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A Keller Box Technique of the Sutterby Nanomaterial Including Gyrotactic Microorganisms Over a Rotating Disk

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Abstract

This work investigates the Sutterby nanofluid due to heated convective boundary features defined across a revolving stretching disk and an applied Darcy-Forchheimer flow. Nanofluids are a mixture of transparent liquids and tiny particles evenly dispersed throughout the base fluid. They have intriguing prospective applications as thermal transfer sources. One of the main purposes of nanofluids is to improve the heat transfer coefficients of base fluids by a considerable amount by the suspension of nanoparticles in the fluids. The Sutterby model, a non-Newtonian fluid, will serve as the foundation for this investigation. Darcy-Forchheimer flow characteristics, heated convective conditions, heat source/sink, chemical reaction, and bioconvection are also taken into account. Appropriate similarity transformations are used to tackle the governing nonlinear differential system. Transformed ordinary differential equations are solved via the Keller box method in the computer program MATLAB. The results of important physical parameters are obtained. Inspirations of important physical parameters are elaborated and briefly studied numerically and visually against the different profiles. The axial, radial, and tangential velocities reduce when the Forchheimer parameter and material parameter increase. Temperature increase in the fluid is a direct consequence of changes in thermal radiation parameters, thermophoresis, and Biot number.

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Data Availability

No datasets were generated or analyzed during the current study.

Abbreviations

\(\Gamma\) :

Porosity parameter

\(Da\) :

Darcy-Forchheimer

\(\alpha\) :

Fluid parameter

\(Bi\) :

Biot number

\(Nb\) :

Brownian motion

\(Nt\) :

Thermohoresis parameter

\(Pr\) :

Prandtl Number

\(Rd\) :

Radiation parameter

\(k\) :

Mean absorption coefficient

\(Sc\) :

Schmidt number

\(F'\) :

Dimensionless radial velocity

\(F\) :

Dimensionless axial velocity

\(G\) :

Dimensionless tangential velocity

\(\vartheta\) :

Dimensionless temperature field

\(\Phi\) :

Dimensionless concentration field

\(\Upsilon\) :

Dimensionless microorganism field

\(\tau\) :

The ratio of effective heat capacity

\(\kappa\) :

Chemical reaction

\(Pe\) :

Peclet number

\(Lb\) :

Bioconvection Lewis number

\(\epsilon\) :

Microorganism concentration difference

\(C_fr,C_gr\) :

Skin friction coefficient

\(Nu_{{}_r}\) :

Nusselt number

\(Sh_r\) :

Sherwood number

\(Nh_r\) :

Motile density

\(r,\phi,z\) :

Cylindrical coordinates

\(u,v,w\) :

Component of velocity

\(\omega\) :

Angular velocity

\(c_p\) :

Specific heat

\(\nu\) :

Kinematic viscosity

\(\alpha^\ast\) :

Thermal diffusivity

\(k_1\) :

Thermal conductivity

\(\rho\) :

Density of Nanofluid

\(D_B\) :

Brownian diffusion coefficient

\(D_T\) :

Thermophoretic diffusion coefficient

\(D_M\) :

Microorganism diffusion coefficient

\(\sigma^\ast\) :

Stefan-Boltzmann constant

\(T\) :

The temperature of the fluid

\(T_w\) :

Wall temperature

\(T_\infty\) :

Ambient temperature

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Funding

This study is supported via funding from Prince sattam bin Abdulaziz University project number (PSAU/2024/R/1445).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Federal Urdu University of Arts, Sciences & Technology, Gulshan-e-Iqbal, Karachi, 75300, Pakistan

    Syed Sohaib Zafar & A. Zaib

  2. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia

    Fuad S. Alduais & Afrah Al-Bossly

  3. Department of Basic Sciences, General Administration of the Preparatory Year, King Faisal University, P.O. Box 400, Al Ahsa, 31982, Saudi Arabia

    Humaira Yasmin

  4. Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al Ahsa, 31982, Saudi Arabia

    Humaira Yasmin

  5. Department of Mathematics, Abdul Wali Khan University, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan

    Anwar Saeed

Authors
  1. Syed Sohaib Zafar
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  2. A. Zaib
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Contributions

Conceptualization, A.S. and H.Y.; methodology, S.S.Z.; software, A.S.; A.A.B.; validation, A.Z., S.S.Z., and F.S.A.; formal analysis, A.A.B.; investigation, S.S.Z. and A.S.; writing—original draft preparation, A.Z. and F.S.A.; writing—review and editing, H.Y. and F.S.A.; visualization, H.Y. and A.A.B.

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Correspondence to Humaira Yasmin or Anwar Saeed.

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Zafar, S.S., Zaib, A., Alduais, F.S. et al. A Keller Box Technique of the Sutterby Nanomaterial Including Gyrotactic Microorganisms Over a Rotating Disk. BioNanoSci. (2024). https://doi.org/10.1007/s12668-024-01404-1

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