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Chapter 7

Heat Pipes for Aerospace Application

Abstract

This chapter gives a review of heat pipes for aerospace applications and also presents the basic principles of the operation of heat pipes. Various types of heat pipes are discussed. Limitations, design and manufacturing considerations, and developments are discussed.

Keywords

Capillary limitation; Design; Heat pipe types; Loop heat pipes; Variable conductance heat pipe

7.1. Introduction

Heat pipes are useful in the thermal control of spacecraft, satellites, and avionics. Cooling of satellite electronic components within a limited surface area represents an example. It is possible to transfer heat over long distances, with minimal temperature gradients. Commonly a heat pipe has no moving parts and high-temperature heat sinks are allowed. Aluminum heat pipes with ammonia as the working fluid are common. Heat pipes can be designed as constant conductance heat pipes, variable conductance heat pipes (VCHPs), and loop heat pipes (LHPs). The LHPs offer effective heat removal over long distances without being sensitive to gravity. LHPs may have multiple evaporators to accommodate distributed heat sources and passive or active thermal control.

An early application of heat pipes for space missions was to make the temperature of satellite transponders uniform. As satellites are on orbit, one side is exposed to direct radiation from the sun, whereas the opposite side is exposed to the deep cold outer space. This results in severe temperature gradients, affecting the reliability and accuracy of the transponders. The cooling system developed was the so-called VCHPs to actively regulate the heat flow or the evaporator temperature.

Heat pipes have attracted a huge interest among researchers and practitioners. An overview was presented by Shukla [1]. Heat pipes have become attractive components for spacecraft cooling and temperature stabilization because of their lightweight, low maintenance requirement, and reliability. As one side of the spacecraft is subject to intense solar radiation and the other is exposed to deep space, heat pipes have been used to transport heat from the side irradiated by the Sun to the cold side to maintain a more uniform temperature in the structure. Heat pipes have also been used to dissipate heat generated by electronic components in satellites [2]. Early experiments of heat pipes for aerospace applications were conducted in sounding rockets. In 1974, 10 separate heat pipe experiments were carried out in the International Heat Pipe Experiment [3]. Aboard the application technology satellite-6, experiments with heat pipes using an ammonia heat pipe with a spiral artery wick were carried out. The heat pipe was used as a thermal diode [4]. Using the space shuttle, flight testing of prototype heat pipe designs continued at a very large scale [5–7]. Heat pipe thermal buses were proposed to facilitate a connection between the heat-generating components and an external radiator [8–10]. In 1992, two different axially grooved oxygen heat pipes were tested aboard the shuttle discovery (STS-53) by NASA and the US Air Force to determine the startup behavior and transport capabilities during microgravity operations [11].

An advanced capillary structure, which combined reentrant and a large number of microgrooves for the heat pipe evaporator, was investigated in microgravity conditions during the so-called 2005 FOTON-M2 mission of the European Space Agency [12]. The NASA thermotechnical challenges and opportunities for space exploration, with emphasis on heat pipes and two-phase thermal loops, were presented in Ref. [13].

In a study [14], a heat pipe laser mirror was designed and fabricated to test the feasibility of this technology compared to water-cooled or uncooled mirrors for high-power lasers. Thermal diodes have been proposed for cooling low-temperature sensors, such as an infrared detector in low subsolar Earth orbits [15]. A replacement of the radioisotope thermoelectric generating systems by radioisotope Stirling systems as a long-lasting electricity generation solution for space missions was proposed in Ref. [16]. Alkali-metal VCHPs were proposed and tested to allow multiple stops and restarts of a Stirling engine [17]. Different shapes and structures of heat pipes were studied and tested in Refs. [18–20].

The constrained vapor bubble experiment [21] provided a state-of-the-art heat pipe research undertaken by NASA to cool the International Space Station (ISS).

