Journal of Thermal Analysis and Calorimetry

, Volume 135, Issue 3, pp 1643–1654 | Cite as

Heat transfer and fluid flow of pseudo-plastic nanofluid over a moving permeable plate with viscous dissipation and heat absorption/generation

  • Hamid Maleki
  • Mohammad Reza SafaeiEmail author
  • Hussein Togun
  • Mahidzal Dahari


The purpose of the present study is investigating the heat transfer of non-Newtonian pseudo-plastic nanofluid flow on a moving permeable flat plate with viscous dissipation and heat absorption/generation. The flow is uniform and parallel to the moving flat plate, and both flat plate and flow are moving on the same directions. The investigated parameters in this study are power-law index, permeability parameter, Eckert number, volume fraction of nanoparticles, nanoparticles type, velocity ratio and heat absorption/generation parameter. The nanoparticles used in this paper are Al2O3, TiO2, Cu and CuO dispersed in sodium carboxymethyl cellulose/water as the base fluid. By using suitable transformations, the governing partial differential equations are converted into the ordinary differential equations, and after that, the resulting ODEs are solved with Runge–Kutta-Fehlberg fourth–fifth-order numerical method. The results of this investigation showed that heat transfer of Newtonian and non-Newtonian nanofluids in the presence of viscous dissipation and generation/absorption of heat has an interesting behavior: For Newtonian fluid, by increasing the amounts of high-conductive nanoparticles to carrying fluid, a higher heat transfer is not obtained. For instance, copper nanoparticles, despite having highest thermal conductivity compared to other nanoparticles, show the lowest local Nusselt number. However, for pseudo-plastic non-Newtonian nanofluids the observed trend was reversed. Furthermore, in both Newtonian and non-Newtonian nanofluids, the local Nusselt number decreased, by increasing injection parameter, heat generation or volume fraction of nanoparticles (in high Eckert numbers). That is while, by enhancing the heat absorption, velocity ratio, suction parameter or volume fraction of nanoparticles (in low Eckert number), the local Nusselt number augments.


Non-Newtonian pseudo-plastic nanofluid Moving permeable plate Heat absorption/generation 

List of symbols


Specific heat at constant pressure (J kg−1 K−1)


Local skin-friction coefficient


Eckert number


Dimensionless stream function


Transpiration rate constant


Heat transfer coefficient (W m−2 K−1)


Thermal conductivity (W m−1 K−1)


The power-law index


Local Nusselt number


Modified local non-Newtonian Prandtl number


Heat generation/absorption coefficient (J m−3 K−1 s−1)


Local non-Newtonian Reynolds number


Fluid temperature (K)


Composite velocity (m s−1)


Velocity components along x and y directions (m s−1)


Mass transfer velocity at the surface (m s−1)


Coordinate along the plate (m)


Coordinate normal to the plate (m)

Greek symbols


Thermal diffusivity (m2 s−1)


Similarity variable


Dimensionless temperature


Velocity ratio parameter


Dynamic viscosity (kg m−1 s−1)


Kinematic viscosity (m2 s−1)


Fluid density (kg m−3)


Nanoparticle volume fraction


Local heat generation/absorption parameter


Stream function





Condition at the surface

Ambient condition






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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIsfahan University of TechnologyIsfahanIran
  2. 2.Division of Computational Physics, Institute for Computational ScienceTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Faculty of Electrical and Electronics EngineeringTon Duc Thang UniversityHo Chi Minh CityVietnam
  4. 4.Biomedical Engineering DepartmentUniversity of Thi-QarNassiriyaIraq
  5. 5.Department of Electrical Engineering, Faculty of EngineeringUniversity of MalayaKuala LumpurMalaysia

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