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

In the present work, we develop a theoretical analysis of a fully developed laminar nanofluid flow in a circular duct in a steady state subject to a uniform heat flux condition. The rheological behavior of the base fluid is described with the aid of the power-law model and the nanofluid properties such as dynamic viscosity, thermal conductivity, density, and specific heat are assumed as constants for a fixed value of the volumetric fraction. An analytical solution can be obtained based on 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 reveal that for a maximum value of the volumetric fraction, the Nusselt number decreases drastically for shear-thinning base fluids, whereas for shear-thickening base fluids it tends asymptotically to a constant value. For an increase in the volumetric fraction value, the dimensionless velocity profiles have shown lower values for shear-thinning base fluids and the dimensionless temperature profiles present a greater difference between the dimensionless wall temperature and the nanofluid stream temperature. © 2022 by Begell House, Inc.