7.2. General Description of Heat Pipes

Passive two-phase heat transfer devices capable of transferring large quantities of heat with a minimal temperature drop were first introduced by Gaugler [22]. These devices, however, received limited attention until Grover et al. [23] published the results from an independent investigation and introduced the notation heat pipe. Since then, heat pipes have been used in a huge number of applications ranging from temperature control of the permafrost layer under the Alaska pipeline to thermal control of electronic components such as high-power semiconductor devices [24].

A conventional heat pipe was described by Rohsenow et al. [25] and it consists of a sealed container lined with a wicking structure. The container is evacuated and backfilled with an amount of liquid to fully saturate the wick. When a heat pipe operates on a closed two-phase cycle with only pure liquid and vapor present, the working fluid remains saturated as long as the operating temperature is between the freezing point and the critical state. As shown in Fig. 7.1, the heat pipe has three distinct regions, namely, the evaporator region where heat is added, the condenser region where heat is rejected, and the adiabatic or isothermal region. The added heat in the evaporator region of the container causes the working fluid in the evaporator wicking structure to vaporize. The high temperature and corresponding high pressure in this region result in flow of the vapor to the other, cooler end of the container, where the vapor condenses and releases the latent heat of vaporization. The capillary forces in the wicking structure then pump the liquid back to the evaporator.

The heat pipe container provides containment and structural stability. It must be fabricated from a material (1) that is compatible with both the working fluid and the wicking structure, (2) that is strong enough to withstand the pressure associated with the saturation temperatures encountered during storage and normal operation, and (3) that has a high thermal conductivity to permit the effective transfer of heat either into or out of the vapor space. In addition, the container material must be resistant to corrosion resulting from interaction with the environment and must be adaptive to be formed into an appropriate size and shape.

Figure 7.1 Principle of heat pipe operation.

The wicking structure has two functions during the heat pipe operation. It transports and provides the mechanism for the return of the working fluid from the condenser to the evaporator. It also ensures that the working fluid is evenly distributed over the evaporator surface. In order to provide a flow path with low flow resistance, an open porous structure with high permeability is desirable. However, to increase the capillary pumping pressure, a small pore size is necessary. Using a nonhomogeneous wick made of several different materials or a composite wicking structure may provide good function.

As the operation of a heat pipe is based on vaporization and condensation of the working fluid, selection of a suitable fluid is an important factor in the design and manufacturing of heat pipes. The most common applications involve the use of heat pipes with a working fluid having a boiling temperature between 250 and 375K. However, both cryogenic heat pipes (operating in the 5–100K temperature range) and liquid metal heat pipes (operating in the 750–5000K temperature range) have been developed and used successfully. In addition to the thermophysical properties of the working fluid, other factors such as the compatibility of the materials and the ability of the working fluid to wet the wick and wall materials must be considered [26,27]. Further criteria for the selection of the working fluids have been presented by Groll et al. [28], Peterson [29], and Faghri [30].

As heat pipes utilize a capillary wicking structure to promote the flow of liquid from the condenser to the evaporator, they can be used in a horizontal orientation, in microgravity environments, or even in applications where the capillary structure must promote the liquid against gravity from the evaporator to the condenser.

7.3. Capillary Limitation

The heat pipe performance and operation are strongly dependent on the shape, working fluid, and wick structure, but the fundamental phenomenon that governs the operation of such devices arises from the difference in capillary pressure across the liquid–vapor interfaces in the evaporator and condenser regions. The vaporization occurring in the evaporator section causes the meniscus to recede into the wick, and condensation in the condenser section causes flooding. The combined effect of vaporization and condensation results in a meniscus radius of curvature that varies along the axial length of the heat pipe, as conjectured in Fig. 7.2a. The location where the meniscus has a minimum radius of curvature is commonly referred to as the dry point and usually occurs in the evaporator at a point farthest from the condenser region. The wet point occurs at the location where the vapor pressure and liquid pressure are approximately equal or where the radius of curvature is maximum. However, this location can be anywhere in the condenser or adiabatic section but is typically found near the end of the condenser farthest away from the evaporator, as reported in Ref. [29].

