Evaporating extended meniscus in a V-shaped channel

Abstract

A mathematical model of the evaporating extended meniscus in a V-shaped channel was developed to investigate the effect of wedge half-angle and vapor mass transfer on meniscus morphology, fluid flow, and heat transfer. The liquid was unsaturated, flowed down the wedge due to gravity, and evaporated into atmospheric air. The average Nusselt number was found to decrease as the wedge half-angle increased, primarily because of an increase in the average wall-interface temperature difference. The mean curvature changed from zero at the interline to a constant, at a distance approximately three times the adsorbed layer thickness from the wall. The capillary pressure calculated from first principles was nearly twice as large as that determined from a semicircular approximation of the mean curvature. We believe that this was partially due to the presence of the van der Waals attraction near the wall. Downstream from the inlet, both thermocapillary convection and pressure recovery in the liquid caused the interline to move downward toward the wedge apex and then upward away from the apex until the piezometric pressure gradient was equal to zero. The locus of liquid dry out points were estimated based on axial locations where the piezometric pressure gradient was equal to zero; this represented a point of zero flow in the channel. As expected, the points where dry out occurred, moved closer to the inlet as the surface mass flux was increased. Nomenclature a = aspect ratio, r 0 /L Ca = capillary number E = evaporation number F = surface mass transfer number G = arc-length function g = gravity vector H = mean curvature of the vapor-liquid interface h = heat transfer coefficient at a given axial location /z ave = average heat transfer coefficient h fg = latent heat of vaporization h m = mass transfer coefficient / = identity tensor / = mass flux at the interface k = thermal conductivity in the liquid M = Marangoni number M A = magnitude of the normal vector MI = magnitude of the tangent vector m = summation index Nw ave = average Nusselt number h = unit normal vector to the interface pointing into the vapor phase P = pressure Pr = Prandtl number R = radial location of the vapor-liquid interfacê va P = g as constant divided by the molecular weight of the vapor r = radial spatial coordinate r 0 = interline location at the wedge inlet T = temperature i = unit tangent vector to the interface u = radial velocity v = azimuthal velocity v = velocity vector w = axial velocity z = axial spatial coordinate z steps = number of steps in the axial direction V = gradient operator a = wedge half-angle /3= wedge inclination angle with respect to the gravity vector y = change in surface tension with respect to temperature Ar = radial spatial increment Az = axial spatial increment A0 = azimuthal spatial increment 8 = adsorbed layer thickness l* r = unit vector in the radial direction j) z = unit vector in the axial direction 8 e = unit vector in the azimuthal direction e = azimuthal coordinate with an origin at the wall, a -0 £ 0 = angle assoc...

Theoretical investigation on the thermal prformance of flat two-phase heat spreaders with microchannels

“…Three zones are considered: a zone of very small thickness where the fluid is adsorbed on the wall in equilibrium phase, a zone where the curvature radius is variable (microregion) and a zone where the curvature radius is constant (macroregion). Many studies ((Kamotani [26], Holm and Goplen [27], Stephan and Büsse [28], Swanson and Peterson [29], Khrustalev and Faghri [30], Ma and Peterson [31]) were developed to solve this problem numerically. In these studies, the models of microregion and macroregion don't consider the axial flow along the microchannel.…”

Heat and Mass Transfer in Capillary-Pumped Liquid Films in Square Cross-Section Minichannels

“…Swanson and Peterson [28] also studied the evaporating meniscus and concluded that the region that dominates heat power removal is an open question.…”

“…For many years, liquid-vapor phase change has been investigated in grooves or channels of various cross-sections [23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Most authors consider that the meniscus is divided into the following three regions: the intrinsic meniscus region, dominated by capillary forces; the evaporating thin film region, in which effects of both capillary and the disjoining pressure are present; and the adsorbed layer region, where the disjoining forces dominate.…”

Experimental study on film combustion formed by spirally fluted horizontal tube

“…Because of the surfacetension and the flow characteristics of the liquid on the smooth wall, it is difficult to obtain a uniform fuel film formation under low pressure and low speed fuel flow. Many researches have been conducted on the possibility of a liquid film on the surface of the combustor to determine the corresponding methods to provide better fuel and air mixture formation under lower fuel flowrate in micro-combustors [2].…”