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Convection in ethylene glycol-based molybdenum disulfide nanofluid

Atangana–Baleanu fractional derivative approach

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Abstract

This article aims to study the flow of ethylene glycol-based molybdenum disulfide generalized nanofluid over an isothermal vertical plate. A fractional model with non-singular and non-local kernel, namely Atangana–Baleanu fractional derivatives, is developed for Casson nanofluid in the form of partial differential equations along with appropriate initial and boundary conditions. Molybdenum disulfide nanoparticles of spherical shape are suspended in ethylene glycol taken as conventional base fluid. The exact solutions are developed for velocity and temperature via the Laplace transform technique. In limiting sense, the obtained solutions are reduced to fractional Newtonian \((\beta \to \infty )\), classical Casson fluid \((\alpha \to 1)\) and classical Newtonian nanofluid. The influence of various pertinent parameters is analyzed in various plots with the useful physical discussion.

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Abbreviations

\(p_{\text{y}}\) :

The yield stress of the non-Newtonian fluid

\(\pi\) :

The product of the component of deformation rate itself

\(\pi_{\text{c}}\) :

The critical value of this product

\(\mu_{\upgamma}\) :

Plastic dynamic viscosity

\(u\) :

Velocity of the fluid

\(T\) :

Temperature of the fluid

\(g\) :

Acceleration due to gravity

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

Specific heat at a constant pressure

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

Thermal conductivity of the fluid

\(T_{\infty }\) :

Fluid temperature far away from the plate

\(q\) :

Laplace transforms parameter

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

Kinematic viscosity of the fluid

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

Dynamic viscosity

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

Fluid density

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

The density of the solid

\(U\) :

The amplitude of the velocity

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

The volumetric coefficient of thermal expansion

\(B_{0}\) :

External magnetic field

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

Nanofluids density

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

Dynamic viscosity of nanofluids

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

The electrical conductivity of nanofluids

\(\beta\) :

The material parameter of Casson fluid

\((\beta_{\text{T}} )_{\text{nf}}\) :

Thermal expansion coefficient of nanofluids,

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

Specific heat capacity of nanofluids

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

The thermal conductivity of nanofluids

\(M\) :

Magnetic parameter

\(Gr\) :

Thermal Grasshof number

\(Pr\) :

Prandtl number

\({\text{Nu}}_{\text{x}}\) :

Nusselt number

\(\phi\) :

Nanoparticles volume fraction

\(\alpha\) :

Fractional order/fractional parameter

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Authors and Affiliations

  1. Computational Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Muhammad Saqib & Farhad Ali

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Muhammad Saqib & Farhad Ali

  3. Department of Mathematics, City University of Science and Information Technology, Peshawar, 25000, Pakistan

    Nadeem Ahmad Sheikh

  4. Basic Engineering Sciences Department, College of Engineering, Majmaah University, Majmaah, 11952, Saudi Arabia

    Ilyas Khan

  5. Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia (UTM), 81310, Skudai, Malaysia

    Nadeem Ahmad Sheikh & Sharidan Bin Shafie

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Correspondence to Farhad Ali.

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Saqib, M., Ali, F., Khan, I. et al. Convection in ethylene glycol-based molybdenum disulfide nanofluid. J Therm Anal Calorim 135, 523–532 (2019). https://doi.org/10.1007/s10973-018-7054-9

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