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Analysis of generalized micropolar nanofluid with swimming of microorganisms over an accelerated surface with activation energy

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Abstract

A fundamental interest has been developed in the twenty-first century toward the significance of nanoparticles due to decisive applications in various thermophysical systems and improved sustainability. Keeping such developments in mind, the present contribution aims to investigate the bioconvection of nanoparticles in flow of generalized micropolar fluid toward an accelerated stretched surface. The activation energy consequences are also encountered in the concentration equations to enhance the mass diffusion phenomenon. Unlike previous investigations, rheological aspects on non-Newtonian materials are signified by involving viscoelastic micropolar which captures the second-grade fluid, micropolar fluid and viscous case simultaneously. The governing equations are rendered in non-dimensional forms by reducing number of independent variables which are further solved analytically by using homotopy analysis technique. The graphical inspection of involved flow parameters is carried out for velocity, temperature, concentration and motile microorganism’s density distributions. It is observed that micro-rotation velocity decreases by increasing buoyancy ratio constraint. Further, motile organism profile declines with an increment in temperature difference parameter and Peclet number.

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Abbreviations

\(k_{1}\) :

Fluid parameter

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

Fluid density

\(\sigma_{\text{e}}\) :

Electric conductivity

\(g^{ * }\) :

Gravity

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

Thermal diffusivity

\(T\) :

Temperature

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

Diffusion constant

\(E_{\text{a}}\) :

Activation energy

\(b_{1}\) :

Chemotaxis constant

\(k\) :

Viscoelastic parameter

\(\varGamma\) :

Vortex viscosity constant

Nr:

Buoyancy ratio constraint

\(\Pr\) :

Prandtl number

Nb:

Brownian motion parameter

Pe:

Peclet number

\(q_{\text{s}}\) :

Surface heat flux

\(g_{\text{s}}\) :

Motile microorganisms’ flux

\({\text{Sh}}_{\text{x}}\) :

Local Sherwood number

\(\alpha_{1}\) :

Viscoelastic parameter

\(B_{0}\) :

Magnetic field strength

\(k^{ * }\) :

Permeability of porous medium

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

Motile microorganism particles density

C :

Concentration

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

Nanoparticles’ density

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

Reaction rate

\(\kappa\) :

Boltzmann constant

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

Swimming cells’ speed

Ha:

Magneto-porosity parameter

Gr:

Mixed convection parameter

Nt:

Thermophoresis parameter

Rb:

Bioconvected Rayleigh number

Lb:

Bioconvected Lewis number

\(\sigma\) :

Microorganisms concentration difference parameter

\(j_{\text{s}}\) :

Surface mass flux

\({\text{Nu}}_{\text{x}}\) :

Local Nusselt number

\({\text{Nn}}_{\text{x}}\) :

Local motile organisms’ density number

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Authors and Affiliations

  1. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Zahra Abdelmalek

  2. Faculty of Medicine, Duy Tan University, Da Nang, 550000, Vietnam

    Zahra Abdelmalek

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

    Sami Ullah Khan

  4. Department of Biosciences, COMSATS University Islamabad, Sahiwal, 57000, Pakistan

    Muhammad Awais

  5. Department of Mechanical Engineering, COMSATS University Islamabad, Sahiwal, 57000, Pakistan

    Muhammad Salman Mustfa

  6. Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Iskander Tlili

  7. Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Iskander Tlili

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  1. Zahra Abdelmalek
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  2. Sami Ullah Khan
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  3. Muhammad Awais
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  5. Iskander Tlili
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Correspondence to Iskander Tlili.

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Abdelmalek, Z., Khan, S.U., Awais, M. et al. Analysis of generalized micropolar nanofluid with swimming of microorganisms over an accelerated surface with activation energy. J Therm Anal Calorim 144, 1051–1063 (2021). https://doi.org/10.1007/s10973-020-09474-5

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