Numerical simulation of fully developed laminar flow and heat transfer in a circular pipe

Abstract

This work involves the computational analysis of two-dimensional heat transfer through convection and laminar flow of a fluid. The application was conducted on a circular pipe with fully developed laminar flow, taking into consideration boundary conditions such as the wall’s uniform temperature and constant heat flux. The physical characteristics of this flow are assumed to be constant and of an incompressible and Newtonian type. The governing equations describing fluid flow, namely, energy, as well as simplifying assumptions and their associated boundary conditions, have been presented in detail. Equations that govern the studied phenomenon are non-linear partial differential equations (PDEs). Therefore, the authors implemented the finite-difference scheme to integrate these equations through iterations. This involves transforming the equations into a linear algebraic system. For this purpose, FORTRAN computer code has been developed to effectively simulate thermal problems in circular pipes and obtain the results for both cases. This allowed for the evaluation of thermal transfer rates, observation of velocity and temperature contours and determination of the distribution of Nusselt numbers, both local and average. In addition, various factors that influence thermal behavior were identified. The development of this code has provided a comprehensive tool for studying thermal behavior in circular pipes. Finally, the authors conducted a comparative analysis for validation, and the results showed excellent agreement with previous studies. The innovation of using an explicit finite difference method (FDM) in FORTRAN to solve the problem centers on computationally tracking the development of the thermal boundary layer without relying on complex, slowly converging infinite series of eigenvalues. An FDM model bypasses this by smoothly moving down the grid to yield localized temperature and heat flux distributions. The innovation involves translating the parabolic PDE into an explicit code. This is achieved by applying the stability condition and an algorithm that easily integrates the nonlinear boundary conditions, resulting in a numerical solution that can be quickly obtained.