Mathematical Modeling of Fluid Flow and Heat Transfer in the Laminar Entrance Region of a Cylindrical Pipe

This study conducted a numerical simulation of laminar flow within a cylindrical pipe using a semi-implicit method. The full Navier–Stokes equations in cylindrical coordinates were solved, with modifications to the SIMPLE algorithm to handle pressure-linked equations. We evaluated three key thermophysical parameters—dynamic viscosity, specific heat capacity, and thermal conductivity—under both constant and variable conditions in the entrance region. Due to the process’s two-dimensional, time-dependent nature, third-kind boundary conditions were used to accurately model the effects of ambient temperature, external wind, and the pipe’s geometric and physical features. From the numerical results, we analyzed the velocity field, pressure distribution, surface friction coefficient, and temperature distribution at various pipe cross-sections. These findings are of practical and scientific importance: they offer insights into the hydrodynamics and thermal behavior of the internal flow and enhance understanding of fluid flow and heat transfer, improving predictive models. This advancement supports better design and operational control in pipeline systems.