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Analysis of MHD Bioconvection Flow of a Hybrid Nanofluid Containing Motile Microorganisms over a Porous Stretching Sheet

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Abstract

This paper presents a numerical investigation of steady two-dimensional bioconvective MHD flow along with the heat and mass transfer phenomena of a water-based hybrid nanofluid containing motile microorganisms over a porous stretching sheet. The study considers effects of various physical parameters, such as thermal radiation, chemical reactions, Joule heating, and heat generation, on the flow and transport characteristics of the system. Copper (Cu) and alumina (Al2O3) nanoparticles are used with water (H2O) as the base fluid. The governing equations are transformed into a set of nonlinear ordinary differential equations using a standard similarity transformation. The reduced equations are solved numerically using the Keller-box method. The impact of different parameters on the velocity, temperature, concentration, and microorganism concentration profile is illustrated graphically, while their influence on the skin-friction coefficient, local Nusselt number, local Sherwood number, and local density number of motile microorganisms is tabulated. This study provides an excellent agreement with previously published works. The results of the study show that the presence of motile microorganisms significantly enhances the heat transfer rate and mixing efficiency of the nanofluid. The analysis demonstrates that the chemical reaction and thermal radiation play crucial roles in controlling the concentration and temperature distributions of the nanofluid, respectively.

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Abbreviations

a, b :

Constant

x, y :

Cartesian coordinates along the surface and normal to it, respectively (m)

u, v :

Velocity component along x-axis and y-axis respectively (m s−1)

T :

Temperature (K)

C :

Nanoparticle concentration (mol l−1)

N :

Concentration of the microorganism

B o :

Magnetic field (T)

k o :

Porous term (m2)

Q o :

Coefficient of heat generation

C p :

Specific heat at constant pressure (J kg−1 K−1)

q r :

Radiative heat flux

D m :

Mass diffusion coefficient

D n :

Microorganisms’ diffusion coefficient

Kr :

First-order chemical reaction coefficient

W c :

Maximum cell swimming speed

k ∗ :

Mean absorption coefficient

M :

Magnetic parameter

Ec :

Eckert number

Q :

Heat generation/absorption

K p :

Permeability parameter

Pr :

Prandtl number

Rd :

Radiation parameter

Sc :

Schmidt number

Sb :

Bioconvection Schmidt number

Pe :

Bioconvection Peclet number

Cf x :

Skin-friction coefficient

Nu x :

Nusselt number

Sh x :

Sherwood number

Nn x :

Density number of motile microorganism

Re x :

Reynold number

ν :

Kinematic viscosity (m2 s−1)

μ :

Dynamic viscosity (kg m−1 s−1)

σ :

Electrically conductivity (S m−1)

ρ :

Density (kg m−3)

κ :

Thermal conductivity of the nanofluid

γ :

Chemical reaction parameter

ϕ 1 :

Volume fraction of Cu nanoparticle

ϕ 2 :

Volume fraction of Al2O3 nanoparticle

Ω:

Microorganism concentration difference parameter

σ ∗ :

Stefan-Boltzmann coefficient

η :

Similarity variable

ψ :

Stream function

f ′ :

Dimensionless velocity

θ :

Dimensional temperature

ϕ :

Dimensionless concentration of nanoparticles

χ :

Dimensionless concentration of microorganism

′ :

Derivative with respect to η

w :

At wall

∞:

At free stream region

hnf :

For hybrid nanofluid

nf :

For nanofluid with single nanoparticle

f :

For base fluid

s 1 :

For Cu nanoparticle

s 2 :

For Al2O3 nanoparticle

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  1. Department of Mathematics, Dibrugarh University, Dibrugarh, 786004, India

    Shiva Rao & P.N. Deka

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The authors confirm contribution to the paper as follows: study conception and figures: 1st author; analysis and interpretation of results: 2nd author; draft manuscript preparation: 1st author. All authors reviewed the results and approved the final version of the manuscript.

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Correspondence to Shiva Rao.

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Rao, S., Deka, P. Analysis of MHD Bioconvection Flow of a Hybrid Nanofluid Containing Motile Microorganisms over a Porous Stretching Sheet. BioNanoSci. 13, 2134–2150 (2023). https://doi.org/10.1007/s12668-023-01180-4

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