Steady non-Darcian natural convection in a square cavity filled with a heat-generating porous medium is studied numerically with the local thermal non-equilibrium model

with SIMPLER algorithm in the spatial coordinates.The top and bottom walls of the enclosure are adiabatic and the left and right walls are partially heated and cooled by sinusoidal temperature profile.The results show that the temperature fields near the left wall and local Nusselt number of left wall vary periodically because of the sinusoidal boundary condition.When the parameter N for temperature fluctuations is larger enough

the streamlines

temperature fields of fluid and solid in the enclosure are similar to the results when the temperature at boundaries are uniform

while the heat transfer is enhanced by the sinusoidal boundary conditions compared with the uniform temperature boundary conditions.