Analytical Solution of Non-Newtonian Nanofluid Flows Within Circular Duct under Convective Boundary Condition

Abstract

At the outset, this work aims to carried out an analytical investigation of forced convection by establishing a laminar flow into circular duct under convective boundary conditions of the third type for non-Newtonian nanofluid, the fluid containing TiO2 uniformly dispersed in aqueous solution with 0.5wt% of CMC solutions (Carboxymethyl Cellulose) is used as working fluid. The viscous dissipation effects are taken into account, the employed methodology is based on a combination of the Ritz variational approach with the Laplace transformation technique, so the power-law fluids flow model is used to describe the non-Newtonian fluid behavior. The effect of dimensionless parameters such as Biot (Bi), Brinkman (Br), Peclet (Pe) numbers, power-law index (n), and nanoparticles concentration (φ) on the temperature distribution contours and on the examined local Nusselt number. Our results have been compared with those found in the literature in particular the cases of base fluids (φ=0) with and without viscous dissipation effects.