The effects of buoyancy force on mixed convection heat transfer of MHD nanofluid flow and entropy generation in an inclined duct with separation considering Brownian motion effects

Abstract

In this paper, an attempt is made to study the buoyancy force influences on the MHD mixed convection nanofluid flow and entropy generation over an inclined step in an inclined duct. This inclined step leads to the flow separation in duct and affects the hydrodynamic and thermal behaviors. Influences of Brownian motion on the effective viscosity and thermal conductivity of Cu-water nanofluid are considered. The second law of thermodynamics is used to calculate the entropy generation number that is an applied criterion to compute the flow irreversibility. The interaction effects of Grashof number $$ \left( {0 \le Gr \le 10,000} \right) $$, duct inclination angle $$ \left( {0^\circ \le \beta \le 90^\circ } \right) $$, Hartmann number $$ \left( {0 \le Ha \le 60} \right) $$ and concentration of $$ Cu $$ nanoparticles $$ \left( {0 \le \phi \le 0.06} \right) $$ on the flow pattern, heat transfer rates and the amount of flow irreversibility are studied with all details. The results show that the Hartmann number has a large influence on the trends of the fiction coefficient, Nusselt number and entropy generation number along the bottom wall. Also, the highest values of average friction coefficient and average Nusselt number occur in the absence of magnetic field and for the vertical duct with highest values of $$ Gr $$ and $$ \phi $$. In addition, an increase in the amounts of flow irreversibility is registered by enhancing the buoyancy force, magnetic field strength and nanoparticles concentration.