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Gyrotactic Mixed Bioconvective Flow of Copper–Water Nanofluid Past a Rotating Cone with Non-uniform Heat Source and Activation Energy

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Abstract

The present study is concerned with the bioconvective magneto-nanofluid flow of copper–water containing gyrotactic motile microorganisms across a vertically spinning cone in a porous regime. Bioconvection in nanofluid is important in bioscience, such as for delivering drugs, content detection, micro-enzymes, biological sensors, and nanotechnology, among other applications. The aim of the current study is to observe flow characteristics following the addition of Cu nanoparticles including the contribution of variable heat source, Joule heating, and Arrhenius energy activation. The research methodology used to construct the article is as follows: The first section is “Introduction,” which contains some literature review. The governing equations for the proposed study were developed in the “Mathematical Formulation” section. The leading partial differential equations (PDEs) are converted to nonlinear ordinary differential equations (ODEs) by applying the proper similarity variables. These equations are then solved by the MATLAB bvp4c tool. The third section contains results and discussion. This section examines the behavior of numerous physical factors for density motile microorganisms (DMM), velocity, concentration, temperature, density number of microorganisms, tangential and azimuthal skin frictions, mass transport rate, and heat transport rate are studied graphically. Results show that activation energy enhances the thickness of the temperature and concentration boundary layer while it reduces the mass transport rate. Eckert number raises tangential velocity while reducing the normal velocity. The volume fraction parameter raises the thermal boundary layer. Moreover, the rate of heat transport reduces for thermophoresis number and buoyancy ratio parameter. The fourth section is “Comparison and Validation,” which contains a comparison of current work, which is intended to constitute a good agreement. The fifth section, “Conclusion,” contains some major conclusions of this study.

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Data Availability

No new data was generated.

Abbreviations

\({E}_{A}\)  :

Activation energy/J

\({R}_{b}\) :

Bioconvective Rayleigh number

\({S}_{b}\) :

Bioconvective Schmidt number

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

Boltzmann constant

\({D}_{M}\) :

Brownian diffusion coefficient

\({N}_{b}\) :

Brownian motion

\({N}_{r}\) :

Buoyancy ratio parameter

\(x,y,z\) :

Cartesian co-ordinates

\({k}_{0}^{2}\) :

Chemical reaction parameter

\(b\) :

Chemotactic constant

\({{\text{g}}}_{1}\) :

Circumferential velocity/m s−1

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

Heat source/sink parameter’s coefficients/J

\(C\) :

Concentration/mol m−3

\(Da\) :

Darcy parameter

\(Ec\) :

Eckert number

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

Fitted rate constant

\(u,v,w\) :

Fluid velocity along x, y, and z-axes/m s−1

\({Gr}_{L}\) :

Grashof number

\({\text{g}}\) :

Gravitational acceleration/m s−2

\(Ha\) :

Hartmann number

\({q}^{{\prime}{\prime}{\prime}}\) :

Heat source/sink

\(v\) :

Kinematic viscosity/m2 s−1

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

Magnetic field strength/T

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

Magnetic parameter

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

Maximum cell swimming speed

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

Microorganism’s diffusivity

\({D}_{T}\) :

Microorganism’s thermophoretic diffusion coefficient

\(M\) :

Motile microorganism’s density/kg m−3

\(E\) :

Energy activation parameter

\(h\) :

Normal velocity of flow/m s−1

\(Pe\) :

Peclet number

\(K\) :

Permeability of porous regime

\(Pr\) :

Prandtl number

\(R\) :

Radiation parameter

\({q}_{r}\) :

Radiative heat flux

\({Re}_{L}\) :

Reynolds number

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

Specific heat

\(Sr\) :

Soret number

\(Sc\) :

Schmidt number

\(f\) :

Tangential velocity/m s−1

\(T\) :

Temperature/K

\({K}_{T}\) :

Thermal diffusion ratio

\({N}_{t}\) :

Thermophoresis number

\(\Omega\) :

Angular velocity/rad s−1

\(\gamma\) :

Chemical reaction

\(\beta\) :

Thermal expansion coefficient

\(\rho\) :

Density/kg m−3

\(\phi\) :

Dimension-free concentration

\(\xi\) :

Dimension-free density of motile microorganism (DMM)

\(\theta\) :

Dimension-free temperature

\(\mu\) :

Dynamic viscosity/Pa s

\(\sigma\) :

Electric conductivity/S m−1

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

Microorganism’s average volume

\({\rho }_{m}\) :

Microorganism’s density/kg m−3

\(\Lambda\) :

Mixed convection parameter

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

Motile parameter

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

Non-dimensional constant temperature

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

Particle’s density/kg m−3

\(\varepsilon\) :

Porosity parameter

\(\tau\) :

Quotient of heat capacity of nanoparticles and fluid

\(\eta\) :

Similarity variable

\(\kappa\) :

Thermal conductivity/W m−1 K−1

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

Volume fraction

\(bf\) :

Base fluid

\(w\) :

Condition at wall

\(\infty\) :

Free stream condition

\(nf\) :

Nanofluid

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Authors and Affiliations

  1. Department of Mathematics, Gauhati University, Guwahati, 781014, Assam, India

    Utpal Jyoti Das & Indushri Patgiri

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  1. Utpal Jyoti Das
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Contributions

The flow model was designed by both authors, Utpal Jyoti Das and Indushri Patgiri. Indushri Patgiri solved the problem and drew the graphs. The “Results and Discussion” section was written by Utpal Jyoti Das. Finally, both authors, Utpal Jyoti Das and Indushri Patgiri, read and approved the final manuscript.

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Correspondence to Indushri Patgiri.

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Das, U.J., Patgiri, I. Gyrotactic Mixed Bioconvective Flow of Copper–Water Nanofluid Past a Rotating Cone with Non-uniform Heat Source and Activation Energy. BioNanoSci. (2024). https://doi.org/10.1007/s12668-024-01442-9

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