Numerical Solution of Simultaneously Developing Laminar Flow in a Plane Duct with Uniform Wall Temperature and Constant Heat Flux

The present study concerns, from the angle of numerical simulation, the case of a laminar flow in a plane duct with simultaneously developing velocity and temperature profiles. We considered that the fluid is Newtonian, viscous, and incompressible with uniform and constant physical properties. We analyzed the problem of laminar flow heat transfer for both constant wall temperature and uniform wall heat flux boundary conditions. The basic equations which describe the flow model are the classical equations of continuity, momentum, and energy that we used here. To accomplish this, we carried out a numerical solution of the governing equations that describe this flow. We introduced dimensionless variables to simplify the proposed procedure and discretized these equations using an explicit finite difference method. The computational method allowed us to predict thermal behavior on an isothermal surface and in constant flux of certain parameters, velocity, temperature, and the Nusselt number, which were discussed graphically and highlighted the effect of certain variables on the achieved results. Finally, our results were compared to those of other works and found to be in good agreement.