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Entropy generation analysis in peristaltic motion of Sisko material with variable viscosity and thermal conductivity

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Abstract

Here, peristaltic flow of Sisko material is modeled with variable characteristics of thermal conductivity and viscosity via curved configuration. Both are taken as space and temperature dependent. Conservation laws for mass, momentum and temperature are first modeled and then simplified by taking small wavelength and large Reynolds number assumptions. Entropy is also under consideration here to study the irregularities in heat transfer process. Here, series solution is developed for stream function, velocity and pressure gradient. Further, heat equation is solved numerically. These solutions are utilized to plot the behaviors of quantities of interest against the pertinent parameters. Graphical results determine that the velocity rises by larger viscosity parameter while temperature reduces. For larger thermal conductivity parameter, the temperature decays, whereas it increases for Sisko fluid parameter. Irregularity in heat transfer is found minimum through entropy generation for larger viscosity and thermal conductivity.

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Abbreviations

U :

Velocity vector

\(\left( {U_{1} ,\,U_{2} } \right)\) :

Velocity components

2a :

Width of curved channel

\((R,X)\) :

Radial and axial components

C :

Wave speed

b :

Wave amplitude

λ :

Wavelength

t :

Time

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

Temperature at upper and lower walls

\(\kappa (T)\) :

Variable thermal conductivity

ρ :

Fluid density

T :

Material temperature

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

Specific heat

c and d :

Material parameters of Sisko fluid

\(\gamma^{ * }\) :

Sisko fluid parameter

\(\mu_{\text{o}}\) :

Constant fluid dynamic viscosity

\(\delta\) :

Wavenumber

\(\alpha^{\prime }\) :

Variable viscosity parameter

\(\beta^{\prime }\) :

Variable thermal conductivity parameter

\(\eta\) :

Channel walls in radial direction

J :

Current density

\(\sigma\) :

Electric conductivity

P :

Pressure

C :

Concentration

S :

Extra stress tensor

\(S_{\text{RR}} ,\,S_{\text{XR}} ,\,S_{\text{XX}}\) :

Stress components

\(\kappa_{0}\) :

Constant thermal conductivity at ambient temperature T0

\(\left( {\beta_{1}^{\prime } ,\,\beta_{2}^{\prime } } \right)\) :

Biot numbers

\(\psi\) :

Stream function

Re:

Reynolds number

Br:

Brinkman number

Pr:

Prandtl number

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

Entropy generation parameter

\(S_{\text{G}}\) :

Entropy generation characteristic

\(\left( {S_{\text{gen}} } \right)_{\text{T}}\) :

Heat transfer irreversibility

\(\left( {S_{\text{gen}} } \right)_{\text{F}}\) :

Fluid friction irreversibility

\(\varLambda\) :

Temperature difference parameters

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Authors and Affiliations

  1. Department of Mathematics and Statistics, International Islamic University 1243, Islamabad, 44000, Pakistan

    Farhat Bibi & A. A. Khan

  2. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan

    T. Hayat

  3. Department of Mathematics and Statistics, PMAS Arid Agriculture University Shamsabad, Rawalpindi, 46300, Pakistan

    S. Farooq

  4. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    T. Hayat & A. Alsaedi

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  1. Farhat Bibi
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Correspondence to Farhat Bibi.

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Bibi, F., Hayat, T., Farooq, S. et al. Entropy generation analysis in peristaltic motion of Sisko material with variable viscosity and thermal conductivity. J Therm Anal Calorim 143, 363–375 (2021). https://doi.org/10.1007/s10973-019-09125-4

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