Convection in ethylene glycol-based molybdenum disulfide nanofluid

Atangana–Baleanu fractional derivative approach
  • Muhammad Saqib
  • Farhad Ali
  • Ilyas Khan
  • Nadeem Ahmad Sheikh
  • Sharidan Bin Shafie
Article
  • 9 Downloads

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.

Keywords

Atangana–Baleanu fractional derivatives Ethylene glycol Heat transfer Exact solutions 

List of symbols

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

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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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Muhammad Saqib
    • 1
    • 2
  • Farhad Ali
    • 1
    • 2
  • Ilyas Khan
    • 4
  • Nadeem Ahmad Sheikh
    • 3
    • 5
  • Sharidan Bin Shafie
    • 5
  1. 1.Computational Analysis Research GroupTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Department of MathematicsCity University of Science and Information TechnologyPeshawarPakistan
  4. 4.Basic Engineering Sciences Department, College of EngineeringMajmaah UniversityMajmaahSaudi Arabia
  5. 5.Department of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia (UTM)SkudaiMalaysia

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