Analysis of heat transfer, including axial fluid conduction, for laminar tube flow with arbitrary circumferential wall heat flux variation

Abstract

An analysis is presented for the exact solution to the problem of thermal-entry-region heat transfer in a circular tube with an arbitrary circumferential wall heat flux, including the effect of axial fluid conduction. The solution is expressed in a power series form; the first 12 eigenvalues and eigenfunctions were obtained numerically. The least squares method was employed to determine the series expansion coefficients for the non-orthogonal system. A simple result is given for heat flux variation in the form q = q av (1 + cos φ) which illustrates the simultaneous influence of circumferential wall heat flux variation and axial fluid conduction on wall temperature and Nusselt number.