The fully developed laminar flow within a reentrant groove has been analyzed using a finite element model. A parametric analysis was carried out to determine the Poiseuille number Po = fRe, the dimensionless mean velocity v * , and the dimensionless volumetric flow rateV * as functions of the geometry of the reentrant groove (groove height 1.0 < -H * < -4.0, slot half-width 0.05 < -W * /2 < -0.9, and fillet radius 0.0 < -R * f < -1.0), and the liquid-vapor shear stress (0.0 < -− −τ * lv < -2.5). The case in which the meniscus recedes into the reentrant groove was examined and could be a result of evaporator dryout or insufficient liquid fill amount. The cross-sectional area of the liquid in the groove, A * l , the meniscus radius R * m , and the aforementioned flow variables were calculated as functions of the meniscus contact angle (0 < -φ < -40 deg) and the meniscus attachment point (0.0 < -H * l < -2.75). Finally, the results of the numerical model were used to determine the capillary limit of a low-temperature heat pipe with two different working fluids, water and ethanol, for a range of meniscus contact angles.
Nomenclaturecenter of circular portion of reentrant groove to top of slot, m H l = vertical location of attachment point of meniscus to reentrant groove wall, m H l,s = vertical location of attachment point of meniscus to sinusoidal groove wall, m H s = height of sinusoidal groove, m H tr = height of trapezoidal groove, m H * = H/R H * l = H l /R h f g = heat of vaporization, J/kg K = thermal conductivity, W/(m · K) L a = adiabatic length, m L c = condenser length, m L e = evaporator length, m L eff = effective heat pipe length, L e /2 + L a + L c /2, m N g = number of grooves n = coordinate normal to the liquid-vapor interface n * = n/R P = wetted perimeter, m Po = Poiseuille number, f Re P * = P/R = pressure, N/m 2 Q cap = capillary limit heat transport, Ẇ Q g = heat transfer due to a single groove, Ẇ Q t = total heat transported, N gQ g , W q lv = heat flux at the liquid-vapor interface, W/m 2 q * lv = q lv /q R q = internal volumetric heat generation, W/m 3 R = radius of circular portion of reentrant groove, m Re = Reynolds number, ρv D h /µ R f = radius of fillet, m R m = radius of meniscus, m R v = radius of heat pipe vapor space, m R * fwidth of slot, m W l = width of liquid meniscus at attachment point to reentrant groove wall, m W l,s = width of liquid meniscus at attachment point to sinusoidal groove wall, m W s = width of sinusoidal groove, m W tr = width of trapezoidal groove, m W * = W/R W * l = W l /R x, y, z = Cartesian coordinate directions x f,0 , z f,0 = location of center point of circular fillet, m x t , z t = point of tangency of fillet and circular portion of reentrant groove, m x * , y * , z * = x/R, y/R, z/R x * f,0circular segment duct half-angle, rad 395 Downloaded by MONASH UNIVERSITY on February 3, 2015 | http://arc.aiaa.org | 396 THOMAS AND DAMLEβ = aspect ratio for rectangular and trapezoidal grooves, 2H r /W r or 2H tr /W tr γ = triangular groove half-angle, rad θ = trap...