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Temperature-dependent viscosity and thermal conductivity effects on peristaltic flow of Carreau–Yasuda nanofluid in a 2D tapered asymmetric channel: applications of solar collectors

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Abstract

This paper aims to investigate the influences of variable viscosity and thermal conductivity on peristaltic flow of Carreau–Yasuda nanofluid in a 2D tapered asymmetric channel. Viscosity is considered as a function on the temperature of the fluid. Consequently, all dimension parameters that are functions of viscosity such as, thermophoresis and Brownian motion, and Prandtl, local temperature, and local nanoparticle Grashof numbers has also been performed as variable within the flow. For the pertinent problem, the flow equations are first established, and then reformulated under the assumption of low Reynolds number and long wavelength. Numerical results have been obtained for the pressure gradient as well as the velocity, temperature, and nanoparticle concentration distributions. Moreover, numerical integration has also been performed to assess the expressions for the pressure rise. It is worth mentioning that increases in the variable viscosity parameter cause diminishes in temperature. Hence, the use of nanofluids with high viscosity is favorable in application of solar energy to get higher performance (by acting as a cooling system for solar cells) and lower operating costs. Increases in Brownian motion and thermophoresis parameters cause better transport of heat, and highly absorption in the solar range.

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Abbreviations

\(B_{0}\) :

Applied magnetic field (\(\mbox{Kg}\,\mbox{s}^{-2}\,\mbox{A}^{-1}\))

\(Cp\) :

Specific heat at constant pressure (\(\mbox{J}\,\mbox{kg}^{-1}\,\mbox{K}^{-1}\))

\(g\) :

Acceleration due to gravity (\(\mbox{m}\,\mbox{s}^{-1}\))

\(Dm\) :

Molecular diffusivity (\(\mbox{m}^{-2}\,\mbox{s}^{-1}\))

\(u, v\) :

Dimensional fluid velocities in the \(x\)- and \(y\)-direction, respectively (\(\mbox{m}\,\mbox{s}^{-1}\))

\(k_{1}\) :

Permeability of the porous medium

\(p\) :

Pressure of the fluid

\(c_{p}\) :

Specific heat

\(D_{B}\) :

Brownian motion coefficient

\(D_{T}\) :

Thermophoretic diffusion coefficient

\(W_{e}\) :

The Weissenberg number

\(T\) :

Temperature (K)

\(T_{m}\) :

Mean temperature (K)

\(T_{1}, T_{0}\) :

Temperature at walls (K)

\(C\) :

Concentration

\(C_{1}, C_{0}\) :

Concentration at walls

\(S\) :

Extra stress tensor

\(D_{a}\) :

Darcy number

\(E_{c}\) :

Eckert number

\(\gamma\) :

Volume expansion coefficient

\(\sigma\) :

Electrical conductivity of the fluid (\(\mbox{m}^{-3}\, \mbox{kg}^{-1}\,\mbox{s}^{3}\,\mbox{A}^{2}\))

\(\tau\) :

Ratio of effective heat capacity of the nanoparticle material to heat capacity of the fluid

\(\delta\) :

Dimensionless wave number

\(\mu_{0}\) :

Dynamic viscosity

\(\beta\) :

Viscosity variation parameter

\(\lambda_{1}\) :

Ratio of relaxation to retardation times

\(\lambda_{2}\) :

Retardation time

\(\dot{\gamma}\) :

Shear rate; dots over the quantities indicate differentiation with respect to time

\(\psi\) :

Stream function (\(\mbox{m}^{2}\,\mbox{s}^{-1}\))

\(\theta\) :

Dimensionless temperature

\(\varphi\) :

Dimensionless concentration

\(\rho_{f}\) :

Density of the fluid (\(\mbox{kg}\,\mbox{m}^{-1}\))

\(\phi\) :

Phase difference

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  1. Applied Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt

    W. M. Hasona

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Hasona, W.M. Temperature-dependent viscosity and thermal conductivity effects on peristaltic flow of Carreau–Yasuda nanofluid in a 2D tapered asymmetric channel: applications of solar collectors. Mech Time-Depend Mater 25, 133–150 (2021). https://doi.org/10.1007/s11043-019-09430-3

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