Heat Transfer Simulation of Simultaneously Developing Laminar Flow in a Plane Duct

In this study, we performed a numerical simulation of two-dimensional laminar fluid flow and heat transfer in a plane duct, where the temperature and velocity fields are simultaneously developed under both uniform wall temperature and constant heat flux boundary conditions. To formulate the problem mathematically, we utilized the continuity, momentum, and energy equations, incorporating dimensionless variables to simplify our approach. Next, we used an explicit finite difference method scheme to discretize these equations, reducing the problem to numerically integrating a system of coupled nonlinear ordinary differential equations, which can be easily programmed in FORTRAN. The computational algorithm accurately predicts all thermal properties, including velocity, temperature, and both mean and local Nusselt number, in cases where wall temperature and wall heat flux are held constant. The obtained numerical results were represented in figures and analyzed separately for the two different wall conditions, demonstrating the effect of some variables on the behavior, such as the Prandtl number and the number of grid points selected. Regarding validation, the accuracy of the numerical solution was checked by comparing the results of local Nusselt numbers with results found in existing literature, demonstrating a much better agreement between the models.