Figure 7.2 (a) Variation of meniscus curvature as a function of axial position and (b) typical liquid and vapor pressure distributions in a heat pipe. Based on Peterson GP. An Introduction to heat pipes: modeling, testing and applications. Washington (DC): J. Wiley & Sons, Inc.; 1994.

Fig. 7.2b illustrates the relationship between the static liquid and static vapor pressures in an operating heat pipe. The capillary pressure gradient across a liquid–vapor interface is equal to the pressure difference between the liquid and vapor phases at any given axial position. For a heat pipe to function properly, the net capillary pressure difference between the wet and dry points (Fig. 7.2b) must be greater than the sum of all pressure losses occurring throughout the liquid and vapor flow paths. This relationship, referred to as the capillary limitation, can be expressed mathematically as

${(Δ P_{c})}_{m} \geq \int_{L_{eff}} \frac{\partial P_{v}}{\partial x} dx + \int_{L_{eff}} \frac{\partial P_{l}}{\partial x} dx + Δ P_{PT, e} + Δ P_{PT, c} + Δ P_{+} + Δ P_{∥}$ ${(Δ P_{c})}_{m} \geq \int_{L_{eff}} \frac{\partial P_{v}}{\partial x} dx + \int_{L_{eff}} \frac{\partial P_{l}}{\partial x} dx + Δ P_{PT, e} + Δ P_{PT, c} + Δ P_{+} + Δ P_{∥}$

(7.1)

where

(ΔP_c)_m = the maximum capillary pressure difference generated within the capillary wicking structure between the wet and dry points;

∂P_v/∂x = sum of the inertial and viscous pressure drop occurring in the vapor phase;

∂P_l/∂x = sum of the inertial and viscous pressure drop occurring in the liquid phase;

ΔP_PT,e = pressure gradient across the phase transition in the evaporator;

ΔP_PT,c = pressure gradient across the phase transition in the condenser;

ΔP₊ = normal hydrostatic pressure drop;

ΔP_∥ = axial hydrostatic pressure drop.

The first two terms on the right hand side of Eq. (7.1), ∂P_v/∂x and ∂P_l/∂x, represent the sum of viscous and inertial losses in the vapor and liquid flow paths, respectively. The next two terms, ΔP_PT,e and ΔP_PT,c, represent the pressure gradients occurring across the phase transition in the evaporator and condenser, but can often be neglected. The last two terms, ΔP₊ and ΔP_∥, represent the normal and axial hydrostatic pressure drops, respectively. When the maximum capillary pressure is equal to or greater than the sum of the normal and axial hydrostatic pressure drops, the capillary structure is capable of returning an adequate amount of the working fluid to prevent dry out of the evaporator wicking structure. If the total capillary pressure across the liquid–vapor interface is not greater than or equal to the sum of all the pressure drops occurring throughout the liquid vapor flow paths, the working fluid will not be returned to the evaporator, causing the liquid in the evaporator wicking structure to vanish, leading to dry out. This condition, referred to as the capillary limitation, depends on the wicking structure, working fluid, evaporator heat flux, and operating temperature. The following sections give a brief description of the individual pressure loss terms based on the information given by Bar-Cohen and Kraus [24] and Peterson and Feng [27].

7.3.1. Capillary Pressure

At the surface of a single liquid–vapor interface, a capillary pressure difference, defined as (P_v−P_l) or ΔP_c, exists. This capillary pressure difference is described mathematically by the Laplace–Young equation, i.e.,

$Δ P_{c} = σ (\frac{1}{r_{1}} + \frac{1}{r_{2}})$ $Δ P_{c} = σ (\frac{1}{r_{1}} + \frac{1}{r_{2}})$

(7.2)

where r₁ and r₂ are the principal radii of curvature and σ is the surface tension. For many heat pipe wicking structures the maximum capillary pressure may be written in terms of a single radius of curvature, r_c. Then the maximum capillary pressure between the wet and dry locations can be expressed as the difference between the capillary pressure across the meniscus at the wet location and the capillary pressure at the dry location, or as

