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Bioconvection of MHD Second-Grade Fluid Conveying Nanoparticles over an Exponentially Stretching Sheet: A Biofuel Applications

  • Research Article-Mechanical Engineering
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Abstract

The current research examines the role of chemical reaction, nonlinear thermal radiation and slippage impact on magnetic second-grade fluid flow with diluted dispersion of nanoparticles using a theoretical bioconvection model over an exponentially stretched sheet. There are also new characteristics such as Brownian motion and thermophoresis. In the problem formulation, the boundary layer approximation is used. Using the suitable transformations, the energy, momentum, micro-organisms and concentration equations are generated into nonlinear ordinary differential equations (ODEs). The solution to the resultant problems was calculated via the Homotopy analysis method (HAM). Environmental parameters' effects on velocity, temperature, microbes and concentration profiles are graphically displayed. When comparing the current results to the previous literature, there was also a satisfactory level of agreement. In comparison with a flow based on constant characteristics, the flow with variable thermal conductivity is shown to be significantly different and realistic. The temperature and motile density of the fluid grew in direct proportion to the thermophoresis motion, buoyancy ratio and Brownian motion parameters. Also, the motile density profile decreases down for Pe and Lb while increasing when bioconvection Rayleigh number and buoyancy ratio. This work is significant to bioinspired nanofluid enhanced fuel cells and nanomaterials production techniques, according to these research studies.

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Abbreviations

\(v\) and \(u\) :

Velocity components (m/s)

T :

Fluid temperature (K)

Tw :

Surface temperature (K)

T∞:

Ambient temperature (K)

\(\chi \left( \eta \right)\) :

The dimensionless density of micro-organisms

C :

Fluid concentration (kg/m3)

Cw :

Surface volume fraction (kg/m3)

C∞:

Ambient nanoparticle volume fraction (kg/m3)

\(\mu_{f}\) :

Dynamic viscosity (kgm2/s)

\(\delta_{f}\) :

The electrical conductivity (s/m)

b :

Chemotaxis constant

Nt :

Thermophoresis diffusion

Nb :

Brownian motion

g :

Gravity (m/s2)

\(\beta\) :

Unsteadiness parameter

\(M\) :

Magnetic parameter

\(\Pr\) :

Prandtl number

\(\alpha\) :

Second-grade fluid parameter

\(Gb\) :

Bioconvection Rayleigh number

\(Gr\) :

Buoyancy ratio parameter

\(Cf_{x}\) :

Local coefficient of skin friction

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

The local Sherwood number

(ρc)p:

Effective heat capacity of a nanoparticle

τw :

Surface shear stress

ν :

Kinematic viscosity (m2/s)

\(\phi \left( \eta \right)\) :

Dimensionless concentration

\(\left( {Cp} \right)_{f}\) :

The heat capacity (J/K)

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

Brownian movement coefficient

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

Stefan–Boltzmann constant (Wm−2 K−4)

\(B_{o}\) :

Magnetic field strength

Kr :

Reaction rate

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

Thermophoresis diffusion coefficient

We :

Swimming cell speed

N :

The micro-organisms

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

Micro-organism coefficients

\(\rho_{f}\) :

Density (kg/m3)

\(\eta\) :

Similarity variable

\(\omega\) :

Stream function

\(v_{w} \left( {x,\,t} \right)\) :

Mass flux velocity (m/s)

\(\lambda\) :

Mixed convection parameter

\({\text{Sc}}\) :

Schmidt number

\(\gamma\) :

Slip parameter

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

Peclet number

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

Bioconvection Schmidt number

\(\delta_{1}\) :

Micro-organism difference parameter

\(Lb\) :

Bioconvection Lewis number

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

Local Nusselt number

\(Nn_{x}\) :

Motile micro-organisms

\(\theta \left( \eta \right)\) :

Dimensionless temperature

Le:

Lewis number

\(f^{\prime}\left( \eta \right)\) :

Dimensionless velocity

\(\tau\) :

Heat capacitance ratio

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Acknowledgements

The authors extend their appreciation to Deanship of Scientific Research at King Khalid University, Saudi Arabia, for funding this work through General Research Project under Grant Number GRP/327/43.

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Authors and Affiliations

  1. Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan

    Imran Siddique & Muhammad Nadeem

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

    Rifaqat Ali

  3. Department of Mathematics, Cankaya University, Etimesgut, Ankara, Turkey

    Fahd Jarad

  4. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Fahd Jarad

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Siddique, I., Nadeem, M., Ali, R. et al. Bioconvection of MHD Second-Grade Fluid Conveying Nanoparticles over an Exponentially Stretching Sheet: A Biofuel Applications. Arab J Sci Eng 48, 3367–3380 (2023). https://doi.org/10.1007/s13369-022-07129-1

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