An exact mathematical solution for entrance-region laminar heat transfer with axial conduction

Summary A relatively simple mathematical scheme is proposed by which the entrance-region temperature solution for laminar flow heat transfer with axial conduction can be rigorously obtained.For Poiseuille pipe flow (parabolic velocity profile) with uniform wall heat flux, the accurate first twelve eigenvalues, eigenfunctions, and the coefficients of the series expansion which are required in the temperature solution have been determined for Peclet numbers of 5, 10, 20, 30, 50, and 100. In addition, asymptotic expressions for the eigenvalues and the eigenfunction,R_n(1), are derived. It is possible to use the asymptotic equation to predict, with satisfactory accuracy, even the first few eigenvalues for all the Peclet numbers considered.By employing the computed eigenvalues and the relevant constants, the effect of axial conduction on the entrance-region temperature profile and local Nusselt numbers has been examined and reported.This work was performed under the auspices of the U.S. Atomic Energy Commission.