The current bipolar-toroidal coordinate system is restricted by its geometrical limitations in which the curvature is a function of eccentricity and radius ratio. In addition, the inner tube is located just on symmetry line in inner bend. The aim of present study is to modify the current coordinate system to take into account any radius of curvature and inner tube angular position independently and then investigate the fluid flow and its thermal characteristics. To do so, metric is obtained and governing equations including the continuity, full Navier-Stokes and energy equations are derived. Using a second-order finite difference method, these equations are solved on the basis of the projection algorithm under hydrodynamic and thermal developing assumptions. The inner and outer walls are maintained at constant and ambient temperatures, respectively. Finally, the effect of non-dimensional parameters such as the Dean, Reynolds and Prandtl numbers, eccentricity and inner tube angular position are investigated. The obtained results show that eccentricity and Dean number increasing significantly deforms the velocity field and the secondary flow field. Moreover, it has been found that increasing eccentricity intensifies the Nusselt number. Furthermore, changing the angular position of inner tube can increase the heat transfer rate.