An in-depth investigation into the flow and heat transfer characteristics of supercritical water (SCW) is essential for designing and operating Supercritical Water-Cooled Reactor (SCWR) systems. Currently, the great majority of existing direct numerical simulations (DNS) utilize boundary conditions without solid domain in studying the thermal-hydraulic performance of supercritical fluids. However, in practical applications, the fluid-solid conjugation may significantly affect the flow and heat transfer, especially in the near-wall region. The present study utilized a DNS solver implemented in OpenFOAM to examine the effect of fluid-solid conjugation on SCW in vertical and horizontal circular pipes. The wall temperature, mean velocity, instantaneous fluctuations, and turbulence statistics were compared and analyzed under both non-conjugate and conjugate conditions. It was found that in vertical upward flow with conjugate heat transfer, the wall temperature was slightly higher than that of non-conjugate heat transfer, leading to a more pronounced heat transfer deterioration. Temperature fluctuations at the wall were significantly suppressed by the solid domain, weakening the turbulence and heat transfer. In horizontal flows, under non-conjugate conditions, severe heat transfer deterioration occurred at the top generatrix due to buoyancy effects, resulting in a highly uneven circumferential distribution in the wall temperature. When the solid domain is taken into consideration, heat conduction within the solid domain redistributed the heat from the top to the sides, leading to a significant reduction in heat flux at the top. The decreased heat flux lowered the wall temperature and alleviated its uneven distribution, notably enhancing the heat transfer in the top region.