Transient and steady-state forced convection to power-law fluids in the thermal entrance region of circular ducts: Effects of viscous dissipation, variable viscosity, and axial conduction

A numerical study was conducted on the transient behavior of a hydrodynamically fully developed, laminar flow of power-law fluids in the thermally developing entrance region of circular ducts with taking into account the effects of viscous dissipation, axial conduction, and variations of viscosity with temperature. In this regard, the unsteady-state thermal energy and momentum equations were solved numerically using a finite-difference method, whereas the steady-state thermal energy equation with constant wall heat flux as the boundary condition was solved analytically as the initial condition of the former. The numerical procedure used in the present work was validated with an analytical solution for the special case of Newtonian fluids. The effects of the power-law index, axial conduction, wall heat flux, and variations of fluid viscosity on the local Nusselt number and thermal entrance length were investigated. Moreover, the local Nusselt number values of steady-state conditions were correlated as a function of the power-law index and wall heat flux. Furthermore, a correlation was derived for the thermal entrance length as a function of the power-law index and wall heat flux.