Numerical Investigation of Heat Transfer in Simultaneously Developing Laminar Flow in a Circular Pipe
Belhocine A. Stojanovic N. Houari M.S.A. Merzouki T. Ben Hamida M.B. Abdullah O.I.
March 2026John Wiley and Sons Inc
Heat Transfer
2026#55Issue 21105 - 1124 pp.
This study involves the computational analysis of two-dimensional heat transfer through convective and laminar fluid flow in a circular pipe. The study considers simultaneously developing velocity and temperature profiles and takes into account boundary conditions such as a uniform temperature and constant heat flux. The physical characteristics of this flow are assumed to be constant, incompressible, and of Newtonian type. The governing equations that describe fluid flow, including continuity, momentum, and energy, have been presented in detail. Additionally, simplifying assumptions and associated boundary conditions have been included. These equations which govern the studied phenomenon are nonlinear partial differential equations (PDE). Therefore, we used the finite-difference scheme to integrate these equations by iterations after transforming them into a linear algebraic system. For this purpose, FORTRAN computer code has been well developed to simulate the thermal problem in a circular pipe and obtain the results presented in both cases. This allowed us to evaluate the rate of heat transfer, observe the velocity and temperature contours, and the distribution of Nusselt number, whether local or average. It also helped us determine various factors that affect thermal behavior. The findings indicate that the number of grid points N significantly influences the accuracy of the solution, thus affecting the accuracy of the temperature and velocity profiles. Moreover, the Prandtl number directly impacts the relationship between temperature and radial position. Finally, we conducted a comparative analysis for validation, and our results showed excellent agreement with previous studies. This further strengthens the reliability of the predictive model through simulation.
constant heat flux , explicit finite difference method , laminar flow , pipe , simultaneously developing flow , uniform wall temperature
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Department of Mechanical Engineering, Laboratory for the Study of Structures and Mechanics of Materials, University Mustapha Stambouli of Mascara, Mascara, Algeria
Faculty of Engineering, Department for Motor Vehicles and Motors, University of Kragujevac, Kragujevac, Serbia
Department of Civil Engineering, Laboratory for the Study of Structures and Mechanics of Materials, University Mustapha Stambouli of Mascara, Mascara, Algeria
LISV, University of Versailles Saint-Quentin, Vélizy, France
Higher School of Sciences and Technology of Hammam Sousse, University of Sousse, Tunisia
Deanship of Scientific Research—Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
Department of Energy Engineering, College of Engineering, University of Baghdad, Iraq
College of Engineering, Al Naji University, Baghdad, Iraq
Department of Mechanics, Al-Farabi Kazakh National University, Almaty, Kazakhstan
Department of Mechanical Engineering
Faculty of Engineering
Department of Civil Engineering
LISV
Higher School of Sciences and Technology of Hammam Sousse
Deanship of Scientific Research—Imam Mohammad Ibn Saud Islamic University
Department of Energy Engineering
College of Engineering
Department of Mechanics
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