Abstract
Abstract This paper is a Direct Numerical Simulation (DNS) of the temperature distribution in the flow with the forward and backward facing steps with buoyancy forces for different lengths of the bottom walls and flow regimes. The different lengths of the bottom walls effect were studied with buoyancy forces. A two-dimensional incompressible Navier–Stokes equation and equations for temperature transfer were used to describe this process. The obtained numerical solutions for the test problem, laminar flow with the backward facing step with buoyancy force, are compared with the numerical results of other authors. A verified numerical algorithm is applied to the problem with the forward and backward facing steps with buoyancy forces. The influence of changes in the bottom wall length on temperature distributions and velocity components is revealed. It was also revealed that the heat transfer characteristics of the bottom wall have strong changes in different lengths. In cases for the lengths of the bottom walls ( X e = 12 , 16 ${X_e} = 12, \,16$ ) at Re=1,000, the rotational movement of the vortices along the channel wall revealed an increase in the exchange of cold and hot fluids, which leads to temperature fluctuations from the lower wall to the upper wall of the channel.