PULSATING FLOW AND HEAT TRANSFER IN CURVED TUBES.

摘要

Curved tube heat transfer in pulsating fully developed laminar flow of an incompressible, viscous Newtonian fluid with constant properties is studied. The thermal boundary condition of axially uniform heat flux and peripherally uniform wall temperature is considered.;This work presents the first numerical solution for pulsating flow and heat transfer in curved tubes. The parameter ranges are: Dean number De from 12 to 294; frequency parameter (alpha) from 15 to 1, the pressure gradient ratio (ratio of the maximum amplitude of oscillating component to the steady component of the pressure gradient) k 0.5,1.0, and 1.5, and Prandtl number Pr from 0.005 to 5.0 . The Dean number is defined in terms of the Reynolds number which is based on the flow produced by the steady component of the pressure gradient alone. In fact, the instantaneous Dean number can fluctuate widely during a cycle depending on (alpha) and k. This Dean number range is large compared with that previously considered in the literature for pulsating flows.;The finite difference form of the governing equations are solved numerically using the Alternating Direction Implicit method (ADI). The major difficulty associated with the unknown initial conditions is surmounted by starting the solution from frozen conditions (high (alpha)) and moving down to solve for lower (alpha).;Detailed information is obtained on the nature of the velocity and the temperature fields. The variation of the local shear stresses and Nusselt number around the periphery and with time is, also, obtained.;The flow equations are written using toroidal geometry and in terms of vorticity, stream function, and axial velocity. No restrictions are made on the tube curvature although the coil pitch effects are neglected.;It is concluded that, for this range of parameters, the effects of pulsation on the local values and the peripheral distribution of shear stresses and Nusselt number are significant. However, the time averaged peripherally averaged shear stresses and Nusselt number are not significantly effected by pulsation unless the frequency parameter (alpha) is low and the pressure ratio k is high ( > 1.0). For these conditions, where flow reversal occurs, the time averaged peripherally averaged Nusselt number decreases significantly (88% from high (alpha) and low k results), whereas, it slightly decreases (10%) if the Prandtl number is high.