$Δ P_{c, m} = (\frac{2 σ}{r_{c, e}}) - (\frac{2 σ}{r_{c, c}})$ $Δ P_{c, m} = (\frac{2 σ}{r_{c, e}}) - (\frac{2 σ}{r_{c, c}})$

(7.3)

Fig. 7.2a illustrates the effect of the vaporization occurring in the evaporator, which causes the liquid meniscus to recede into the wick, and the condensation occurring in the condenser section, which causes flooding of the wick. This combination of meniscus recession and flooding results in a reduction in the local capillary radius r_c,e and increases the local capillary radius r_c,c, respectively, which further results in a pressure difference and accordingly pumping of the liquid from the condenser to the evaporator. During steady-state operation, it is generally assumed that the capillary radius in the condenser or at the wet location r_c,c approaches infinity, so that the maximum capillary pressure for a heat pipe operating at steady state can be expressed as a function of only the effective capillary radius of the evaporator wick [29]

$Δ P_{c, m} = (\frac{2 σ}{r_{c, e}})$ $Δ P_{c, m} = (\frac{2 σ}{r_{c, e}})$

(7.4)

Values for the effective capillary radius r_c are provided in Table 7.1 [29] for some common wicking structures. In the case of other geometries, the effective capillary radius can be found theoretically using the methods proposed by Chi [31] or experimentally using the methods described by Ferrell and Alleavitch [32], Freggens [33], or Tien [34]. In addition, limited information on the transient behavior of capillary structures is available in Ref. [35].

7.3.2. Normal Hydrostatic Pressure Drop

Two hydrostatic pressure drop parts are of importance in heat pipes, namely, a normal hydrostatic pressure drop ΔP₊, which occurs only in heat pipes that have circumferential communication of the liquid in the wick, and an axial hydrostatic pressure drop. The first one is the result of the body force component acting perpendicularly to the longitudinal axis of the heat pipe and can be expressed as

$Δ P_{+} = ρ_{l} g d_{v} \cos ψ$ $Δ P_{+} = ρ_{l} g d_{v} \cos ψ$

(7.5)

Table 7.1

Effective Capillary Radius of Several Wick Structures

Structure	r_c	Data
Circular cylinder (artery or tunnel wick)	r	Radius of liquid flow passage
Rectangular groove	ω	Groove width
Triangular groove	ω/cos β	β = half include angle
Parallel wires	ω	Wire spacing
Wire screens	(ω + d_w)/2 = 1/2N	d = wire diameter N = screen mesh number
Packed spheres	0.41r_s	r_s = sphere radius

Based on Peterson GP. An Introduction to heat pipes: modeling, testing and applications. Washington (DC): J. Wiley & Sons, Inc.; 1994.

where ρ_l is the density of the liquid; g, the gravitational acceleration; d_v, the diameter of the vapor portion of the pipe; and ψ, the angle the heat pipe makes with respect to the horizontal.

7.3.3. Axial Hydrostatic Pressure Drop

The axial hydrostatic pressure drop, ΔP_∥, results from the component of the body force acting along the longitudinal axis. This term can be expressed as

$Δ P_{∥} = ρ_{l} gL \sin ψ$ $Δ P_{∥} = ρ_{l} gL \sin ψ$

(7.6)

where L is the overall length of the heat pipe.

In an environment with gravity, the normal and axial hydrostatic pressure drop parts may either assist or hinder the capillary pumping process depending on whether the inclination of the heat pipe promotes or hinders the flow of liquid back to the evaporator (i.e., the evaporator is placed either below or above the condenser). In a zero-gravity environment, both the parts can be neglected because of the absence of body forces.

