A numerical analysis of developing flow and heat transfer in a curved annular pipe

Developing incompressible viscous fluid flow and heat transfer in a curved annular pipe is studied numerically. The governing equations consisting of continuity, full Navier–Stokes, and energy equations are solved using a projection method based on the second order central difference discretization. Considering the outer wall to be adiabatic, two different thermal boundary conditions involving constant temperature and constant heat flux are applied at the inner wall to analyze the heat transfer rate in the two different cases. The effects of governing non-dimensional parameters involving the aspect ratio, the curvature, Reynolds number, Dean number, and Prandtl number on the flow and temperature field both in developing and fully developed regions of the curved annular pipe are studied in detail. Two major different developing patterns of the flow are determined based on the location of maximum axial velocity either in the semi-inner or in the semi-outer region of the curved annular pipe. Also the numerical results obtained indicate that the friction factor and the Nusselt number in a curved annular pipe are both proportional to the square root of Dean number (κ1/2). At κ1/2⩽8 the friction factor for both curved and straight annular pipes are the same, beyond that it increases in the circular curved pipe by increasing Dean number and decreasing aspect ratio.