Journal of Thermal Analysis and Calorimetry

, Volume 135, Issue 1, pp 523–532 | Cite as

Convection in ethylene glycol-based molybdenum disulfide nanofluid

Atangana–Baleanu fractional derivative approach
  • Muhammad Saqib
  • Farhad AliEmail author
  • Ilyas Khan
  • Nadeem Ahmad Sheikh
  • Sharidan Bin Shafie


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.


Atangana–Baleanu fractional derivatives Ethylene glycol Heat transfer Exact solutions 

List of symbols


The yield stress of the non-Newtonian fluid


The product of the component of deformation rate itself


The critical value of this product


Plastic dynamic viscosity


Velocity of the fluid


Temperature of the fluid


Acceleration due to gravity


Specific heat at a constant pressure


Thermal conductivity of the fluid

\(T_{\infty }\)

Fluid temperature far away from the plate


Laplace transforms parameter


Kinematic viscosity of the fluid


Dynamic viscosity


Fluid density


The density of the solid


The amplitude of the velocity


The volumetric coefficient of thermal expansion


External magnetic field


Nanofluids density


Dynamic viscosity of nanofluids


The electrical conductivity of nanofluids


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


The thermal conductivity of nanofluids


Magnetic parameter


Thermal Grasshof number


Prandtl number


Nusselt number


Nanoparticles volume fraction


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
    Email author
  • 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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