FULLY DEVELOPED TEMPERATURE PROFILE FOR A POWER-LAW LAMINAR NANOFLUID FLOW IN A CIRCULAR DUCT SUBJECT TO A UNIFORM HEAT FLUX

Abstract

In the present work, we develop a theoretical analysis of a fully developed laminar nanofluid flow in a circular duct in steady state, subject to a uniform heat flux condition. The rheological behavior of the base fluid is described by the power-law model and the nanofluid properties such as dynamic viscosity, thermal conductivity, density and specific heat are assuming as constants for a fixed value of the volumetric fraction. An analytical solution can be obtained by the mean temperature concept. The Nusselt number was defined and depends on the dimensionless parameter of the viscosity and the power-law index. The main results reveals that, for a maximum value of the volumetric fraction, the Nusselt number decreases drastically for shear-thinning base fluids, for shear-thickenning base fluids tends asymptotically to a constant value. For an increase in the volumetric fraction value, the dimensionless velocity profiles shown lower values for shear-thinning base fluids and the dimensionless temperature profiles showed a greater difference between the dimensionless wall temperature and the nanofluid stream temperature.