Non-linear interaction of buoyancy with von Kármán’s swirling flow in mixed convection above a heated rotating disc

Abstract

In this paper, a systematic computational and theoretical study of the thermo-fluid-dynamics governing the flow above a heated horizontal rotating disc is presented. The fluid flow field is much more complex here as compared to von Kármán’s original solution (which took into account only the effect of disc rotation), and the effects of non-linear interaction between buoyancy and rotation are critically analysed here by studying the separate and combined roles of disc rotation and buoyancy on the fluid dynamic and heat transfer characteristics. The self-similarity of von Kármán’s flow field is lost, and the present paper establishes, for the first time, that the flow field above a heated rotating disc is divided into three distinct fluid dynamic regions. The three regions are demarcated by the loci of V̂z=0 and V̂r=0. In region 1 (R-1), V̂r is positive and V̂z is negative (such directions of the velocity components are characteristic of von Kármán’s flow or pure forced convection). In region 2 (R-2), V̂r is negative and V̂z is positive (such directions of the velocity components are characteristic of pure natural convection near a static disc surface). In region 3 (R-3), both V̂r and V̂z are negative. The forced convection results are obtained asymptotically at a large non-dimensional radius R within the region R-1 showing the dominance of forced convection mechanism, however, the fluid retains the signature of natural convection even at large values of R in the region R-3 where there is an inward radial velocity. Similarly, although a plume forms in the central portion of the disc where the solution is dominated by the effects of buoyancy, the fluid retains a signature of the disc rotation in the helical pathlines of fluid particles rising in the plume (whereas there is no swirl velocity present in pure natural convection above a static disc). The non-linear interaction between buoyancy and rotation results in several peculiar, rather non-intuitive, flow phenomena. Examples of such peculiarity include (i) the presence of a very sensitive spot on the upper boundary such that for a small change in this initial position the fluid pathlines may face drastically different final outcomes, (ii) the presence of a small portion near the centre of the disc where the fluid supplies energy to the disc, (iii) the effect of rotation on the rate of convective heat transfer being diminished by buoyancy over certain part of the disc while being enhanced over another part. This non-linear effect on Nusselt number is quantified here in terms of a Grashof number defined for mixed convection (Grmc).