Fluid Flow in Axial Reentrant Grooves with Application to Heat Pipes

Abstract

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...

Investigation on Microheat Pipe Array with Arteries

“…The friction between liquid and substrate is described in Eq. (7) with no concern about the friction between liquid and vapor. The differential form of liquid velocity and radius of meniscus can be obtained from the Eqs.…”

“…1b and 1c. Besides those different designs of cross section of MHP, several different grooves were also proposed and fabricated with metal material as substrate, such as OMEGA groove [7,8] and swallow tailed groove [9], which can enhance the thermal performance of heat pipe. Unfortunately, it seems impossible to apply in our silicon-based MHP due to the difficulties of fabrication processes.…”

Evaporative Heat Transfer Analysis of a Heat Pipe With Hybrid Axial Groove

“…This causes the liquid fill amount inside the liquid channel to be so critical that a small decrease in liquid fill may result in a significant decrease in the capillary pumping pressure and, hence, a significant decrease in the maximum heat transport capacity. Heat pipe with axial "X"-shaped groove has been introduced as an attractive option for a wide variety of advanced electronic devices, such as in the spacecraft thermal control system and microelectronic cooling system, due to the high efficiency heat transfer capability, stable operation under microgravity conditions and the high degree of temperature uniformity [18][19][20]. As an optimum choice of high capacity heat pipe with axial grooves in the frame provided by the European Space Agency [21], heat pipe with axial "X"-shaped grooves combines a high capillary pumping pressure with a low axial pressure drop in the return liquid, whose cross-sectional structure is shown in Fig.…”

“…Moreover, the liquid viscous pressure drop is minimal because the liquid flows through a channel with a much larger cross-sectional area compared with that of traditional groove geometries. The circumferential grooves in the vapor channel not only provide an effective liquid distribution but also maximize the heat transfer area for the evaporation of liquid in the evaporator section [3,5,[12][13][14][15][16][17][18]. At present, among all the groove geometries, heat pipe with axial monogroove has the largest heat transport capability with high heat transfer coefficient.…”

An experimental and numerical investigation of capillary limit in an arterial heat pipe

“…As such, this dynamic contact angle could be any value. Certain authors have given a range of 0 to 40 degrees [39]. Other authors have noted that the dynamic contact angle is an unknown that, with internal surface contamination, could be in excess of 45 degrees [6].…”