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Significance of bioconvection in chemical reactive flow of magnetized Carreau–Yasuda nanofluid with thermal radiation and second-order slip

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Abstract

Several non-Newtonian fluids are of practical interest, and it is fascinating to examine the rheology of such fluids with various flow features. In this study, the flow of Carreau–Yasuda nanofluid has been analyzed in the presence of gyrotactic microorganisms. The impressive features of nanofluid are displayed by abiding the thermophoresis and Brownian motion aspects. The second-order velocity slip effects are decomposed in the mathematical simulations. Further, the governing flow problem governed the impact of thermal radiation, chemical reaction and convective Nield boundary conditions. Although some attempts are available in the literature which examines the rheological features of Carreau–Yasuda nanofluid, whereas the analysis for bioconvection of flow of this non-Newtonian fluid model in the presence of second-order slip features is not proposed yet. Further, it has been noticed that many investigators used first-order or partial slip effects associated with their flow problems. The flow problem becomes more realistic due to the interaction of second-order slip constrains and subsequently develops a more stable boundary layer. The governing equations for the formulated flow problem are partial differential equations. Standard dimensionless quantities are recommended to alter the flow equations in dimensionless forms. The solution of the locally similar problem has been computed numerically via shooting technique. All the computations are performed by using bvp4c with the help of MATLAB software. Following the iterative procedure, the solution is accurate up to convincing accuracy of \( 10^{ - 4} . \) The step size for the present simulation is taken as \( \Delta \eta = 1 \times 10^{ - 4} . \) The results are also verified by comparing with already reported numerical computation and found a convincible accuracy. The implication of each parameter is executed for velocity, temperature, concentration and microorganisms’ distributions. Moreover, the substantial quantities, namely skin friction coefficient, motile density number, local Nusselt number, and local Sherwood number numerically evaluated and are overviewed for various parameters. The study reveals that velocity distribution decays with the presence of first-order slip parameter and Rayleigh number, while an enhanced velocity profile has been noted for variation of Weissenberg number. An improved nanoparticle temperature and concentration distributions have been found with the utilization of the second-order slip factor and combine parameter. It is further observed that the density of motile microorganisms declined with Peclet number and bioconvection Lewis number. In recent days, a growing interest has been developed from scientists toward the significance of nanoparticles because of their diverse engineering, industrial and commercial applications. The proposed observations can be useful in extrusion systems applications, biomolecules, biomimetic systems, energy production improvement and enhancement of manufacturing processes.

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Abbreviations

\( \left( {u,v} \right) \) :

Velocity component

\( \tilde{\mu }_{\infty } \) :

Infinity shear rate viscosity

\( K^{ * } \) :

Permeability of porous medium

\( g^{ * } \) :

Gravity

\( \left( {\rho {\text{c}}} \right)_{\text{p}} \) :

Nanoparticles effective heat capacity

\( T_{\infty } \) :

Atmospheric temperature

\( N \) :

Microorganism density

\( T \) :

Nanoparticles temperature

\( B \) :

Magnetic field strength

\( \rho_{\text{m}} \) :

Motile microorganism particles density

\( \rho_{\text{f}} \) :

Nanoparticles density

\( \alpha \) :

Momentum coefficient

\( \alpha_{1} \) :

Thermal diffusivity

\( D_{\text{T}} \) :

Thermophoretic diffusion coefficient

\( K_{\text{n}} \) :

Knudsen number

\( b_{1} \) :

Chemotaxis constant

\( {\text{Bi}} \) :

Thermal Biot number

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

Chemical reaction parameter

\( \Gamma \) :

Mixed convection parameter

\( {\text{Nr}} \) :

Buoyancy ratio constant

\( {\text{Rn}} \) :

Thermal radiation parameter

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

Lewis number

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

Peclet constant

\( \delta_{1} \) :

Bioconvection constant

\( \delta \) :

Second-order slip constant

\( \left( {n,d,\Gamma } \right) \) :

Carreau–Yasuda constants

\( \tilde{\mu }_{0} \) :

Zero shear rate viscosity

\( \beta^{ * } \) :

Volume fraction coefficient

\( \left( {\rho {\text{c}}} \right)_{\text{f}} \) :

Liquid heat capacity

\( C \) :

Concentration profile

\( C_{\infty } \) :

Atmospheric concentration

\( {\text{We}} \) :

Weissenberg number

\( \sigma \) :

Electrical conductivity

\( C \) :

Volume concentration of magnetic particles

\( T \) :

Nanoparticles temperature

\( \rho_{\text{p}} \) :

Liquid density

\( D_{\text{B}} \) :

Brownian motion constant

\( W_{\text{c}} \) :

Speed of gyrotactic cell

\( \Lambda \) :

Mixed convection parameter

\( \beta \) :

Molecular mean path

\( K \) :

Combine parameter

\( {\text{Nc}} \) :

Rayleigh number

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

Brownian motion

\( \Pr \) :

Prandtl number

\( K \) :

Combine parameter

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

Bioconvection Lewis number

\( \gamma \) :

First-order slip constant

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

Thermophoresis parameter

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Authors and Affiliations

  1. Department of Mathematics, Government College University, Faisalabad, Pakistan

    H. Waqas & M. Imran

  2. Department of Mathematics, COMSATS University Islamabad, Sahiwal, 57000, Pakistan

    Sami Ullah Khan

  3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, China

    M. M. Bhatti

  4. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, China

    M. M. Bhatti

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  1. H. Waqas
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  2. Sami Ullah Khan
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  4. M. Imran
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Correspondence to M. M. Bhatti.

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Waqas, H., Khan, S.U., Bhatti, M.M. et al. Significance of bioconvection in chemical reactive flow of magnetized Carreau–Yasuda nanofluid with thermal radiation and second-order slip. J Therm Anal Calorim 140, 1293–1306 (2020). https://doi.org/10.1007/s10973-020-09462-9

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