7.3.4. Liquid Pressure Drop

The capillary pumping pressure promotes the flow of liquid through the wicking structure but the viscous forces in the liquid result in a pressure drop ΔP_l, which resists the capillary flow through the wick. This liquid pressure gradient may vary along the longitudinal axis of the heat pipe, and hence the total liquid pressure drop might be determined by integrating the pressure gradient over the length of the flow passage [28], or

$Δ P_{l} (x) = - \int_{0}^{x} \frac{d P_{l}}{dx} dx$ $Δ P_{l} (x) = - \int_{0}^{x} \frac{d P_{l}}{dx} dx$

(7.7)

where the limits of integration are from the evaporator end to the condenser end (x = 0) and dP_l/dx is the gradient of the liquid pressure resulting from frictional drag. Introduction of the Reynolds number Re_l and drag coefficient f_l and substituting the local liquid velocity, which is related to the local heat flow, the wick cross-sectional area, the wick porosity ε, and the latent heat of vaporization λ, yield

$Δ P_{l} = (\frac{μ_{l}}{K A_{w} λ ρ_{l}}) L_{eff} q$ $Δ P_{l} = (\frac{μ_{l}}{K A_{w} λ ρ_{l}}) L_{eff} q$

(7.8)

where L_eff is the effective heat pipe length, which is defined as

$L_{eff} = 0.5 L_{e} + L_{a} + 0.5 L_{c}$ $L_{eff} = 0.5 L_{e} + L_{a} + 0.5 L_{c}$

(7.9)

and the wick permeability K is given in Table 7.2.

7.3.5. Vapor Pressure Drop

Addition of mass and mass removal in the evaporator and condenser, respectively, along with the compressibility of the vapor phase, complicate the vapor pressure drop in heat pipes. Applying the continuity condition to the adiabatic region of the heat pipe ensures that for continued operation, the liquid mass flow rate and vapor mass flow rate must be equal. Because of the difference in density between these two phases, the vapor velocity is significantly higher than the velocity of the liquid phase. For this reason, in addition to the pressure gradient resulting from frictional drag, the pressure gradient due to variations in the dynamic pressure must also be considered. Chi [31], Dunn and Reay [35], and Peterson [29] all addressed this problem. The results indicate that on integration of the vapor pressure gradient, the dynamic pressure effects cancel. The result is an expression that is similar to that developed for the liquid,

Table 7.2

Wick Permeability of Several Structures

Structure	K	Data
Circular cylinder (artery or tunnel wick)	r²/8	r = radius of liquid flow passage
Open rectangular grooves	2ε(r_h,l)²/(f_lRe_l)	ε = wick porosity w = groove width s = groove pitch δ = groove depth (r_h,l) = 2ωδ/(ω + 2δ)
Circular annular wick	2(r_h,l)²/(f_lRe_l)	(r_h,l) = r₁−r₂
Wrapped screen wick	$\frac{d_{w}^{2} ε^{3}}{122 {(1 - ε)}^{2}}$ $\frac{d_{w}^{2} ε^{3}}{122 {(1 - ε)}^{2}}$	d_w = wire diameter ε = 1 − (1.05πNd_w/4) N = mesh number
Packed sphere	r_s²ε³/37.5(1 − ε)²	r_s = sphere radius ε = porosity (dependent on packing mode)

From Peterson GP. An Introduction to heat pipes: modeling, testing and applications. Washington (DC): J. Wiley & Sons, Inc.; 1994.

$Δ P_{v} = (\frac{C (f_{v} {Re}_{v}) μ_{v}}{2 {(r_{h, v})}^{2} K A_{v} ρ_{v} λ}) L_{eff} q$ $Δ P_{v} = (\frac{C (f_{v} {Re}_{v}) μ_{v}}{2 {(r_{h, v})}^{2} K A_{v} ρ_{v} λ}) L_{eff} q$

(7.10)

where (r_h,v) is the hydraulic radius of the vapor space and C is a constant that depends on the Mach number.

During steady-state operation, the liquid mass flow rate m must be equal to the vapor mass flow rate m, at every axial position, and although the liquid flow regime is always laminar, the vapor flow might be either laminar or turbulent. As a result, the vapor flow regime must be written as a function of the heat flux. It is also necessary to determine whether the flow is compressible or incompressible by evaluating the local Mach number.

