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Numerical study of melting effect with entropy generation minimization in flow of carbon nanotubes

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Abstract

Optimization of entropy generation in squeezing flow of carbon nanotubes is addressed. Nanoparticles consist of single- and multiple-walled carbon nanotubes. Heat transfer subject to melting effect is employed. Shooting technique along with the fifth-order Runge–Kutta algorithm (bvp4c) is employed for the simulation. Bejan number, entropy generation rate, velocity and temperature are studied. Nusselt number and skin friction are also discussed. Velocity intensifies for higher estimations of squeezing parameter, nanoparticle volume fraction and melting parameter, while it reduces the temperature of fluid. Nusselt number enhances with an increment in estimations of squeezing parameter, nanoparticle volume fraction and melting parameter. Rate of entropy production decays with higher nanoparticle volume fraction and squeezing parameter. Bejan number is an increasing function of squeezing parameter, while it decays with an increment in melting parameter and nanoparticle volume fraction. Furthermore, prominent behavior is shown by multiple-walled CNTs.

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Abbreviations

\(u,\) \(v\) :

Velocity components

\(x\), \(y\) :

Coordinates

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

Fluid dynamic viscosity

\(\nu_{\text{nf}}\) :

Kinematic nanofluid viscosity

\(\rho_{\text{f}}\) :

Fluid density

\(\nu_{\text{f}}\) :

Kinematic fluid viscosity

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

Base fluid thermal conductivity

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

Specific heat of base fluid

\(f^{{^{\prime } }}\), \(\theta\) :

Dimensionless (velocity, temperature)

\(\varOmega\) :

Non-dimensional temperature difference

P 1 :

Pressure

\(T\) :

Temperature of nanoliquid

\(T_{\text{m}}\) :

Melting surface temperature

\(T_{\text{h}}\) :

Upper wall temperature

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

Nanofluid dynamic viscosity

\(S_{{{\text{G}}_{0} }}\) :

Characteristic entropy generation

\(\alpha_{\text{f}}\) :

Thermal diffusivity of base fluid

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

Specific heat of base fluid

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

Nanofluids thermal conductivity

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

Specific heat of nanofluid

\(\alpha_{{\text{nf}}}\) :

Thermal diffusivity of nanofluid

\(Pr\) :

Prandtl number

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

Thermal conductivity of CNTs

CNTs:

Carbon nanotubes

\(\phi\) :

Nanoparticle volume fraction

\(Ec_{1}\) :

Local Eckert number

\({\varvec{\uptau}}_{{\text{w}}}\) :

Shear stress

\({\text{Sq}}\) :

Squeezing parameter

\(M\) :

Melting parameter

\(T_{0}\) :

Solid surface temperature

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

Solid surface heat capacity

\(Ec\) :

Eckert number

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Authors and Affiliations

  1. Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia

    Fawaz E. Alsaadi

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

    Khursheed Muhammad & T. Hayat

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

    T. Hayat & A. Alsaedi

  4. Department of Mathematics, CUI, Park Road Chak Shahzad, Islamabad, Pakistan

    S. Asghar

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  1. Fawaz E. Alsaadi
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Correspondence to Khursheed Muhammad.

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Alsaadi, F.E., Muhammad, K., Hayat, T. et al. Numerical study of melting effect with entropy generation minimization in flow of carbon nanotubes. J Therm Anal Calorim 140, 321–329 (2020). https://doi.org/10.1007/s10973-019-08720-9

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