This paper presents a numerical study of heat transfer through a downstream annulus using water as the working fluid within the laminar flow region. The annulus consisted of an outer twisted square duct and an inner circular pipe. A three-dimensional formulation was used to solve the Navier-Stokes equations numerically for the laminar flow system with a low Reynolds number. Three parameters were used in the numerical simulation: the length of the twisted square (a: 6.6, 8.2 10.2, 12.6 mm) the inner diameter of the inner circular pipe (d: 19, 21, 23 and 25 mm); and the twist angle (θ: 0° (smooth), 45°, 60°, and 90°). Numerical calculations were conducted on sixteen twisted square duct heat exchangers, with water flowing within a Reynolds number range of 220 – 1100. The results were illustrated as a profile of the thermal enhancement factor, the friction factor and the Nusselt number. The results show that the twisted outer duct of the heat exchanger can create a swirl flow along the length of the heat exchanger. It also caused a boundary layer separation-reattachment on the wall of the inner pipe. Moreover, an increase in the twist angle increased the Nusselt number by 20 %, and the friction factor was also increased as the annular gap of the heat exchanger decreased.