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Entropy production minimization and non-Darcy resistance within wavy motion of Sutterby liquid subject to variable physical characteristics

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Abstract

Non-Darcy resistance in peristaltic transport of Sutterby liquid in curved configuration is modeled. Variable characteristics of material (i.e., thermal conductivity and viscosity) are taken as temperature-dependent. Soret and Dufour features have also been retained. Problem is modeled by using conservation laws. Long wavelength and small Reynolds number have been invoked. Resulting problems have been solved numerically. Entropy optimization analysis is made. Axial velocity, temperature, concentration, entropy, Bejan number and heat transfer rate are examined for influential variables. It is found that velocity increases for variable viscosity coefficient and porous-space parameter. Temperature decreases for increased values of variable thermal conductivity. Opposite behavior of mass and energy is noted for Soret and Dufour parameters. Entropy minimized for thermal conductivity and viscosity coefficients. Entropy enhancement is noticed for Soret and Dufour parameters. Heat transfer rate at upper wall is enhanced for Soret and Dufour variables.

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Abbreviations

W :

Velocity

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

Velocity components

\( v \) :

Wave speed

\( (X,R) \) :

Axial and radial coordinates

\( \left( {O,R^{\prime}} \right) \) :

Origin and radius of channel

f :

Wavelength

\( b_{1} \) :

Wave amplitude

\( T,C \) :

Temperature and concentration

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

Concentrations at upper and lower boundaries

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

Temperatures at upper and lower boundaries

\( \rho \) :

Fluid density

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

Specific heat

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

Mass diffusion coefficient

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

Concentration susceptibility

\( k_{\text{T}} \) :

Thermal diffusion ratio

\( {\varvec{\uptau}} \) :

Cauchy stress tensor

\( \left( {\kappa \left( T \right),\mu \left( T \right)} \right) \) :

Thermal conductivity and viscosity as a function of temperature

\( h \) :

Dimensionless peristaltic wall

\( \delta \) :

Wave number

k :

Curvature

\( \eta \) :

Sutterby fluid parameter

\( \kappa_{0} ,\mu_{0} \) :

Constant thermal conductivity and viscosity

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

Viscosity and thermal conductivity coefficients

\( K \) :

Permeability parameter

P :

Pressure

\( Da \) :

Permeability parameter (Dimensionless)

\( \left( {Sr,Du} \right) \) :

Soret and Dufour parameters

\( \psi \) :

Stream function

\( {\mathbf{S}} \) :

Extra stress tensor

t :

Time

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

Stress components

\( {\mathbf{q}} \) :

Heat flux

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

Dimensionless entropy

\( Be \) :

Bejan number

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Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan

    T. Hayat

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

    T. Hayat & A. Alsaedi

  3. Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan

    Farhat Bibi & A. A. Khan

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  1. T. Hayat
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  2. Farhat Bibi
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  4. A. Alsaedi
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Correspondence to A. A. Khan.

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Hayat, T., Bibi, F., Khan, A.A. et al. Entropy production minimization and non-Darcy resistance within wavy motion of Sutterby liquid subject to variable physical characteristics. J Therm Anal Calorim 143, 2215–2225 (2021). https://doi.org/10.1007/s10973-020-10007-3

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