Title: The paradigm shift of convective instability in pipe flow: a comprehensive review

Authors: Saurabh Kapoor; Durgaprasad Nayak

Addresses: Department of Mathematics, Regional Institute of Education (NCERT), Bhubaneswar, India ' Department of Mathematics, Regional Institute of Education, Utkal University, Bhubaneswar, India

Abstract: This article provides a comprehensive overview of various methods used to enhance the thermal performance of heat exchangers, along with the stability mechanisms of convective flows. Heat transfer occurs through three primary modes: radiation, conduction and convection. Among these, convection is one of the most significant and can be categorised as free, forced, granular, gravitational or thermomagnetic. Over the past few decades, numerous studies have investigated convective heat transfer in pipes. This paper presents a detailed review of fluid flow in pipes, aiming not only to evaluate previous research comprehensively but also to provide readers with valuable existing knowledge that may facilitate future studies. The effects of key dimensionless parameters such as the Rayleigh, Reynolds, Prandtl, Grashof, Nusselt and Darcy numbers, as well as pipe length, on heat transfer are also discussed. Additionally, the paper includes a brief discussion on the instability mechanisms of mean flow in pipes based on recent stability analyses.

Keywords: Poiseuille flow; convection; heat transfer; stability analysis.

DOI: 10.1504/PCFD.2026.153733

Progress in Computational Fluid Dynamics, An International Journal, 2026 Vol.26 No.3, pp.174 - 185

Received: 10 Feb 2025
Accepted: 28 Jun 2025
Published online: 22 May 2026 *

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