Numerical solution of flow and heat transfer of pulsating motions

Abstract

Studies are made of the unsteady flow and heat transfer characteristic in the laminar boundary layer when the flow contains a pulsating component. A Blasius flow and a pipe inside flow are considered individually. The complete, unsteady, boundary layer equations are solved by using a recentlydeveloped numerical solution procedure. A wide range of the key external parameters, i.e., the amplitude of pulsation (A) and the frequency parameter ($α[≡ωx^*/Ue]$ or $ β[≡R(ω/ν)^{1/2}]$), is dealt with in the present numerical computations. Comprehensive and systematically-organized numerical computational results have been acquired, which provide descriptions of the details of unsteady flow and thermal fields. The present numerical results indicate consistency with the available experimental data and the previous linearized analytical predictions. The time-averaged profiles of the flow and the temperature are substantially unaffected by the pulsating components, i.e., A and α (or β). The amplitudes and the phases of the fluctuating parts of these are nearly unaffected by the variations of the given oscillation amplitude, A. For Blasius flow containing pulsating component, the present computational results supply the details of the behavior of the skin friction and the heat transfer in the range of intermediate values of α and for finite values of A. And, for small values of α, both the skin friction and heat transfer are in phase with each other. However, as α increases, the conventional Reynolds analogy is shown to be inapplicable. For the pulsating flow in a pipe, the heat transfer which might be of great interest in engineering applications is seen to either increase or decrease over the steadyflow value depending on the frequency parameter in the downstream fullyestablished region. Such trend of the Nusselt number is amplified as A increases and when the Prandtl number is low below unity. These heat transfer characteristics are qualitatively consistent with the previ...