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Computational modeling of unsteady MHD nanofluid over a cylinder using gyrotactic microorganisms

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Abstract

The appearance of gyrotactic microorganisms unsteady MHD nanofluid is explored numerically using a cylinder in this study for the two-dimensional scenario. Boundary layer approaches are used to simulate the basic equations of the flow. The novelty of this study is due to the analysis of gyrotactic microorganisms over a cylinder in terms of unsteady nanofluids. The recommended model can greatly improve the fields of thermal and industrial engineering, which is advantageous. Using appropriate variables, the primary mathematical model has been transformed into dimensionless form. Explicit finite difference method (EFDM) is used to model the current statement. Earlier to that a stability test has been performed to gather information on the restrictions of using appropriate parameters. The effects of flow patterns have been studied from a variety of angles. All the computed results and the consequences are analyzed and illustrated graphically. When the findings are contrasted with those from earlier inquiries into the specific situation, there is a significant degree of agreement. The addition of Brownian motion due to the cross-diffusion effect and the coupling parameter for the interaction of the dissipative heat promotes the nanofluid velocity throughout the region, further reverse influence is shown through the shear stress profiles. An important finding of the present investigation can be identified as, the profiles of the heat transport phenomenon increase significantly for the growing values of several parameters such as Brownian, thermophoresis, Eckert number and the resistivity of the magnetic parameter; however, enhanced Lewis number retards it significantly. Furthermore, the present investigation has great use in the field of medical sciences, chemical engineering, mechanical engineering, plasma research and so on.

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Data of manuscript are stored in a data repository. All data in this work can be obtained by contacting the corresponding author.

Abbreviations

2D:

Two dimension

CHF:

Critical heat flux

EFDM:

Explicit finite difference method

MHD:

Magnetohydrodynamics

GM:

Gyrotactic microorganisms

PDE:

Partial differential equation

\(a\) :

Radius of the cylinder

\(D_{{\text{B}}}\) :

Brownian diffusion coefficient

\(D_{{\text{n}}}\) :

Diffusivity of the microorganism

\(D_{{\text{T}}}\) :

Thermophoresis coefficient

\(E_{{\text{m}}}\) :

Modified Eckert number

\(G_{{\text{m}}}\) :

Modified Grashof number

\(G_{{\text{r}}}\) :

Grashof number

\(l\) :

Characteristic length

\(N_{{\text{b}}}\) :

Brownian motion

\(N_{{\text{t}}}\) :

Thermophoresis parameter

\(n_{w}\) :

Constant motile microorganism

\(P_{{\text{e}}}\) :

Peclet number

\(P_{{\text{r}}}\) :

Prandtl number

\(S_{{\text{cm}}}\) :

Microorganism Lewis number

\(S_{{\text{r}}}\) :

Soret number

\(T\) :

Temperature

\(U_{0}\) :

Uniform velocity

\(\alpha\) :

Thermal diffusivity

\(\gamma\) :

Curvature parameter

\(\sigma\) :

Bioconvection parameter

\(\sigma_{{\text{e}}}\) :

Electrical conductivity

\(\tau\) :

Effective heat capacitance

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Authors and Affiliations

  1. Mathematics Discipline, Science, Engineering and Technology School, Khulna University, Khulna, 9208, Bangladesh

    Md. Abu Sayeed, Avijit Podder & Md. Mahmud Alam

  2. Department of Mathematics, Siksha ‘O’ Anusandhan Deemed to be University, Khandagiri Square, Bhubaneswar, Odisha, 751030, India

    S. R. Mishra

  3. UniSA STEM, University of South Australia, Adelaide, SA, 5000, Australia

    Mohammad Afikuzzaman

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Contributions

The entire team of authors worked together to finish the manuscript, i.e., MAS and MMA have formulated the problem and verified the problem statement. AP has written the first draft, MA and SRM worked through the code, SRM and MMA checked the draft with results and discussion section and, finally, MA checked the overall.

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Correspondence to Mohammad Afikuzzaman.

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Sayeed, M.A., Podder, A., Mishra, S.R. et al. Computational modeling of unsteady MHD nanofluid over a cylinder using gyrotactic microorganisms. J Therm Anal Calorim 148, 11855–11870 (2023). https://doi.org/10.1007/s10973-023-12479-5

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