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Scrutinization of Unsteady Bio-convective Stagnation Slip Flow of Hybrid Nanofluid Past a Riga Wedge in the Presence of Activation Energy and Chemical Reaction

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Abstract

This study examines the rheological effects of a hybrid nanofluid and the swimming behavior of gyrotactic microorganisms in an unsteady flow over an expandable Riga wedge. A stagnation point region, suspended with hybrid nanofluid and microorganisms, is considered, subject to velocity slip at the boundary. The study investigates the bio-convection fluid flow phenomenon and considers the effects of chemical reaction, heat source/sink, mass suction, and activation energy. A precise similarity transformation is used to convert the governing partial differential equations into ordinary differential equations. These are then numerically solved using the shooting technique in MATLAB, specifically with the BVP4C solver. The study scrutinizes the effects of various relevant parameters on the dimensionless profiles of velocity, temperature, concentration, and microorganisms. Furthermore, the surface drag force, heat transfer rate, Sherwood number, and motile microorganism density are calculated. To validate the accuracy of the adopted numerical scheme, a tabular comparison is made between the current results and those from the literature in a limiting case. It is observed that adding Al2O3 nanoparticles decreases the fluid velocity, while adding Cu nanoparticles increases it; however, in both cases, the fluid temperature decreases. Increasing the wedge angle parameter enhances the fluid temperature and motile density. The heat transfer coefficient decreases with increasing nanoparticle concentration and wedge angle parameter, whereas the opposite behavior is observed for the Biot number.

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Data Availability

No datasets were generated or analysed during the current study.

Abbreviations

A :

Unsteadiness parameter

B :

Constant

Bi:

Biot number

C :

Concentration of the fluid (kg/m3)

C 0 :

Initial reference concentration (kg/m3)

C w :

Concentration at the surface (kg/m3)

c p :

Specific heat (J/kg K)

C ∞ :

Concentration far away from the disk (kg/m3)

d :

Width of the electrodes and magnets (m)

D B :

Brownian diffusion coefficient (m2/s)

D M :

Diffusivity of the microorganisms (m2/s)

D T :

Thermophoresis diffusion coefficient (m2/s)

E :

Dimensionless activation energy

\({E}_{a}\) :

The activation energy (kcal/mol)

\({\left(\frac{T}{{T}_{\infty }}\right)}^{n}exp\left(-\frac{{E}_{a}}{{K}_{B}T}\right)\)  :

The modified Arrhenius function

g :

Gravitational constant

h f :

Heat transfer coefficient

J 0 :

External flow rate in the electrodes

k :

Thermal conductivity(W/m K)

K r :

Chemical reaction rate

Lb:

Bio-convection Lewis number

M 0 :

Magnetic properties of the fixed magnet

M h :

Modified Hartmann number

N :

Microorganism density

N 0 :

Initial reference motile density

N w :

Microorganism density at the surface

Nb:

Brownian motion parameter

N r :

Buoyancy ratio factor

Nt:

Thermophoresis parameter

Nux :

Local Nusselt number

n :

Constant

Pe:

Peclet number

Pr:

Prandtl number

Q n :

Nonlinear thermal radiation

q m :

Surface mass flux

\({q}_{{w}_{1}}\) :

Surface heat transfer

\({q}_{{w}_{2}}\) :

Dispersion of motile microbes

R :

Radiation parameter

R b :

Rayleigh number

Rex :

Local Reynolds number

s :

Suction/injection parameter

Sc:

Schmidt number

Shx :

Local Sherwood number

T :

Temperature (K)

T 0 :

Initial reference temperature (K)

T R :

Temperature ratio parameter

T w :

Temperature at the surface (K)

u e :

Free stream velocity (m/s)

u,v :

Velocity components of the fluid along x- and y-axes, respectively (m/s)

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

Velocity of the Riga wedge (m/s)

v w :

Velocity of the fluid through the wall (m/s)

α * :

Angle of the wedge

α h :

Dimensionless constant

β :

Wedge angle parameter

χ :

Dimensionless motile density of the fluid

δ :

Constant dimension \({\left({\text{time}}\right)}^{-1}\)

δ l :

Microorganism concentration difference factor

η :

Similarity variable

λ :

Velocity ratio parameter

μ :

Dynamic viscosity

ν :

Kinematic viscosity (m2/s)

ω :

Mixed convection parameter

Ω c :

Chemical reaction parameter

ϕ :

Dimensionless concentration of the fluid

ψ :

Stream function

ρ :

Density of the fluid (kgm−3)

ρ m :

Density of motile microorganisms (kgm−3)

ρ p :

Density of nanoparticles (kgm−3)

τ ω :

Shear stress

σ* :

The Stefan-Boltzmann constant

θ :

Dimensionless temperature of the fluid

hnf :

Hybrid nanofluid

f :

Base fluid

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Acknowledgements

We thank the reviewers for their valuable comments and suggestions which enabled us to make an improved presentation of the paper.

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Authors and Affiliations

  1. Department of Physics, A.K.P.C.Mahavidyalaya, Bengai, Hooghly, 712611, West Bengal, India

    Rajib Kumar Mandal

  2. Department of Mathematics, A.K.P.C.Mahavidyalaya, Bengai, Hooghly, 712611, West Bengal, India

    Hiranmoy Maiti & Samir Kumar Nandy

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Author R.K.Mandal wrote the main manuscript draft, draw figures and tables. Author H.Maiti gives the numerical solution, its validity, convergence and writes introduction section. Author S.K. Nandy formulates the mathematical problem and gives the final draft of the manuscript and also writes the physical interpretation of the results.

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Correspondence to Samir Kumar Nandy.

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Mandal, R.K., Maiti, H. & Nandy, S.K. Scrutinization of Unsteady Bio-convective Stagnation Slip Flow of Hybrid Nanofluid Past a Riga Wedge in the Presence of Activation Energy and Chemical Reaction. BioNanoSci. (2024). https://doi.org/10.1007/s12668-024-01439-4

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