A number of early investigations summarized by Bar-Cohen and Kraus [24] have shown that the following conditions can be used with reasonable accuracy.

$\begin{matrix} {Re}_{v} < 2300, {Ma}_{v} < 0.2 \\ (f_{v} {Re}_{v}) = 16 \\ C = 1.00 \end{matrix}$ $\begin{matrix} {Re}_{v} < 2300, {Ma}_{v} < 0.2 \\ (f_{v} {Re}_{v}) = 16 \\ C = 1.00 \end{matrix}$

(7.11)

$\begin{matrix} {Re}_{v} < 2300, {Ma}_{v} > 0.2 \\ (f_{v} {Re}_{v}) = 16 \\ C = {[1 + (\frac{γ_{v} - 1}{2}) {Ma}_{v}^{2}]}^{- \frac{1}{2}} \end{matrix}$ $\begin{matrix} {Re}_{v} < 2300, {Ma}_{v} > 0.2 \\ (f_{v} {Re}_{v}) = 16 \\ C = {[1 + (\frac{γ_{v} - 1}{2}) {Ma}_{v}^{2}]}^{- \frac{1}{2}} \end{matrix}$

(7.12)

$\begin{matrix} {Re}_{v} > 2300, {Ma}_{v} < 0.2 \\ (f_{v} {Re}_{v}) = 0.038 {(\frac{2 (r_{h, v}) q}{A_{v} μ_{v} λ})}^{\frac{3}{4}} \\ C = 1.00 \end{matrix}$ $\begin{matrix} {Re}_{v} > 2300, {Ma}_{v} < 0.2 \\ (f_{v} {Re}_{v}) = 0.038 {(\frac{2 (r_{h, v}) q}{A_{v} μ_{v} λ})}^{\frac{3}{4}} \\ C = 1.00 \end{matrix}$

(7.13)

$\begin{matrix} {Re}_{v} > 2300, {Ma}_{v} > 0.2 \\ (f_{v} {Re}_{v}) = 0.038 {(\frac{2 (r_{h, v}) q}{A_{v} μ_{v} λ})}^{\frac{3}{4}} \\ C = {[1 + (\frac{γ_{v} - 1}{2}) {Ma}_{v}^{2}]}^{- \frac{1}{2}} \end{matrix}$ $\begin{matrix} {Re}_{v} > 2300, {Ma}_{v} > 0.2 \\ (f_{v} {Re}_{v}) = 0.038 {(\frac{2 (r_{h, v}) q}{A_{v} μ_{v} λ})}^{\frac{3}{4}} \\ C = {[1 + (\frac{γ_{v} - 1}{2}) {Ma}_{v}^{2}]}^{- \frac{1}{2}} \end{matrix}$

(7.14)

Because the equations used to evaluate both the Reynolds number and the Mach number are functions of the heat transport capacity, the conditions of the vapor flow must first be assumed. Using these assumptions, the maximum heat capacity q_c,m can be determined by substituting the values of the individual pressure drops in Eq. (7.1) and solving for q_c,m. Once the value of q_c,m is known, it can then be substituted into the expressions for the vapor Reynolds number and the Mach number to determine the accuracy of the original assumption. Using this iterative approach [31], accurate values for the capillary limitation as a function of the operating temperature can be determined for (qL)_c,m (in W m) and q_c,m (in W).

7.4. Other Limitations

In addition to the capillary limitation, there are several other important mechanisms that limit the maximum amount of heat transferred during steady-state operation of a heat pipe. Among these mechanisms are the viscous limit, sonic limit, entrainment limit, and boiling limit. The capillary wicking limit and viscous limits are related to the pressure drops occurring in the liquid and vapor phases, respectively. The sonic limit is established by the choked flow occurring in the vapor passage, whereas the entrainment limit is a result of the high liquid–vapor shear forces developed when the vapor passes in counterflow over the liquid saturated wick. The boiling limit is reached when the heat flux applied in the evaporator portion is so high that nucleate boiling occurs in the evaporator wick. This creates vapor bubbles that partially block the return of the liquid.

