Boundary layer development on a semi-infinite suddenly heated vertical plate

Abstract

The flow resulting from suddenly heating a semi-infinite, vertical wall immersed in a stationary fluid has been described in the following way: at any fixed position on the plate, the flow is initially described as one-dimensional and unsteady, as though the plate is doubly infinite; at some later time, which depends on the position, a transition occurs in the flow, known as the leading-edge effect (LEE), and the flow becomes two-dimensional and steady. The transition is characterized by the presence of oscillatory behaviour in the flow parameters, and moves with a speed greater than the maximum fluid velocities present in the boundary layer. A stability analysis of the one-dimensional boundary layer flow performed by Armfield & Patterson (1992) showed that the arrival times of the LEE determined by numerical experiment were predicted well by the speed of the fastest travelling waves arising from a perturbation of the initial one-dimensional flow. In this paper, we describe an experimental investigation of the transient behaviour of the boundary layer on a suddenly heated semi-infinite plate for a range of Rayleigh and Prandtl numbers. The experimental results confirm that the arrival times of the LEE at specific locations along the plate, relatively close to the leading edge, are predicted well by the Armfield & Patterson theory. Further, the periods of the oscillations observed following the LEE are consistent with the period of the maximally amplified waves calculated from the stability result. The experiments also confirm the presence of an alternative mechanism for the transition from one-dimensional to two-dimensional flow, which occurs in advance of the arrival of the LEE at positions further from the leading edge.

An experimental study of the unsteady thermal flow around a thin fin on a sidewall of a differentially heated cavity

“…Armfield and Patterson (1992) in an analytical and numerical study demonstrated that the speed of the LEE was better estimated by the maximum speed of travelling waves initiated by the perturbation at the leading edge on start up. This was supported by the experiments of Patterson et al (2002). Much of this work was in the context of isothermal wall boundary conditions.…”

“…12a shows the temperature time series measured by Thermistors 1 and 4 in the boundary layer at early times (up to 60 s). The features of the LEE are clear, which are characterized by an overshoot followed by a group of travelling waves (Patterson et al, 2002). Subsequently, the temperature measured by Thermistor 1 approaches an approximate constant, whereas the temperature measured by Thermistor 4 remains approximately constant for a short while until it is perturbed by the impact of the plume front from the thermal flow around the fin.…”

“…It is expected that the temperature signals taken at the same distance from the heated sidewall would be identical prior to the arrival of the LEE at the respective locations. The variation of the initial temperature growth at the two different locations may be attributed to a small variation of the actual distance from the wall, which could lead to a large variation of the measured temperature due to the existence of a very high lateral temperature gradient in the thermal boundary layer (Patterson et al, 2002).…”

“…Lin and Armfield, 2005;Xu et al, 2005;Lin et al, 2007). The relevance of the behaviour of the boundary layer on a semi-infinite plate to that on the heated wall of a cavity was identified numerically by Patterson and Armfield (1990), Schladow (1990) and Armfield and Patterson (1992), and experimentally by Schö pf and Patterson (1995) and Patterson et al (2002).…”

Dynamic and heat transfer of a Pr < 1 thermal flow around a fin on the thermal wall

“…For sudden heating and cooling, the development of natural convection flows in the cavity is classified into three stages: an initial stage, a transitional stage and a fully developed stage [2,5,6]. In the initial stage, a thermal boundary layer forms adjacent to the sidewall, and the leading edge effect (LEE) occurs in the thermal boundary layer due to the presence of the leading edge of the sidewall [7][8][9][10]. After the LEE is convected, the development of natural convection flows in the cavity enters the transitional stage.…”