Applied Mathematics and Mechanics

, Volume 40, Issue 9, pp 1285–1300 | Cite as

Heat transfer and entropy generation analysis of non-Newtonian flu flow through vertical microchannel with convective boundary condition

  • M. Madhu
  • N. S. Shashikumar
  • B. Mahanthesh
  • B. J. GireeshaEmail author
  • N. Kishan


The entropy generation and heat transfer characteristics of magnetohydro-dynamic (MHD) third-grade fluid flow through a vertical porous microchannel with a convective boundary condition are analyzed. Entropy generation due to flow of MHD non-Newtonian third-grade fluid within a microchannel and temperature-dependent viscosity is studied using the entropy generation rate and Vogel's model. The equations describing flow and heat transport along with boundary conditions are first made dimensionless using proper non-dimensional transformations and then solved numerically via the finite element method (FEM). An appropriate comparison is made with the previously published results in the literature as a limiting case of the considered problem. The comparison confirms excellent agreement. The effects of the Grashof number, the Hartmann number, the Biot number, the exponential space- and thermal-dependent heat source (ESHS/THS) parameters, and the viscous dissipation parameter on the temperature and velocity are studied and presented graphically. The entropy generation and the Bejan number are also calculated. From the comprehensive parametric study, it is recognized that the production of entropy can be improved with convective heating and viscous dissipation aspects. It is also found that the ESHS aspect dominates the THS aspect.

Key words

microchannel entropy generation Bejan number third-grade fluid magnetic field 

Chinese Library Classification


Mathematics Subject Classification

76W05 76S05 


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One of the authors (M. MADHU) acknowledges the University Grants Commission (UGC) for financial support under the Dr. D. S. KOTHARI Postdoctoral Fellowship Scheme (No. F.4-2/2006 (BSR)/MA/16-17/0043).


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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • M. Madhu
    • 1
  • N. S. Shashikumar
    • 1
  • B. Mahanthesh
    • 2
  • B. J. Gireesha
    • 1
    Email author
  • N. Kishan
    • 3
  1. 1.Department of Studies and Research in MathematicsKuvempu UniversityShankaraghattaIndia
  2. 2.Department of MathematicsChrist Deemed to be UniversityBangaloreIndia
  3. 3.Department of MathematicsOsmania UniversityTelanganaIndia

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