Numerical Simulation for Simultaneously Developing Laminar Flow and Heat Transfer in a Circular Pipe

Belhocine A. Stojanovic N. Houari M.S.A. Merzouki T. Hamida M.B.B. Abdullah O.I.
2025 Springer Nature

Arabian Journal for Science and Engineering
2025

This work consists of the computational analysis of two-dimensional heat transfer by convection and laminar flow of a fluid. The application was done through a circular pipe with simultaneously developing velocity and temperature profiles, considering two different wall boundary conditions that were alternatively introduced: constant temperature and constant specific heat flux. The physical characteristics of this flow were assumed to be constant and of an incompressible and Newtonian type. The governing equations describing fluid flow, namely, continuity, momentum, energy, and simplifying assumptions, along with associated boundary conditions, have also been presented in detail. These equations, which govern the studied phenomenon, are non-linear partial differential equations (PDE), and we therefore used the explicit finite-difference scheme (EFDS) to integrate these equations by iterations after transforming them into a linear algebraic system. For this purpose, a FORTRAN computer code has been well developed to simulate the thermal problem in a circular pipe and obtain the results presented in both cases. The results were computed in terms of various parameters when the Peclet number was between 0.7 and 100; the number of grid points ranged between 10 and 100, and the distance Z between 0.05 and 0.5. This allowed us to evaluate the rate of heat transfer, to observe the velocity and temperature contours, the distribution of Nusselt number, whether local or average, and to determine the impact of the various factors on the performance and heat transfer characteristics of the fluid flow. Finally, we conducted a critical comparison in order to validate the computer code developed in this study, and our results showed excellent agreement with previous studies. This further strengthens the reliability of the predictive model via digital simulation.

Constant heat flux , Explicit finite difference method , Laminar flow , Pipe , Simultaneously developing flow , Uniform wall temperature

Text of the article Перейти на текст статьи

Department of Mechanical Engineering, Laboratory for the Study of Structures and Mechanics of Materials, University Mustapha Stambouli of Mascara, Mascara, 29000, Algeria
Department for Motor Vehicles and Motors, Faculty of Engineering, University of Kragujevac, 6 SestreJanjić STR., Kragujevac, 34000, Serbia
Department of Civil Engineering, Laboratory for the Study of Structures and Mechanics of Materials, University Mustapha Stambouli of Mascara, Mascara, 29000, Algeria
LISV, University of Versailles Saint-Quentin, 10-12 Avenue de L’Europe, Vélizy, 78140, France
Deanship of Scientific Research - Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
Department of Energy Engineering, College of Engineering, University of Baghdad, Baghdad, Iraq
College of Engineering, Al Naji University, Baghdad, Iraq
Department of Mechanics, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan

Department of Mechanical Engineering
Department for Motor Vehicles and Motors
Department of Civil Engineering
LISV
Deanship of Scientific Research - Imam Mohammad Ibn Saud Islamic University
Department of Energy Engineering
College of Engineering
Department of Mechanics

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026