Numerical solution of the heat transfer problem in a short channel with backward-facing step

A test problem of the laminar steady incompressible flow and heat transfer over backward-facing step in a $\mathrm{2D}$ short channel is presented. The focus of the study is on the changes in heat transfer characteristics of the flow field inside the channel due to different boundary conditions for heat flux at the outflow border of the domain. The Navier–Stokes equations in a velocity-pressure formulation and energy equation are numerically solved using a uniform grid of $6001\times301$ points. The control-volume technique for the second-order difference approximation for spatial derivatives is used. The solutions were validated for a wide range of Reynolds numbers $(100 \leq \text{Re} \leq 1000)$ and Prandtl number $\text{Pr} = 0.71$, comparing them to experimental and numerical results found in the literature. The isotherm patterns and behaviors of Nusselt number along the heated bottom wall of the channel are examined. The study results showed that a condition for the heat flow (temperature) at the outlet border can influence the heat transfer in the whole domain. The nonlinear boundary condition for temperature at the outflow border is claimed as the best.