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Dynamic pathways for the bioconvection in thermally activated rotating system

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Abstract

This article communicates Cattaneo-Christov heat and mass flux theory in the flow of Maxwell nanofluid and gyrotactic microorganisms towards a spinning disk with the effects of Hall current, and Darcy porous medium. Entropy generation is also taken into account in the presence of Brownian motion, thermophoresis, thermal radiation, heat source/sink, and chemical reaction. Non-dimensional equations are derived for the velocities, temperature, nanoparticles concentration, and motile gyrotactic microorganisms concentration with the help of similarity transformations. Homotopy analysis method (HAM) is used to obtain the solution. Graphs and a table are plotted to show the effects of physical parameters. Numerical computations are given to analyze the values of skin friction coefficients which present a nice agreement with the published results.

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Data availability

Upon reasonable request to the corresponding author, the data will be provided.

Abbreviations

m :

Hall parameter

(u, v, w):

Velocity components

(r, \(\vartheta\), z):

Cylindrical coordinates

a :

Stretching rate

Sc :

Schmidt number

\({k_{r}}\) :

Dimensional chemical reaction parameter

k\(_{c}\) :

Non-dimensional chemical reaction parameter

M :

Magnetic field parameter

Pr :

Prandtl number

\(E^{\prime \prime \prime }_{gen}\) :

Entropy generation

\(E^{\prime \prime \prime }_{0}\) :

Characteristic entropy generation

\(N_{G}\) :

Non-dimensional entropy generation rate

Le :

Lewis number

Pe :

Peclet number

Nb :

Brownian motion parameter

Nt :

Thermophoresis parameter

R :

Ideal gas constant

Br :

Brinkman number

\({C_{i}}\), i = 1, 2, 3..., 11:

Arbitrary constants

Re :

Reynolds number

T :

Temperature

C :

Nanoparticles concentration

N :

Motile microorganisms concentration

P :

Pressure

\({c_{P}}\) :

Specific heat at constant pressure

\({D_{B}}\) :

Diffusivity

B :

Chemical species

\({f^{\prime }}(\zeta )\) :

Dimensionless radial velocity

\({g}(\zeta )\) :

Dimensionless azimuthal velocity

\({h}(\zeta )\) :

Dimensionless axial velocity

\({B_{0}}\) :

Applied magnetic field strength

\(\varvec{L}\) :

Linear operator

\(\Omega\) :

Angular velocity

\(\sigma\) :

Electrical conductivity

\(\psi\) :

Stream function

\(\zeta\) :

Similarity variable

\(\phi (\zeta )\) :

Dimensionless nanoparticles concentration

\(\theta (\zeta )\) :

Dimensionless temperature

\(\chi (\zeta )\) :

Dimensionless gyrotactic microorganisms concentration

\(\lambda _{1}\) :

Relaxation time parameter

\(\gamma _{1}\) :

Thermal relaxation time parameter

\(\gamma _{2}\) :

Mass relaxation time parameter

\(\gamma _{3}\) :

Non-dimensional thermal relaxation time parameter

\(\gamma _{4}\) :

Non-dimensional solutal time relaxation parameter

\(\gamma _{5}\) :

Gyrotactic microorganisms concentration difference parameter

\(\gamma _{6}\) :

Temperature difference parameter

\(\gamma _{7}\) :

Diffusion constant parameter

\(\nu\) :

Kinematic viscosity

\(\mu\) :

Dynamic viscosity

\(\rho\) :

Density

\(\alpha\) :

Thermal diffusivity

\(\Omega _{1}\) :

Dimensionless stretching parameter

f:

Base fluid

\({\prime }\) :

Differentiation with respect to \(\zeta\)

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Acknowledgements

The authors are thankful to the respectable reviewers for their comments and suggestions. The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this research was supported by The Science, Research and Innovation Promotion Funding (TSRI) (Grant no. FRB650070/0168). This research block grants was managed under Rajamangala University of Technology Thanyaburi (FRB65E0633M.2). The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia for funding this work through research groups program under grant number RGP.1/248/43. The first author is thankful to the Higher Education Commission (HEC) Pakistan for funding through the SRGP project No. 10534.

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Authors and Affiliations

  1. KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, 10140, Thailand

    Poom Kumam

  2. Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Poom Kumam

  3. Department of Mathematics, Division of Science and Technology, University of Education, Lahore, 54000, Pakistan

    Noor Saeed Khan

  4. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Usa Wannasingha Humphries

  5. Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani, 12110, Thailand

    Wiyada Kumam

  6. Department of Mathematics, College of Sciences, King Khalid University, Abha, 61413, Saudi Arabia

    Taseer Muhammad

Authors
  1. Noor Saeed Khan
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  2. Usa Wannasingha Humphries
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  3. Wiyada Kumam
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  4. Poom Kumam
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Contributions

All authors contributed to the study conception and design. Conceptualization: Noor Saeed Khan, methodology: Poom Kumam, formal analysis: Usa Wannasingha Humphries, investigation: Wiyada Kumam, resources: Noor Saeed Khan, supervision: Taseer Muhammad, writing—original draft: Taseer Muhammad, writing—review and editing: Noor Saeed Khan.

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Correspondence to Noor Saeed Khan, Usa Wannasingha Humphries or Poom Kumam.

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Khan, N.S., Humphries, U.W., Kumam, W. et al. Dynamic pathways for the bioconvection in thermally activated rotating system. Biomass Conv. Bioref. 14, 8605–8623 (2024). https://doi.org/10.1007/s13399-022-02961-9

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  • DOI: https://doi.org/10.1007/s13399-022-02961-9

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