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Çengel, Y.A. and Ghajar, A.J. (2020) Heat and Mass Transfer Fundamentals and Applications. 6th Edition, Mcgraw-Hill Education.

has been cited by the following article:

• 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.