Numerical Analysis of Heat Transfer in Simultaneously Developing Laminar Flow in a Plane Duct With Constant Wall Temperature and Heat Flux Boundary Conditions

The present study concerns, from the angle of numerical simulation, a laminar flow in a plane duct with simultaneously developing velocity and temperature profiles. It is assumed that the fluid is Newtonian, viscous, and incompressible, with uniform and constant physical properties. The problem of laminar flow heat transfer is analyzed for both constant wall temperature and uniform wall heat flux boundary conditions. The basic equations governing the flow, including continuity, momentum, and energy, are solved numerically. Dimensionless variables are introduced to simplify the proposed procedure, and an explicit finite-difference method is used to discretize the equations. The resulting computational method allows for the prediction of thermal behavior on an isothermal surface and under constant flux of certain parameters, such as velocity, temperature, and the Nusselt number. These results are presented graphically and discussed, highlighting the effect of certain variables on the outcome. Finally, a comparison is made with previous work, demonstrating good agreement.