Axial conduction in laminar pipe flows with nonlinear wall heat fluxes

A numerical analysis to determine the heat-transfer parameters of a fluid flow rejecting heat to the surrounding medium by convection and radiation is developed. The influence of axial conduction is included and the velocity profile is taken as nonuniform in the transverse direction. Use of a transformation eliminates the required boundary conditions at infinity. Approximate numerical techniques are employed to solve the nonlinear conjugate problem. As Péclet number increases, the temperature fields simplify to those where axial conduction is excluded. The computed results indicate that the effects of axial conduction are strongly altered by the parameters responsible for the convection and radiation. Bulk fluid temperatures, wall heat fluxes and Nusselt numbers are plotted against Graetz numbers. Critical Péclet numbers for a variety of cooling conditions are presented using the bulk fluid temperature as a reference.