Numerical Investigation of Heat Transfer in Simultaneously Developing Laminar Flow in a Circular Pipe

ABSTRACT 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.