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

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.