Effects of Gyro-Tactic Organisms in Bio-convective Nano-material with Heat Immersion, Stratification, and Viscous Dissip
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RESEARCH ARTICLE-PHYSICS
Effects of Gyro-Tactic Organisms in Bio-convective Nano-material with Heat Immersion, Stratification, and Viscous Dissipation Muhammad Awais1 · Saeed Ehsan Awan2 · Muhammad Asif Zahoor Raja2,3
· Muhammad Shoaib1
Received: 11 June 2020 / Accepted: 23 October 2020 © King Fahd University of Petroleum & Minerals 2020
Abstract Analysis has been conducted to investigate the nonuniform heat immersion phenomenon in bio-convective rheology of nanoparticles combined with gyro-tactic microorganisms. Inclined magnetic field effects are incorporated to predict magnetonano properties. Simultaneous properties of motile microorganisms along with heat and mass transfer effects are investigated. Bio-convective phenomenon (addition of gyro-tactic microorganisms in the system to stabilize the nanoparticles) has been analyzed along with thermal stratification, viscous dissipation, and Joule heating processes. Mathematical modeling has been presented to obtain the solution numerically and analytically. Error analysis and comparison with published data have been presented to show the validity of the obtained results. Bar charts and velocity plots have been prepared for the emerging physical quantities. Numerically computed magnitudes of skin friction, local Sherwood number, motile microorganism density function, and local Nusselt number for various physical quantities have been presented in tabular form. Keywords Heat immersion · Magnetic field · Microorganisms · Nanofluidic
List of symbols T p M Nb Nt λ Nr
B
Fluid temperature Fluid pressure Hartman number Brownian motion Thermophoresis characteristics Mixed convection Buoyancy ratio parameter Muhammad Asif Zahoor Raja [email protected] Muhammad Awais [email protected] Saeed Ehsan Awan [email protected] Muhammad Shoaib [email protected]
1
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan
2
Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, Pakistan
3
Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou 64002, Yunlin, Taiwan, ROC
Rb Pr S Sc Pe Ω B Nux Shx f (η) φ(η) ρf ρm g α α1 DB DT n ns n∞ ρf Ec Lb Dn
Bio-convection Rayleigh number Prandtl number Thermal stratification quantity Schmidt number Bio-convection Peclet number Microorganisms concentration Motile density Local Nusselt number Local Sherwood number Velocity profile Concentration profile Nanofluid density Density of microorganism Gravitational angle Inclination angle Thermal diffusivity Brownian motion Thermophoresis effect Motile density of microorganisms Surface concentration of nanoparticles Ambient concentration of the microorganisms Nanofluid density Eckert number Bio-convection Lewis number Microorganisms diffusion coefficient
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Arabian Journal for Science and Engineering
Cf Nnx θ (η) ξ (η)
Surface friction Local density number Temperature profile Motile density profile
1 Introductio
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