, 93:53 | Cite as

Enhancement in heat and mass transfer over a permeable sheet with Newtonian heating effects on nanofluid: Multiple solutions using spectral method and stability analysis

  • Irfan Mustafa
  • Tariq Javed
  • Abuzar GhaffariEmail author
  • Hammad Khalil


This paper investigates the Newtonian heating effect on nanofluid flow over a nonlinear permeable stretching / shrinking sheet near the region of stagnation point. Only two important mechanisms on the transportation of nanoparticles in base fluid are discussed: the Brownian motion and thermophoresis. This physical problem is modelled using the Buongiorno (ASME J. Heat Transfer 128, 240 (2006) model in terms of nonlinear governing partial differential equations and transformed into dimensionless ordinary differential equations by using similarity transformation and the solution is calculated using the numerical scheme known as the Chebyshev spectral collocation method. The main interest of this study is the region of the boundary layer where viscous effects are dominant. Dual solutions are reported against the shrinking parameter in which the first solution is stable due to positive eigenvalues and the second is unstable due to negative eigenvalues and ranges of these solutions are effected by the suction parameter which is discussed using graphs and tables. The effects of dimensionless parameters, namely, velocity ratio, suction, Schmidt number, Prandtl number, thermophoresis and Brownian motion on temperature and concentration profiles, skin friction coefficient and Nusselt number are also shown using graphs. For the validity of the applied scheme, a comparison is established with published studies in the limiting case. Through the results, it is concluded that temperature and concentration increase by increasing the values of the thermophoresis parameter and the opposite behaviour is observed in the case of Brownian motion and Schmidt number. Skin friction coefficient, Nusselt and Sherwood numbers increase on increasing the suction parameter. Also, an enhancement in temperature and concentration profiles is observed in the presence of Newtonian heating parameter.


Nanofluid nonlinear stretching / shrinking sheet suction Newtonian heating boundary condition 

PACS 47.15.Cb 44.20.+b 


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Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  • Irfan Mustafa
    • 1
  • Tariq Javed
    • 2
  • Abuzar Ghaffari
    • 3
    Email author
  • Hammad Khalil
    • 3
  1. 1.Department of MathematicsAllama Iqbal Open UniversityIslamabad Pakistan
  2. 2.Department of Mathematics and Statistics, FBASInternational Islamic UniversityIslamabad Pakistan
  3. 3.Department of MathematicsUniversity of EducationLahore (Attock Campus, 43600)Pakistan

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