Thermal boundary-layer structure in laminar horizontal convection

Abstract

Abstract We present experimentally obtained time-averaged vertical temperature profiles $\\theta (z)$ in horizontal convection (HC) in water (Prandtl number $Pr \\simeq 6$), which were measured near the heating and cooling plates that are embedded in the bottom of HC samples. Three HC rectangular samples of different sizes but the same aspect ratio $\\varGamma \\equiv L:W:H = 10:1:1$ ($L$, $W$ and $H$ are the length, width and height of the sample, respectively) were used in the experiments, which allowed us to study HC in a Rayleigh-number range $2 \\times 10^{10} \\lesssim {Ra} \\lesssim 9 \\times 10^{12}$. The measurements revealed that above the cooling plate, the mean temperature profiles have a universal scaling form $\\theta (z/\\lambda _c)$ with $\\lambda _c$ being a $Ra$-dependent thickness of the cold thermal boundary layer (BL). The $\\theta (z/\\lambda _c)$-profiles agree well with solutions to a laminar BL equation in HC, which is derived under assumption that the large-scale horizontal velocity achieves its maximum near the plate and vanishes in the bulk. Above the heating plate, the mean temperature field has a double-layer structure: in the lower layer, the $\\theta$ profiles scale with the hot thermal BL thickness $\\lambda _h$, while in the upper layer, they again scale with $\\lambda _c$. Both scaling forms are in good agreement with the solutions to the BL equation with a proper parameter choice.