forced turbulent heat convection in a square duct with non-uniform wall temperature

in the present work, the numerical simulation to calculate the problem of the turbulent convection with non-uniform wall temperature in a square cross-section duct was adopted. to solve this problem some assumptions for the flow, such as: the condition of fully developed turbulence and incompressible flow have been assumed. the methodology of the dimensionless energy equation was used to calculate the fluid temperature field in the square cross-section in function of the non-uniform wall temperatures prescribed. numerical simulations were done using two different turbulent models to resolve the momentum equations and two more models to resolve the energy equation. the models of turbulence k–ε nonlinear eddy viscosity model (nlevm) and the reynolds stress model (rsm) were used to determine the turbulent intensities as well as the profiles of axial and secondary mean velocities. the turbulence model rsm was simulated using a commercial software. the thermal field was determined from other two models: simple eddy diffusivity (sed), based in the hypothesis of the constant turbulent prandtl number; and generalized gradient diffusion hypothesis (ggdh). in this last model, as the turbulent heat transfer depends on the shear tensions, the anisotropy is considered. these two last equation models of the energy equation of the fluid have been implemented in fortran, a code of programming. the performances of the models were evaluated by validating them based in the experimental and numerical results published in the literature. two important parameters of great interest in engineering are presented: the friction factor and the nusselt number. the results of this investigation allow the evaluation of the behavior of the turbulent flow and convective heat fluxes for different square cross-sectional sections throughout the direction of the main flow, which is mainly influenced by the temperature distribution in the wall.