Heat and mass transmission of an Oldroyd-B nanofluid flow through a stratified medium with swimming of motile gyrotactic
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Heat and mass transmission of an Oldroyd‑B nanofluid flow through a stratified medium with swimming of motile gyrotactic microorganisms and nanoparticles E. Elanchezhian1 · R. Nirmalkumar2 · M. Balamurugan3 · K. Mohana4 · K. M. Prabu1 · Amelec Viloria5 Received: 31 January 2020 / Accepted: 14 May 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract This paper focuses on the research of motile microorganism rates in the bioconvective Oldroyd-B nanoliquid flow over a vertical stretching sheet with mixed convection and inclined magnetic field. Additionally, interesting characteristics of thermophoresis, Brownian motion, viscous dissipation, Joule heating, and stratification are examined. Similarity transformations are employed to reduce the mathematical model to higher-order ODE. The convergent serious solution is applied to solve the nonlinear differential system. The analysis of temperature, velocity, motile microorganisms’ density, and nanoparticle concentration are represented through graphs. Local Nusselt number, density number of motile microorganisms, and Sherwood number are examined via contour plots. Keywords Bioconvection · Gyrotactic microorganisms · Oldroyd-B nanofluid · Stratification · Inclined magnetic field ( ) ̂ ∞ Ambient concentration kg m−3 C List of symbols ( −1 ) ( ) ̂ w Surface concentration of nanoparticles kg m−3 C a Stretching rate s ( ) A1 Relaxation time (−) DB Brownian diffusion coefficient m2 s−1 ( 2 −1 ) A2 Retardation time (−) DT Thermophoretic diffusion coefficient (m s ) b Chemotaxis constant (m) Dm Microorganism’s diffusion coefficient m2 s−1 ⎧b ,b EC Eckert number (−) ⎪ 1 2 F(𝜂) Velocity similarity function (−) ⎨ d1 , d2 Dimensionless constants (−) Temperature similarity( function (−) ) G(𝜂) ⎪ e1 , e2 ⎩ k Thermal conductivity m kg s−3 K−1 ( ) −1 −2 kg s A B0 Constant magnetic field Le Lewis number (−) ( ) ̂ Concentration kg m−3 C Lb Bioconvection Lewis number (−) ̂ 0 Reference concentration of nanoparticles C M Magnetic parameter (−) ( ) kg m−3 Nb Brownian motion parameter (−) ( ) Cp Specific heat J kg−1 K−1 Nt Thermophoresis parameter (−) ̂ nw (Surface )concentration of microorganisms kg m−3 * K. Mohana ̂ n∞ (Ambient) concentration of microorganisms [email protected] kg m−3 1 Department of Physics, Sri Vidya Mandir Arts & Science ̂ n0 (Reference ) concentration of microorganisms College, Uthangarai, Tamil Nadu 636902, India kg m−3 2 Department of Mathematics, Sri Ramakrishna Mission Nr Buoyancy ratio parameter (−) Vidyalaya College of Arts and Science, Coimbatore, Nu x Nusselt number (−) Tamil Nadu 641020, India Pr Prandtl number (−) 3 Department Mathematics, Sri Vidya Mandir Arts & Science Bioconvection Peclet number (−) P e College, Uthangarai, Tamil Nadu 636902, India Bioconvection Rayleigh number (−) R b 4 Department Mathematics, Sasurie College of Engineering, Thermal stratification parameter (−) S 1 Tirupur, Tamil Nadu 638056, India S2 Mass stratification parameter (−) 5
Universidad de la Costa, Barranquilla, Colombia
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