Irreversibility analysis of a vertical annulus using TiO2/water nanofluid with MHD flow effects

Omid Mahian, Ioan Pop, Ahmet Sahin, Hakan F. Oztop, Somchai Wongwises

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73 Scopus citations


In this paper, an analytical study of the second law of thermodynamics is performed for the flow and heat transfer of TiO2/water nanofluid in a vertical annulus with isoflux walls and under the influence of magnetohydrodynamic (MHD) field. The governing equations in cylindrical coordinates are written and then simplified with reasonable assumptions. The simplified equations are solved analytically to obtain expressions for the velocity, temperature, and entropy generation distributions. The results are presented for different values of nanofluid volume fractions φ(0%≤φ≤2%), Hartmann number M and the flow parameter Gr/Re. To calculate the thermal conductivity and viscosity of TiO2/water nanofluid, relations based on experimental data are used. Finally, using the well-known theoretical models for the thermal conductivity and viscosity, the effects of Hartmann number on the results are investigated.

Original languageEnglish
Pages (from-to)671-679
Number of pages9
JournalInternational Journal of Heat and Mass Transfer
StatePublished - 2013


  • Analytical solution
  • Entropy generation
  • MHD flow
  • Nanofluid
  • Vertical annulus


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