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Numerical simulation for non-constant parameters effects on blood flow of Carreau–Yasuda nanofluid flooded in gyrotactic microorganisms: DTM-Pade application

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Abstract

The peristaltic flow of Carreau–Yasuda fluid through a micro-vessel involving oxytactic microorganisms and nanoparticles in a vertical asymmetric channel is examined. In early times, scientific research shows that the cancer cells exposed to low oxygen conditions had the advantage of staying in the bloodstream more and can invade healthy cells as well, whereas the oxytactic microorganisms exhibit negative chemotaxis to gradients of oxygen (oxygen repellents). So, it had to be studied the behavior of oxytactic microorganisms and nanoparticle and their roles in the drug-carriers system. All non-dimensional physical parameters are supposed to be variable as the viscosity of blood variable with fluid temperature and nanoparticle concentration. This system of partial differential equations was formulated and transformed mathematically using new theories of differential transform method combined by Pade' approximation (DTM-Pade′). The solution of the mentioned system is displayed digitally in tables and graphically in sketches. The existing study assured that the microorganism density in the direction near to the hypoxic tumor tissues regions grows with a rising in oxygen concentrations and the blood viscosity diminutions. Results show that the number of pores increases the flow and the particles of fluid moving more freely with increment in distribution of temperature.

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Abbreviations

\(U, V\) :

Velocities in x and y directions in fixed frame

g:

Acceleration due to gravity

P:

Pressure

\({a}_{1}, {b}_{1}\) :

Amplitudes of waves

\({D}_{B}\) :

Brownian diffusion coefficient

\(\lambda \) :

Wave length

\(\tau \) :

Extra stress tensor

\(\Gamma \) :

Time constant parameter

σ*,k* :

Stefan–Boltzmann and the Rosseland mean absorption coefficient

\({\rho }_{f}\) :

Density of nanoparticle

\({\rho }_{m}\) :

Density of microorganism

\(C\) :

Nanoparticle concentration

T:

Temperature

\({\beta }_{T}\) :

Coefficient of thermal expansion

\({D}_{m}\) :

Coefficient of thermophoresis diffusion

\({D}_{s}\) :

Oxytactic microorganisms diffusivity

\(k\) :

Thermal conductivity

\({\omega }_{1}\) :

Rate of oxygen production

\({\omega }_{2}\) :

Rate of oxygen break down

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

Fluid viscosity in constant case

\(\nu \) :

Fluid kinematic viscosity

\({\mathrm{R}}_{\mathrm{e}}\) :

Reynold’s number

\({\mathrm{P}}_{\mathrm{r}}\) :

Prandtl number

\(\mathrm{M}\) :

Hartman number

\({\mathrm{N}}_{\mathrm{b}}\) :

Brownian motion parameter

\({\mathrm{N}}_{\mathrm{t}}\) :

Thermophoresis parameter

\({\mathrm{G}}_{\mathrm{t}}\) :

Temperature graph of number

\({\mathrm{G}}_{\mathrm{c}}\) :

Mass graph of number

\({\mathrm{R}}_{\mathrm{b}}\) :

Bioconvection Rayleigh number

\({\mathrm{R}}_{\mathrm{n}}\) :

Thermal radiation

\({\rho }_{e}\) :

Bioconvection Peclet

\({W}_{e}\) :

Weissenberg number

\({\sigma }_{1}\) :

Bioconvection constant

\(\psi \) :

Stream function

\({\mathrm{E}}_{\mathrm{c}}\) :

Eckert number

\(\Omega \) :

Oxytactic microorganisms density

\(\phi \) :

Phase difference

\(\alpha \) :

Non-constant viscosity parameter (Temperature)

\(\beta \) :

Non-constant viscosity parameter (Concentration)

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  1. Department of Basic and Applied Science, International Academy for Engineering and Media Science, Cairo, 11311, Egypt

    M. G. Ibrahim

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Ibrahim, M.G. Numerical simulation for non-constant parameters effects on blood flow of Carreau–Yasuda nanofluid flooded in gyrotactic microorganisms: DTM-Pade application. Arch Appl Mech 92, 1643–1654 (2022). https://doi.org/10.1007/s00419-022-02158-6

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  • DOI: https://doi.org/10.1007/s00419-022-02158-6

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