Vortex Instability of Free Convection Flow Over Horizontal and Inclined Surfaces

Abstract

The vortex instability characteristics of laminar free convection flow over horizontal and inclined isothermal surfaces are studied analytically by linear theory. As a prelude to the analysis, the effects of the angle of inclination on the main flow and thermal fields are re-examined by a new approach. Numerical results are presented for wall shear stress, surface heat transfer, neutral stability curve, and critical Grashof number for Prandtl numbers of 0.7 and 7 over a wide range of angles of inclination, φ, from the horizontal. It is found that as the angle of inclination increases the rate of surface heat transfer increases, whereas the susceptibility of the flow to the vortex mode of instability decreases. The present study provides new vortex instability results for small angles of inclination (φ≤30 deg) and more accurate results for large angles of inclination (φ ≥ 30 deg) than previous studies. The present results are also compared with available wave instability results.

The influence of higher order effects on the vortex instability of thermal boundary layer flow in a wedge-shaped domain

“…We now make the same assumption as [4][5][6] and assume that marginal stability corresponds to where there is no streamwise variation with x, and that the onset of vortices is stationary in time. Therefore, we assume that the vortices are functions solely of y and z, and that they are periodic in the spanwise direction z. Consequently, the disturbance quantitiesû,v,ŵ,θ, andp may be Fourier decomposed usinĝ…”

“…But rather we are concerned with the effect on the vortex stability criterion of the induced flow which is external to the boundary layer itself. Haaland and Sparrow [4], Chen and Tzuoo [5], and Kahawita and Meroney [6] used the leading order boundary layer flow as the basic flow to analyse stability. Thus their analyses take no account of the overall shape of the flow domain.…”

Numerical simulation of fluid flow and heat transfer in a plasma spray gun

“…However, the majority of the research on natural convection has been reported since the early 1980s. For the purpose of understanding flow patterns and heat transfer near a wall, a theoretical analysis of vortex instability over horizontal and inclined heated surfaces is reported by Chen and Tzuoo [3]. However, few experiments have been done to in order to understand the heat transfer mechanism of the cooling in a plasma spray gun, which is a very complicated process due to the fact that there are no efficient ways to measure the temperature within the gun.…”

Thermal receptivity of free convective flow from a heated vertical surface: Linear waves

“…Examples of such situations include the classical Bénard convection problem, and boundary layer flows over inclined heated surfaces. For the latter example the primary mode of instability takes the form of longitudinal vortices in the direction of the induced basic flow (see Haaland and Sparrow [1] and Chen and Tzuoo [2]). On the other hand, for free convection boundary layer flow over a vertical heated surface, buoyancy forces generate the basic flow, but the primary instability is known to be hydrodynamic in origin.…”