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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad , 44000, Pakistan

    Irfan Mustafa

  2. Department of Mathematics and Statistics, FBAS, International Islamic University, Islamabad , 44000, Pakistan

    Tariq Javed

  3. Department of Mathematics, University of Education, Lahore (Attock Campus, 43600), Pakistan

    Abuzar Ghaffari & Hammad Khalil

Authors
  1. Irfan Mustafa
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  2. Tariq Javed
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  3. Abuzar Ghaffari
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  4. Hammad Khalil
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Correspondence to Abuzar Ghaffari.

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Mustafa, I., Javed, T., Ghaffari, A. et al. Enhancement in heat and mass transfer over a permeable sheet with Newtonian heating effects on nanofluid: Multiple solutions using spectral method and stability analysis. Pramana - J Phys 93, 53 (2019). https://doi.org/10.1007/s12043-019-1814-3

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  • DOI: https://doi.org/10.1007/s12043-019-1814-3

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