Three-Dimensional Natural Convection Experiments in an Enclosure

Abstract

This paper presents an experimental investigation for the phenomenon of three-dimensi onal natural convection inside a rectangular cavity driven by a single vertical wall with a warm and a cold region. The warm and the cold regions on this wall were located side-by-side. The remaining walls are adiabatic. The experiments focus on the high Rayleigh number regime (3 x 109 < Ra < 5 x 10 10). Apart from the region near the vertical driving wall and along the adjoining top and bottom surfaces close to the driving wall, the temperature field is remarkably two-dimensional, linearly stratified in the vertical direction. The fluid in the remainder of the enclosure is practically stagnant. The flow, wherever it exists, is laminar except for two small local turbulent regions near the top and bottom corners of the driving wall. Heat transfer results are correlated by Nu = 0.031 x Ra0-324. The study is concluded with a scaling analysis which aims to explain in a fundamental sense the experimental findings. Nomenclature cp = specific heat, J/kg K f(Rd) = function of Rayleigh number, Eq. (19) g = gravitational acceleration, m/s2 H = height of the enclosure, m k = thermal conductivity, W/mK L = length of the enclosure, m Nu = Nusselt number, Eq. (1) P = pressure, N/m2 Pb — power dissipated by bottom heater, W pt = power dissipated by top heater, W Q = heat transfer rate, W, Eq. (1) Ra = Rayleigh number, Eq. (2) Tc = cold wall temperature, K TH = hot wall temperature, K AT = temperature difference between cold and hot walls, K u = vertical velocity component, m/s v = horizontal velocity component, m/s W — width of the enclosure, m x = vertical coordinate, m y = horizontal coordinate, m a = thermal diffusivity, m2/s f$ = coefficient of volumetric thermal expansion, K1 dt = thermal boundary layer thickness, m v = kinematic viscosity, m2/s 0 = temperature scale of the core region, K (j) — temperature scale of the bottom layer of fluid, K p = density, kg/m3