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Stefan blowing on chemically reactive nano-fluid flow containing gyrotactic microorganisms with leading edge accretion (or) ablation and thermal radiation

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Abstract

The present study analyzes the forced convective boundary layer flow of viscous incompressible time-established fluid. The base fluid containing water-based nanoparticles and gyrotactic microbes. The flat surface is considered with leading-edge accretion (or) ablation. Characteristics of flow are explored by the impacts of thermal radiation and constructive/destructive chemical reaction. The present flow problem is formed with the partial differential equations, and transformed nonlinear boundary value problems are solved mathematically by the finite difference with the collocation method. There is a good correlation between present work and previous work. Results of selected parameters on velocity, temperature, nanoparticles volume fraction, and microbe density function are discovered. Skin friction, heat transport, mass transfer, and microbes transfer rates are tabular. Efforts of the current work rise in progressive microflow devices to bio-modified nanomaterial dispensation.

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Abbreviations

\(\overrightarrow {{V_{1} }}\) :

Velocity vector \(\left( {{\text{ms}}^{{ - 1}} } \right)\)

\(\overrightarrow {{V_{2} }}\) :

Average swimming velocity vector of microorganisms \(\left( {{\text{m}}^{2} {\text{s}}^{{ - 1}} } \right)\)

\(\left( {u_{1} ,v_{1} } \right)\) :

Velocity components \(\left( {{\text{ms}}^{{ - 1}} } \right)\)

\(\left( {x_{1} ,y_{1} } \right)\) :

Cartesian coordinates \(\left( {\text{m}} \right)\)

\(C_{\infty }\) :

Ambient nanoparticle volume fraction

\({\text{Cf}}_{{x_{1} }}\) :

Skin friction coefficient

\(C_{w}\) :

Wall nanoparticle volume fraction

\(D_{B}\) :

Brownian diffusion coefficient

\(D_{T} ~\) :

Thermophoresis diffusion coefficient

\(D_{n}\) :

Micoorganism diffusion coefficient

\({\text{Nn}}_{{x_{1} }}\) :

Local density number of motile microorganisms

\({\text{Nu}}_{{x_{1} }}\) :

Local Nusselt number

\({\text{Sh}}_{{x_{1} }}\) :

Local Sherwood number

\(T_{\infty }\) :

Ambient temperature \(\left( {\text{K}} \right)\)

\(T_{w}\) :

Wall temperature \(\left( {\text{K}} \right)\)

\(U_{\infty }\) :

Dimensional ambient velocity \(\left( {{\text{ms}}^{{ - 1}} } \right)\)

\(W_{c}\) :

Maximum cell swimming speed \(\left( {{\text{ms}}^{{ - 1}} } \right)\)

\(\bar{b}\) :

Chemotaxis constant \(\left( {\text{m}} \right)\)

\(c_{p}\) :

Specific heat \(\left( {{\text{Jkg}}^{{ - 1}} {\text{K}}^{{ - 1}} } \right)\)

\(\vec{j}\) :

Vector flux of microorganisms \(\left( {{\text{kgm}}^{{ - 2}} {\text{s}}^{{ - 1}} } \right)\)

\(k^{*}\) :

Mean absorption coefficient \(\left( {1{\text{m}}^{{ - 1}} } \right)\)

\(n_{w}\) :

Wall motile microorganisms

\(C\) :

Nanoparticle volume fraction

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

Chemical reaction parameter

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

Bioconvection Lewis number

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

Lewis number

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

Brownian motion parameter

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

Thermophoresis parameter

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

Bioconvection Péclet number

\({\text{Pr}}\) :

Prandtl number

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

Radiation parameter

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

Reynolds number

\(T\) :

Nano-fluid temperature \(\left( {\text{K}} \right)\)

\(f\) :

Dimensionless stream function

\(k\) :

Thermal conductivity \(\left( {{\text{Wm}}^{{ - 1}} {\text{K}}^{{ - 1}} } \right)\)

\(n\) :

Number of motile microorganisms

\(s\) :

Wall mass flux (Stefan blowing)

\(t\) :

Dimensional time \(\left( {\text{s}} \right)\)

\(\sigma ^{*}\) :

Stefan Boltzmann constant \(\left( {{\text{Wm}}^{{ - 2}} {\text{K}}^{{ - 4}} } \right)\)

\(\alpha\) :

Thermal diffusivity \(\left( {{\text{m}}^{2} {\text{s}}^{{ - 1}} } \right)\)

\(\gamma\) :

Leading edge accretion/ablation

\(\theta\) :

Dimensionless temperature

\(\mu\) :

Dynamic viscosity \(\left( {{\text{kg~}}\;{\text{m}}^{{ - 1}} {\text{s}}^{{ - 1}} } \right)\)

\(\rho\) :

Fluid density \(\left( {{\text{kg~}}\;{\text{m}}^{{ - 3}} } \right)\)

\(\chi\) :

Dimensionless number for motile microorganisms

\(\psi\) :

Stream function

\(\phi\) :

Dimensionless nanoparticles volume fraction

\(w\) :

Condition at wall

\(\infty\) :

Condition in free stream

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Authors and Affiliations

  1. Department of Mathematics, Acharya Nagarjuna University Campus, Ongole, Andhra Pradesh, 523001, India

    K. Gangadhar

  2. Department of Mathematics, Lakireddy Balireddy College of Engineering, L.B. Reddy Nagar, Mylavaram, Andhra Pradesh, 521230, India

    K. Bhanu Lakshmi

  3. Department of Mathematics, School of Humanities and Sciences, SASTRA Deemed University, Thanjavur, TN, India

    T. Kannan

  4. Faculty of Engineering, Kuwait College of Science and Engineering, Doha District, Kuwait

    Ali J. Chamkha

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  1. K. Gangadhar
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  2. K. Bhanu Lakshmi
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  3. T. Kannan
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  4. Ali J. Chamkha
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Correspondence to Ali J. Chamkha.

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Gangadhar, K., Lakshmi, K.B., Kannan, T. et al. Stefan blowing on chemically reactive nano-fluid flow containing gyrotactic microorganisms with leading edge accretion (or) ablation and thermal radiation. Indian J Phys 96, 2827–2840 (2022). https://doi.org/10.1007/s12648-021-02179-x

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