Effect of free-stream fluctuations on laminar forced convection from a straight tube

The effect of free-stream fluctuations on forced convection heat transfer from a straight tube of circular cross-section is investigated. The tube is assumed to have an isothermal surface and is placed in an unsteady but uniform cross stream. The free-stream fluctuations are represented by periodic (sinusoidal) fluctuations superimposed on the average stream velocity. The resulting unsteady velocity and thermal fields are obtained by solving the conservation equations of mass, momentum and energy. The main parameters involved are Reynolds number, Strouhal number, Prandtl number and the relative amplitude of fluctuations. The paper focuses on the effects of the amplitude and frequency of free-stream fluctuations on the local and average Nusselt numbers while keeping Prandtl number unchanged (Pr = 0.7). The average flow Reynolds number ranges from 50 to 500, the Strouhal number ranges from π/4 to π and the amplitude ranges from 20 to 50% of the free-stream average velocity. The study revealed that the effect of fluctuations on the time-average Nusselt number becomes more pronounced with increasing Reynolds number. It also revealed that the rate of heat transfer increases with the increase of the amplitude but decreases with the increase of frequency. The time-average Nusselt number is tabulated for all cases studied and the details of flow and thermal fields are presented in the form of local Nusselt number and surface vorticity distributions as well as streamline and temperature contours for some selected cases.