Journal of Thermal Analysis and Calorimetry

, Volume 135, Issue 3, pp 1655–1666 | Cite as

Flow and heat transfer in non-Newtonian nanofluids over porous surfaces

  • Hamid Maleki
  • Mohammad Reza SafaeiEmail author
  • Abdullah A. A. A. Alrashed
  • Alibakhsh Kasaeian


In the present study, heat transfer and fluid flow of a pseudo-plastic non-Newtonian nanofluid over permeable surface has been solved in the presence of injection and suction. Similarity solution method is utilized to convert the governing partial differential equations into ordinary differential equations, which then is solved numerically using Runge–Kutta–Fehlberg fourth–fifth order (RKF45) method. The Cu, CuO, TiO2 and Al2O3 nanoparticles are considered in this study along with sodium carboxymethyl cellulose (CMC)/water as base fluid. Validation has been done with former numerical results. The influence of power-law index, volume fraction of nanoparticles, nanoparticles type and permeability parameter on nanofluid flow and heat transfer was investigated. The results of the study illustrated that the flow and heat transfer of non-Newtonian nanofluid in the presence of suction and injection has different behaviors. For injection and the impermeable plate, the non-Newtonian nanofluid shows a better heat transfer performance compared to Newtonian nanofluid. However, changing the type of nanoparticles has a more intense influence on heat transfer process during suction. It was also observed that in injection, contrary to the other two cases, the usage of non-Newtonian nanofluid can decrease heat transfer in all cases.


Non-Newtonian nanofluid Permeable surface Runge–Kutta–Fehlberg method Similarity solution 

List of symbols






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


Non-dimensional stream function


Constant for transpiration rate


Heat transfer coefficient (W m−2 K−1)


Thermal conductivity (W m−1 K−1)


Prandtl number


The power-law exponent


Temperature of the fluid (K)


Velocity of the free stream (ms−1)

u, v

Components of velocity in x and y directions (ms−1)


Coordinate along the plate (m)


Coordinate normal to the plate surface (m)

Greek symbols


Thermal diffusivity (m2 s−1)


Variable for similarity solution


Non-dimensional temperature


Dynamic viscosity (kg m−1 s−1)


Kinematic viscosity (m2 s−1)


Fluid density (kg m−3)


Volume fraction of nanoparticles


Stream function





Condition at the surface of the plate

Ambient condition






Compliance with ethical standards

Conflict of interest

The authors declare that there are no conflicts of interest.


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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.Department of Automotive and Marine Engineering Technology, College of Technological StudiesThe Public Authority for Applied Education and TrainingAdailiyahKuwait
  5. 5.Faculty of New Sciences and TechnologiesUniversity of TehranTehranIran

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