Theoretical investigation of laminar flow convective heat transfer in a circular duct for a non-Newtonian nanofluid

In this study, laminar flow forced convection heat transfer of a non-Newtonian nanofluid flowing inside a circular tube that is subjected to a constant wall temperature was investigated analytically. By taking into account the effect of viscous dissipation, a new methodology based on a variational Ritz approach combined with Laplace transform technique is presented. The effects of Brinkman numbers (Br), power low index (n) and nanoparticle concentrations (φ) on the developing temperature fields and the local Nusselt number were examined. The obtained results were validated with available solutions for the special cases of conventional fluids (φ = 0) and non-viscous dissipation effect (Br = 0). Bulk temperature distribution and local Nusselt number are presented graphically for Br = 0, 0.5, 1, −0.5 and 1 for non-Newtonian fluids described by the power-law model with the flow index n = 0.5, 1.0 and 1.5. The Nusselt numbers of nanofluids were obtained for different Al2O3 nanoparticle concentrations as well as various Peclet and Brinkman numbers.