  Using molecular dynamics simulations, we study supercritical fluids near the
gas-liquid critical point under heat flow in two dimensions. We calculate the
steady-state temperature and density profiles. The resultant thermal
conductivity exhibits critical singularity in agreement with the mode-coupling
theory in two dimensions. We also calculate distributions of the momentum and
heat fluxes at fixed density. They indicate that liquid-like (entropy-poor)
clusters move toward the warmer boundary and gas-like (entropy-rich) regions
move toward the cooler boundary in a temperature gradient. This counterflow
results in critical enhancement of the thermal conductivity.
