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Investigation of hydromagnetic bioconvection flow of Oldroyd-B nanofluid past a porous stretching surface

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Abstract

This article focuses on the examination of various features of microorganism flow of Oldroyd-B nanofluid considering the effects of the magnetic field, porous medium, Joule heating, Brownian motion, mixed convection, thermal radiation, and thermophoresis. With the help of similarity transformations, the governing mathematical equations of the problem are reduced to the nonlinear ordinary differential equations. These equations are solved with the help of a MATLAB function named as bvp4c method. The most important outcomes of the study reveal that the rate of heat transport is boosting with the boosting values of Eckert and Prandtl number although the boosting values of thermophoresis and Brownian motion parameter cause to decline the Nusselt number. The Sherwood number is an increasing function of both thermophoresis and Schmidt number although it is declining with the boosting values of the solutal stratified parameters. Likewise, the transfer rate of microorganism is decreasing and increasing, respectively, with the boosting values of Peclet number, microorganisms’ concentration difference parameter, and bio-convection Schmidt number.

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Abbreviations

\({k}^{*}\)  :

Mean absorption constant

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

Stefan-Boltzmann constant

\({U}_{w}\) :

Stretching velocity

\(u, v\) :

Components of velocity

\(a\) :

Rate of stretching

\({k}_{1}^{*}\) :

Permeability of porous medium

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

Density of nanofluids

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

Magnetic field intensity

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

Relaxation time

\(\nu\) :

Kinematic viscosity

\({\lambda }_{2}\) :

Retardation time

\(k\) :

Thermal conductivity

\(\tau\) :

Heat capacity ratio

\(\sigma\) :

Electrical conductivity

\({b}_{1},{b}_{2}, {e}_{1},{e}_{2}, {d}_{1},{d}_{2}\) :

Dimensional constant

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

Reference temperature

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

Reference concentration of nanoparticles

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

Reference concentration of microorganisms

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

Ambient temperature

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

Ambient concentration of nanoparticles

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

Ambient concentration of microorganisms

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

Surface temperature

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

Surface concentration of nanoparticles

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

Surface concentration of microorganisms

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

Thermal stratified parameters

\({S}_{2}\) :

Solutal stratified parameters

\({S}_{3}\) :

Motile density stratified parameters

\({\beta }_{1}, {\beta }_{2}\) :

Deborah numbers

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

Thermophoresis parameter

\(\epsilon\) :

Porosity parameter

\(Pr\) :

Prandtl number

\(Sc\) :

Schmidt number

\(Rd\) :

Radiation parameter

\(M\) :

Hartmann number

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

Brownian motion parameter

\(Sb\) :

Bio-convection Schmidt number

\(S\) :

Suction parameter

\(Pe\) :

Peclet number

\(Ec\) :

Eckert number

\(\lambda\) :

Mixed convection parameter

\(N\) :

Buoyancy ratio parameter

\(\Omega\) :

Microorganism concentration difference parameter

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

Bioconvection Rayleigh number

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Funding

This study is supported by the Deanship of Scientific Research at Umm Al-Qura University by Grant Code: 22UQU4310392DSR07 and the Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R163), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Mechanical Engineering Department, College of Engineering, Umm Al-Qura University, Makkah, Kingdom of Saudi Arabia

    Khalid Abdulkhaliq M. Alharbi

  2. Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad, 44000, Pakistan

    M. Riaz Khan

  3. T-M2A Laboratory, Mathematics Department, College of Science, Jouf University, P.O. Box: 2014, Sakaka, Saudi Arabia

    Maawiya Ould Sidi

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

    A. M. Algelany

  5. Department of Mathematics, Faculty of Sciences, Fayoum University, Fayoum, 63514, Egypt

    A. M. Algelany

  6. Department of Industrial & Systems Engineering, College of Engineering, Princess Nourah bint Abdulrahman University, P.O.Box 84428, Riyadh, 11671, Saudi Arabia

    Samia Elattar

  7. Department of Mathematics, Faculty of Science, University of Tabuk, P. O. Box741, Tabuk, 71491, Saudi Arabia

    N. Ameer Ahammad

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  1. Khalid Abdulkhaliq M. Alharbi
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Contributions

M. Riaz Khan generated the research idea, stated the problem, and wrote the codes to perform the numerical calculations and plot the graphical results. Model modification, result verification, and validation were performed by Khalid Abdulkhaliq M Alharbi and Maawiya Ould Sidi. The first draft of the manuscript was written by M. Riaz Khan, whereas the revised draft was written by A.M. Algelany and Samia Elattar. N. Ameer Ahammad commented on the manuscript and reviewed the revised version. All authors contributed to the final version of the manuscript.

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Correspondence to M. Riaz Khan.

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Alharbi, K., Khan, M.R., Ould Sidi, M. et al. Investigation of hydromagnetic bioconvection flow of Oldroyd-B nanofluid past a porous stretching surface. Biomass Conv. Bioref. 13, 4331–4342 (2023). https://doi.org/10.1007/s13399-022-02785-7

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