On the solution of fluid flow and heat transfer problem in a 2D channel with backward-facing step

The stable stationary solutions of the test problem of hydrodynamics and heat transfer in a plane channel with the backward-facing step have been considered in the work for extremely high Reynolds numbers and expansion ratio of the stream $ER$. The problem has been solved by numerical integration of the 2D Navier–Stokes equations in ‘velocity-pressure’ formulation and the heat equation in the range of Reynolds number $500 \leqslant \mathrm{ Re} \leqslant 3000$ and expansion ratio $1.43 \leqslant ER \leqslant 10$ for Prandtl number $\mathrm{ Pr} = 0.71$. Validity of the results has been confirmed by comparing them with literature data. Detailed flow patterns, fields of stream overheating, and profiles of horizontal component of velocity and relative overheating of flow in the cross section of the channel have been presented. Complex behaviors of the coefficients of friction, hydrodynamic resistance and heat transfer (Nusselt number) along the channel depending on the problem parameters have been analyzed.