Numerical solutions of pulsating flow and heat transfer characteristics in a pipe

Numerical studies are made of flow and heat transfer characteristics of a pulsating flow in a pipe. Complete time-dependent laminar boundary-layer equations are solved numerically over broad ranges of the parameter spaces, i.e., the frequency parameter β and the amplitude of oscillation A. Recently developed numerical solution procedures for unsteady boundary-layer equations are utilized. The capabilities of the present numerical model are satisfactorily tested by comparing the instantaenous axial velocities with the existing data in various parameters. The time-mean axial velocity profiles are substantially unaffected by the changes in β and A. For high frequencies, the prominent effect of pulsations is felt principally in a thin layer near the solid wall. Skin friction is generally greateer than that of a steady flow. The influence of oscillation on skin friction is appreciable both in terms of magnitude and phase relation. Numerical results for temperature are analyzed to reveal significant heat transfer characteristics. In the downstream fully established region, the Nusselt number either increases or decreases over the steady-flow value, depending on the frequency parameter, although the deviations from the steady values are rather small in magnitude for the parameter ranges computed. The Nusselt number trend is amplified as A increases and when the Prandtl number is low below unity. These heat transfer characteristics are qualitatively consistent with previous theoretical predictions.