Application of the Random Vortex Method to Natural Convection Heat Transfer from an Open Channel

Abstract

Natural convection flows in channels have been studied using numerical tools such as finite difference and finite element techniques. These techniques are much demanding in computer skills and memory. Random Vortex Element method which has been used successfully in fluid flow was adopted in this work in view of its relative simplicity. The simulation was carried out for conditions wherein Rayleigh Number is in the range of 1036 and 10 and channel aspect ratio in the range of 0.03 to 0.2.Both vertical and inclined channels were treated. In the case of the inclined channel, inclination angle to the horizontal was varied between 0° and 90°. The temperature and velocity distributions obtained for each of the cases was used to compute the Nusselt Numbers. A logarithmic plot of obtained Nusselt number against Rayleigh number yielded a slope of 0.22 and an intercept of –0.37 for the vertical channel. Comparative finite element solution from literature yielded a slope of 0.26 and an intercept of –0.16. Nusselt number also increased with angle of inclination up to 90º when investigated in inclined channels Investigation of the velocity distributions along the axis of the channel showed that the fluid is faster at the top of the channel than the bottom. For channel width in the range of 0.03m to 0.05m normal dome-like parabolic velocity profiles were obtained , while widths above 0.05m had dome-like parabolic velocity profiles with the middle sagged. For all range of widths the temperature profiles are inverted parabolic.This study apart from demonstrating the applicability of the random vortex method , thus showed that maximum natural convective heat transfer occurred when the channel is vertical (i.e. angle of inclination is 90º).

Keywords: Heat Transfer, Natural Convection, Simulation, Vortex Method, Channel