TITLE:
Integral Transform Solution through Confluent Hypergeometric Functions for Convective Heat Transfer in a Circular Pipe under Axially Varying Wall Heat Flux
AUTHORS:
Bernard Lamien, Satafa Sanogo, Inoussa Tougri, Mohamed Beidari
KEYWORDS:
Convective Heat Transfer, Integral Transform Technique, Nusselt Number, Confluent Hypergeometric Function
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.16 No.9,
September
10,
2026
ABSTRACT: In this paper, convective heat transfer in a circular pipe is investigated for the case of a thermally developing laminar flow, by considering an axially varying wall heat flux and heat losses to the surrounding. The Integral Transform Technique is used in combination with a boundary filter solution, aiming to improve the convergence behavior of the associated eigenfunctions expansion. The associated linear eigenvalue problem yields a transcendental equation and eigenfunctions in the form of confluent hypergeometric function. The developed analytical solution is computed with MATLAB symbolic computation offering a straightforward way for the evaluation of the integral terms. Solution verification is performed by comparing the computed analytical solution with the solution obtained with COMSOL Multiphysics, a commercial Finite Element software, for the case of a uniform and a variable wall heat flux. Finally, it is shown that the temperature distribution and the local Nusselt number quickly converge with a relatively small number of eigenfunctions for the prescribed exponential wall heat flux examined herein.