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Numerical investigation on bioconvection flow of Oldroyd-B nanofluid with nonlinear thermal radiation and motile microorganisms over rotating disk

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Abstract

In this paper, the mechanism of radiative Oldroyd-B nanofluid flow over a rotating disk with activation energy and motile microorganisms is examined. The perspective of fluid flow due to disk rotation encompasses both theoretical and practical relevance of it in engineering and applied sciences. Nonlinear ordinary differential equations are firstly converted from the corresponding partial differential equations and are formerly renovated using appropriate transformation to achieve set of nondimensional equations that were subsequently solved by shooting technique. The solution for regulating flow equations is carried out with the execution of the prominent numerical method bvp4c built-in function of MATLAB software. The observed response is supported by a comparison with existing resources, and a comprehensive graphical representation has been taken into account for parameters such as Deborah number, buoyancy ratio parameter, thermophoresis, Brownian motion, Biot number, and for motile microorganisms. Graphs and tables demonstrate the pertinent flow characteristics of the governing problem.

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Abbreviations

u, v, w :

Velocity components

γ, φ, z :

Cylindrical coordinates

\(Nur\) :

Local Nusselt number

\(\tilde{C}_{\infty }\) :

Ambient concentration

\(\tilde{N}_{\infty }\) :

Ambient motile microorganisms

\(\left( {\rho c} \right)_{\text{f}}\) :

Heat capacity of fluid

\({\text{Sn}}_{\text{r}}\) :

Local microorganism number

\(\tilde{N}\) :

Motile microorganisms

\(\tilde{C}\) :

Nanoparticles concentration

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

Brownian diffusion coefficient

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

Activation energy coefficient

\(L\) :

Velocity ratio parameter

\({\text{Rd}}\) :

Radiation parameter

\({\text{Nt}}\) :

Thermophoresis parameter

\(\theta_{\text{f}}\) :

Temperature ratio parameter

\({\text{Nr}}\) :

Buoyancy ratio constant

\(E\) :

Activation energy parameter

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

Coefficient of thermal diffusion

\(w_{\text{c}}\) :

Cell swimming speed

\(S_{1}\) :

Thermal stratification Biot number

\(S_{3}\) :

Microorganism stratification Biot number

\(\tilde{T}_{\text{w}}\) :

Wall temperature

\(F\left( \zeta \right)\) :

Radial velocity

\(H\left( \zeta \right)\) :

Axial velocity

\(\text{Re}_{\text{x}}\) :

Reynolds number

\(Q\) :

Heat source/sink coefficient

\({\text{Sh}}_{\text{r}}\) :

Local Sherwood number

\(\tilde{T}_{\infty }\) :

Ambient temperature

\(B_{0}\) :

Magnetic field strength

\(\left( {\rho c} \right)_{\text{p}}\) :

Heat capacity of nanoparticles

\({\text{Lb}}\) :

Bioconvection Lewis number

\(\tilde{T}\) :

Temperature

\(b\) :

Chemotaxis constant

\({\text{Kr}}\) :

Chemical reaction constant

\(M\) :

Magnetic parameter

\(S\) :

Velocity ratio constant

\(\Pr\) :

Prandtl number

\({\text{Nb}}\) :

Brownian motion parameter

\({\text{Le}}\) :

Lewis number

\({\text{Nc}}\) :

Bioconvection Rayleigh number

\({\text{Pe}}\) :

Peclet number

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

Microorganisms diffusion coefficient

\(w_{\text{s}}\) :

Suction/injection constant

\(S_{2}\) :

Solutal stratification Biot number

\(\tilde{C}_{\text{w}}\) :

Wall concentration

\(\tilde{N}_{\text{w}}\) :

Wall microorganisms

\(G\left( \zeta \right)\) :

Azimuthal velocity

\(\nu\) :

Kinematic viscosity

\(\varOmega\) :

Angular velocity

\(\sigma^{ * }\) :

Electrical conductivity

\(\tau\) :

Thermal diffusion coefficient

\(\beta_{1}\) :

Relaxation to time

\(\beta^{*}\) :

Volume fraction constant

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

Microorganisms density

\(k^{*}\) :

Roseland mean spectral coefficient

\(\omega_{1}\) :

Relaxation to time parameter

\(\delta_{0}\) :

Heat generation/absorption parameter

\(\delta_{1}\) :

Thermal stratified parameter

\(\delta_{3}\) :

Microorganism stratified parameter

\(\lambda\) :

Rotation parameter

\(\theta\) :

Temperature distribution

\(\varpi\) :

Motile microorganism differences parameter

\(w_{0}\) :

Mass flux velocity

\(g^{*}\) :

Gravity

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

Stefan–Boltzmann

\(\beta_{2}\) :

Retardation to time

\(\rho_{\text{f}}\) :

Nanofluid density

\(\rho_{\text{p}}\) :

Nanoparticles density

\(\sigma\) :

Chemical reaction parameter

\(\omega_{2}\) :

Retardation to time parameter

\(\delta\) :

Mixed convection parameter

\(\delta_{2}\) :

Solutal stratified parameter

\(\omega\) :

Temperature difference parameter

\(\gamma\) :

Stretching/shrinking parameter

\(\phi\) :

Volumetric concentration

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Acknowledgements

Authors S. M. Sait and R. Ellahi acknowledge King Fahd University of Petroleum & Minerals (Grand No. ORCP), Dhahran, Saudi Arabia, for support.

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Authors and Affiliations

  1. Department of Mathematics, Government College University, Faisalabad, 38000, Pakistan

    H. Waqas & M. Imran

  2. Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia

    Taseer Muhammad

  3. Center for Communications and IT Research, Research Institute, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Sadiq M. Sait

  4. Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan

    R. Ellahi

  5. Center for Modeling and Computer Simulation, Research Institute, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    R. Ellahi

  6. Department of Mechanical Engineering, University of California Riverside, Riverside, USA

    R. Ellahi

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Waqas, H., Imran, M., Muhammad, T. et al. Numerical investigation on bioconvection flow of Oldroyd-B nanofluid with nonlinear thermal radiation and motile microorganisms over rotating disk. J Therm Anal Calorim 145, 523–539 (2021). https://doi.org/10.1007/s10973-020-09728-2

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