Numerical and experimental investigation of laminar free convection around a thin wire: Long time scalings and assessment of numerical approach

Abstract

Transient and steady free convection around a line heat source is studied experimentally and numerically. Experiments are performed with a thin platinum wire of 50 μm in radius immersed in water and heated by Joule effect. Time evolution of velocity and temperature fields are measured by PIV (Particle Image Velocimetry) and micro-thermocouple for three different heating rates. Numerical simulations are done using a time-stepping algorithm based on a velocity–pressure formulation. The equations are discretized on a domain of limited extension, using spectral type approximations and a domain decomposition technique, and a pressure condition is imposed at the outer boundary. A three-stage scenario is proposed for the development of transient free convection around a thin wire, and, at each stage, the numerical approach is assessed through detailed comparison between numerical and experimental results. Previously established scaling laws for the onset of convective motion are checked for long time behavior. Numerical and experimental results confirm that these laws remain meaningful at long time and a qualitative similarity is observed for the transients. In addition, a steady case of a heated wire in air is studied and compared with the experimental study of Brodowicz and Kierkus [Brodowicz, K., Kierkus, W., 1966. Experimental investigation of free-convection in air above horizontal wire with constant flux. Int. J. Heat Mass Trans. 9, 81–94]. Despite a wire superheat of 210 K, good agreement is observed between the experiment and numerical simulations performed under the Boussinesq assumption. In particular, numerical simulations match with the scaling laws of the far-field above the wire.