Entropy Generation Between Two Rotating Cylinders with Magnetohydrodynamic Flow Using Nanofluids

The flow between two cylinders where one or both of the cylinders rotate has many practical applications such as swirl nozzles, rotating electrical machines, rotating disks, standard commercial rhymesters, and chemical and mechanical mixing equipment. In this paper, the effect of using TiO2-water nanofluid (phi <= 2%) on entropy generation between two corotating cylinders in the presence of magnetohydrodynamic flow is investigated. An analytical approach is applied to solve the simplified governing equations in the cylindrical coordinate system. To calculate the thermal conductivity and viscosity of the nanofluid, two correlations, which are based on the experimental data, are used. The velocity field is obtained as modified Bessel functions, and then, using the expansions of these Bessel functions with three terms, the temperature field and, subsequently, the entropy generation rate are estimated. The results are presented for various parameters, including the entropy generation number (N-S), Bejan number (Be), Hartmann number (M), Brinkman number (Br), and a group parameter (Omega/Br). From the results, it is concluded that, at low Brinkman numbers (depending on the value of Omega/Br-f), the average entropy generation number (N-S)(ave) decreases with the increase in nanoparticle volume fraction.