Effect of viscous dissipation on MHD water-Cu and EG-Cu nanofluids flowing through a porous medium

A comparative study of Stokes second problem
  • Ilyas Khan
  • Waqar A. Khan


This paper provides a comparative analysis of two different types of nanofluids for Stokes second problem. Additional effects of MHD, porosity and viscous dissipation are also considered. Two types of Newtonian liquids (water and ethylene glycol) are considered as base fluids with suspended nanosized Cu particles. A homogenous model of Newtonian nanofluids over a flat plate is used to describe this phenomenon with Stokes boundary conditions such that the ambient fluid is static and with uniform temperature. The problem is first written in terms of nonlinear partial differential equations with physical conditions; then after non-dimensional analysis, the Laplace transform method is used for its closed-form solution. Exact expressions are determined for the dimensionless temperature, velocity field, Nusselt number and skin friction coefficient and arranged in terms of exponential and complementary error functions satisfying the governing equations and boundary conditions. They are also reduced to the known solutions of Stokes second problem for Cu-water nanofluids. Results are computed using Maple software. The results showed that both skin friction and rate of heat transfer increase with increasing solid volume fraction of nanoparticles. MHD and porosity had an opposite effect on velocity for both types of nanofluids. The dimensionless temperature increases by increasing the Eckert and Hartmann numbers.


Stokes problems Cu-H2 O and Cu-EG nanofluids Viscous dissipation MHD Porosity Exact solutions 

List of symbols


Strength of magnetic field (wb m−2)


Heat capacity at a (J kg−1 K−1) constant pressure

\(\left( {c_{\text{p}} } \right)_{\text{nf}}\)

Nanofluid heat capacity(J kg−1 K−1) at a constant pressure


Heaviside function


Permeability (H m−1)


Porosity parameter


Base fluid thermal conductivity (W m−1 k−1)


Solid particle thermal conductivity (W m−1 k−1)


Nanofluid thermal conductivity (W m−1 k−1)


Hartmann number


Prandtl number


Temperature of the fluid (K)

\(T_{{\infty }}\)

Ambient temperature (K)


Time (s)


Velocity of the fluid (m s−1)


Complementary error function

Greek symbols


Base fluid dynamic viscosity (m2 s−1)


Nanofluid dynamic viscosity (m2 s−1)


Base fluid density (kg m−3)


Solid particle density (kg m−3)


Nanofluid density (kg m−3)


Electric conductivity (S m−1)


Stefan–Boltzmann constant (W m−2 K−4)


Dimensionless temperature


Porosity of the medium (H m−1)


Frequency of the oscillation (Hz)



Base fluid


Solid particle nanofluid




Condition at wall


Condition at infinity



Dimensional variables


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Department of Mechanical Engineering, College of EngineeringPrince Mohammad Bin Fahd UniversityAl KhobarKingdom of Saudi Arabia

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