Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (1): 63-72.doi: https://doi.org/10.1007/s10483-014-1772-8

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Numerical solutions to heat transfer of nanofluid flow over stretching sheet subjected to variations of nanoparticle volume fraction and wall temperature

M. SALARI1, M. MOHAMMADTABAR2, A. MOHAMMADTABAR3   

  1. 1. Department of Mechanical Engineering, Imam Hussein University, Tehran 16756-00995, Iran;
    2. Department of Mechanical Engineering, University of Alberta, Edmonton AB T6G 2G8, Canada;
    3. Department of Mechanical Engineering, Islamic Azad University, Tehran 11365-04435, Iran
  • 收稿日期:2012-12-28 修回日期:2013-06-21 出版日期:2014-01-20 发布日期:2013-12-27

Numerical solutions to heat transfer of nanofluid flow over stretching sheet subjected to variations of nanoparticle volume fraction and wall temperature

M. SALARI1, M. MOHAMMADTABAR2, A. MOHAMMADTABAR3   

  1. 1. Department of Mechanical Engineering, Imam Hussein University, Tehran 16756-00995, Iran;
    2. Department of Mechanical Engineering, University of Alberta, Edmonton AB T6G 2G8, Canada;
    3. Department of Mechanical Engineering, Islamic Azad University, Tehran 11365-04435, Iran
  • Received:2012-12-28 Revised:2013-06-21 Online:2014-01-20 Published:2013-12-27

摘要:

The numerical analysis of heat transfer of laminar nanofluid flow over a flat stretching sheet is presented. Two sets of boundary conditions (BCs) are analyzed, i.e., a constant (Case 1) and a linear streamwise variation of nanoparticle volume fraction and wall temperature (Case 2). The governing equations and BCs are reduced to a set of nonlinear ordinary differential equations (ODEs) and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the
increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers.

关键词: laminar boundary layer, Brownian motion, numerical solution, nanofluid, partial differential equation, thermophoresis, stretching sheet

Abstract:

The numerical analysis of heat transfer of laminar nanofluid flow over a flat stretching sheet is presented. Two sets of boundary conditions (BCs) are analyzed, i.e., a constant (Case 1) and a linear streamwise variation of nanoparticle volume fraction and wall temperature (Case 2). The governing equations and BCs are reduced to a set of nonlinear ordinary differential equations (ODEs) and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the
increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers.

Key words: Brownian motion, nanofluid, numerical solution, null, stretching sheet, partial differential equation, thermophoresis, laminar boundary layer

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