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Impact of oxytactic microorganisms and variable species diffusivity on blood-gold Reiner–Philippoff nanofluid

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Abstract

Currently, researchers across the world achieved theoretical and experimental works to investigate the significance of nanofluid due to their diverse application in heat transport phenomena. Nanofluids are actually the suspension of nanoparticles in the base liquid. Embedding nanoparticles in the base fluid enhances thermal conductivity and heat transfer rate. The present article shed light on the influence of gold nanoparticles along with oxytactic microorganisms on radiative Reiner–philippoff fluid due to extendable sheet. Suitable transformation convert the partial differential equations (PDEs) are renovated into nonlinear ordinary differential equations (ODEs) and furthermore tackled these equations numerically via bvp4c Matlab builtin scheme. Further the investigations are carried out in the presence of molecular diffusivity, oxytactic microorganisms and nonlinear thermal radiation. The effect of influential parameters on heat transfer, mass transfer, motile density of microorganisms profile are investigated with the assistance of tables and graphs. Embedding the nanoparticles and nonlinear thermal radiation amplifies the heat transfer process and motile density profile depreciates owing to an augmentation in Peclet number. The novel outcomes of this investigation will advance the field of nanomaterials.

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Data Availability Statement

The data supporting the findings of this study are available within the article.

Abbreviations

C :

Concentration of fluid

\(C_{0}\) :

Wall concentration

\(C_{\infty }\) :

Ambient concentration

\(\gamma\) :

Bingham number

\(Sc\) :

Schmidt number

\(Nu _{x}\) :

Nusselt number

\(Pr\) :

Prandtl number

\(\theta _{w}\) :

Temperature ratio parameter

\(\tau\) :

Shear stress

\(\mu _{0}\) :

Shear viscosity

\(\rho _{nf}\) :

Bio-nanofluid density

\(c_{p}\) :

Specific heat at constant pressure

\(\rho _{b}\) :

Density of the blood

\((\rho C_{p})_{b}\) :

Heat capacity of blood

\(k_{b}\) :

Thermal conductivity of blood

\(\sigma ^{*}\) :

Stefan-Boltzmann constant

\(\epsilon\) :

Variable molecular diffusivity parameter

\(D_{B_{\infty }}\) :

Ambient Brownian diffusion coefficient

\(T_{\infty }\) :

Ambient temperature

U(x):

Stretching velocity

\(\lambda\) :

Fluid parameter

\(q_{w}\) :

Surface heat flux

\(Sh _{x}\) :

Sherwood number

Rd :

Radiation parameter

\(q_{r}\) :

Radiative heat flux

\(\tau _{s}\) :

Reference shear stress

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

Limiting viscosity

\(\alpha _{nf}\) :

Bio-nanofluid thermal diffusivity

\(k_{nf}\) :

Bio-nanofluid thermal conductivity

\(\rho _{g}\) :

Densities of the gold

\((\rho C_{p})_{g}\) :

Heat capacity of gold

\(k_{g}\) :

Thermal conductivity of gold

\(\kappa ^{*}\) :

Absorption coefficient

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Authors and Affiliations

  1. Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan

    T. Sajid, S. Tanveer, M. Munsab & Z. Sabir

  2. Department of Mathematics, Government Degree College for Women, Fateh Jang, Attock, Pakistan

    T. Sajid, S. Tanveer, M. Munsab & Z. Sabir

  3. Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan

    T. Sajid, S. Tanveer, M. Munsab & Z. Sabir

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  1. T. Sajid
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Correspondence to T. Sajid.

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Sajid, T., Tanveer, S., Munsab, M. et al. Impact of oxytactic microorganisms and variable species diffusivity on blood-gold Reiner–Philippoff nanofluid. Appl Nanosci 11, 321–333 (2021). https://doi.org/10.1007/s13204-020-01581-x

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