O Ellis Hybrid Nanofluid Flow Along a Radiative Stretched Tube with Inclined Magnetic Field

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Abstract

This investigation aims to delineate bioconvection in cylindrical-shaped Ag-CuO/H2O Ellis hybrid nanofluid containing gyrotactic microorganisms around a steady stretched cylindrical tube. Considering Brownian and thermophoretic diffusions, along with effects from an inclined magnetic field and slip, we derive a nonlinear system using boundary layer equations. Employing MATLAB’s bvp4c function for numerical solutions, validated against established studies, we observe strong agreement. Graphical and tabular analyses demonstrate the impact of various parameters on velocity, temperature, concentration, gyrotactic microorganism profiles, skin friction coefficient, local Nusselt and Sherwood numbers, and gyrotactic microorganism coefficient, offering valuable interpretations. Observations reveal that the Ellis fluid parameter heightens velocity but reduces temperature, concentration, and gyrotactic microorganism profiles. Conversely, thermophoresis and Brownian motion enhance heat and mass transfer rates, while slip exhibits an opposite trend. Peclet number and bioconvective constants exhibit intriguing but contrary trends with gyrotactic microorganism profiles, yielding notable insights. A comparison between Ellis hybrid nanofluid and Ellis nanofluid reveals approximate variations in skin friction coefficients (up by 46.5%) and Nusselt numbers (down by 4%), suggesting improved aerodynamics and enhanced biomedical heat control for industrial optimization. Moreover, the reduction in Sherwood numbers (down by 56%) suggests potential applications in tailored environmental remediation and the optimisation of substance diffusion in pharmaceutical and biomedical therapeutics. This comprehensive analysis delves into intricate fluid dynamics, offering empirical insights applicable across engineering, biomedical sciences, and environmental remediation domains.

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Data Availability

No datasets were generated or analysed during the current study.

Abbreviations

\({r}^{\prime},z^{\prime}\)  :

Velocity component along \(w^{\prime}\) and \(r^{\prime}\) respectively (m s−1)

\(T^{\prime}\)  :

Fluid temperature (K)

\(C^{\prime}\)  :

Fluid concentration (kg m−3)

\({T}_{w}^{\prime}\)  :

Wall temperature (K)

\({C}_{w}^{\prime}\)  :

Wall concentration (kg m−3)

\(R^{\prime}\)  :

The radius of the cylinder (m)

\({T}_{\infty }^{\prime}\)  :

Ambient temperature (K)

\({C}_{\infty }^{\prime}\)  :

Ambient concentration (kg m−3)

\(Pr\) :

Prandtl number

\({D}_{T}^{\prime}\)  :

Thermophoresis diffusion coefficient (m2 s−1)

\(K\) :

Thermal conductivity (W m−1 K−1)

\(Sc\) :

Schmidt number

\({C}_{{F}_{g}}\) :

Skin friction coefficient

\(Th\) :

Thermophoresis parameter

\({D}_{B}^{\prime}\)  :

Brownian diffusion coefficient (m2 s−1)

\(M\) :

Magnetic parameter

\(N{u}_{x}\) :

Nusselt number

\(S\) :

Slip parameter

\(Bm\) :

Brownian motion parameter

\(S{h}_{x}\) :

Sherwood number

\({F}_{g}\) :

Non-dimensional stream function

\(R{e}_{x}\) :

Local Reynolds number

\({k}^{*}\) :

Mean absorption coefficient

\({Q}_{n}\) :

Radiative heat flux (W m−2)

\({C}_{p}\) :

Specific heat capacity (J kg−1 K−1)

\({B}_{0}\) :

Constant magnetic flux

\(Nd\) :

Radiation parameter

\(Lb\) :

Bio-convective Lewis number

\({D^{\prime}}_{m}\)  :

Microorganism diffusion coefficient (m2 s−1)

\(Pe\) :

Bio-convective Peclet number

\({A}_{1}\) :

First Rivlin-Ericksen tensor

\({W}_{c}\) :

Maximum cell swimming speed

\({U}_{w}^{\prime}\)  :

Stretching velocity along \(z^{\prime}\) direction

\(N{n}_{x}\) :

Microorganism coefficient

\({F}_{\chi }\) :

Non-dimensional temperature

\({\sigma }^{*}\) :

Stefan-Boltzmann coefficient

\({\beta }_{e}\) :

Ellis fluid parameter

\({\alpha }_{1}\) :

Thermal diffusivity (m2 s−1)

\(\gamma\) :

Curvature parameter

\(\zeta\) :

Similarity transformation variable

\({F}_{\phi }\) :

Non-dimensional concentration

\(\mu\) :

Dynamic viscosity (mPa)

\({\tau }_{1}\) :

Ratio of heat transfer capacity of the particles of the fluid

\(\rho\) :

Density (kg m−3)

\({\pi }_{s}\) :

Second order invariant of the stress tensor

\({F}_{\psi }\) :

Non-dimensional microorganism

\(\nu\) :

Kinematic viscosity (m2 s−1)

\({\tau }_{0},\alpha\) :

Material constants

\(\xi\) :

Inclination of magnetic field

\(\tau\) :

Extra stress tensor

\(\sigma\) :

Electrical conductivity (S m−1)

\(\delta\) :

Bio-convective constant

\(Ag\) :

Silver

\(CuO\) :

Cupric oxide

\(f\) :

Base fluid (water)

\(hnf\) :

Hybrid nanofluid

\(w\) :

Cylinder surface

\(\infty\) :

Far field

\({\text{MHD}}\) :

Magnetohydrodynamics

\({\text{G}}.{\text{M}}.\) :

Gyrotactic microorganisms

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Authors and Affiliations

  1. Department of Mathematics, Cotton University, Guwahati, Assam, 781001, India

    Neelav Sarma & Ashish Paul

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  1. Neelav Sarma
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Contributions

N.S. developed the proposed model and defined the governing PDEs, transformed the equations to ODEs, and computation was done numerically and results and discussion were initiated, illustrated, and graphical figures were drawn. A.P. initiated the idea of the research, supervised the research and contributed to the revision of the manuscript with grammatical and technical checking.

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Correspondence to Neelav Sarma.

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Sarma, N., Paul, A. Thermophoresis and Brownian Motion Influenced Bioconvective Cylindrical Shaped Ag–CuO/H2O Ellis Hybrid Nanofluid Flow Along a Radiative Stretched Tube with Inclined Magnetic Field. BioNanoSci. (2023). https://doi.org/10.1007/s12668-023-01280-1

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