In low-temperature applications using cryogenic working fluids, either the viscous limit or capillary limit occurs first. In high-temperature heat pipes using, e.g., liquid metal working fluids, the sonic and entrainment limits are of increased significance. The theory and fundamental phenomena that cause these limitations have been the objectives of quite many investigations and these are well documented by Chi [31], Dunn and Reay [35], Tien [34], Peterson [29], Faghri [30], and proceedings from the International Heat Pipe Conference series.

7.4.1. Viscous Limitation

When the operating temperature is very low, the vapor pressure difference between the closed end of the evaporator (the high-pressure region) and the closed end of the condenser (the low-pressure region) might be very small. Accordingly the viscous forces within the vapor region might dominate and hence limit the heat pipe operation. Dunn and Reay [35] discussed this limit in more detail and suggested the criterion

$\frac{Δ P_{v}}{P_{v}} < 0.1$ $\frac{Δ P_{v}}{P_{v}} < 0.1$

(7.15)

for determining when this limit is of major concern.

7.4.2. Sonic Limitation

The sonic limit in heat pipes is similar to the sonic limit that occurs in converging-diverging nozzles [29], except that in a converging-diverging nozzle the mass flow rate is constant and the vapor velocity varies because of the change in cross-sectional area, whereas in heat pipes the area is constant and the vapor velocity varies because of the evaporation and condensation along the heat pipe. Similar to nozzle flow, a decreased outlet pressure, or, in this case, condenser temperature, results in a decrease in the evaporator temperature until the sonic limit is reached. A further increase in the heat rejection rate does not reduce the evaporator temperature or the maximum heat transfer capacity, but reduces the condenser temperature because of the choked flow.

The sonic limitation in heat pipes can be determined by

$q_{s, m} = A_{v} ρ_{v} λ {(\frac{γ_{v} R_{v} T_{v}}{2 (γ_{v} + 1)})}^{\frac{1}{2}}$ $q_{s, m} = A_{v} ρ_{v} λ {(\frac{γ_{v} R_{v} T_{v}}{2 (γ_{v} + 1)})}^{\frac{1}{2}}$

(7.16)

where T_v is the mean vapor temperature within the heat pipe.

7.4.3. Entrainment Limitation

Because of the high vapor velocities, liquid droplets can be picked up or entrained in the vapor flow and this results in excess liquid accumulation in the condenser and dry out of the evaporator wick [36]. For proper operation the onset of entrainment in countercurrent two-phase flow must be avoided. The most commonly quoted criterion to determine this onset is based on the Weber number, We, defined as the ratio of the viscous shear force to the force resulting from the liquid surface tension, i.e.,

$We = \frac{2 (r_{h, w}) ρ_{v} V_{v}^{2}}{σ}$ $We = \frac{2 (r_{h, w}) ρ_{v} V_{v}^{2}}{σ}$

(7.17)

If the Weber number is equal to unity, the onset of entrainment of liquid droplets in the vapor flow is reached. Thus the Weber number must be less than unity.

By relating the vapor velocity to the heat transport capacity, a value for the maximum heat transport capacity based on the entrainment limitation can be determined as

$V_{v} = \frac{q}{A_{v} ρ_{v} λ}$ $V_{v} = \frac{q}{A_{v} ρ_{v} λ}$

(7.18)

$q_{e, m} = A_{v} λ {(\frac{σ ρ_{v}}{2 (r_{h, w})})}^{- \frac{1}{2}}$ $q_{e, m} = A_{v} λ {(\frac{σ ρ_{v}}{2 (r_{h, w})})}^{- \frac{1}{2}}$

(7.19)

where (r_h,w) is the hydraulic radius of the wick structure, defined as twice the area of the wick pore at the wick–vapor interface divided by the wet perimeter at the wick–vapor interface. Rice and Fulford [37] developed a different approach resulting in an expression to define the critical dimensions for wicking structures to prevent entrainment.

7.4.4. Boiling Limitation

At very high radial heat fluxes, nucleate boiling may occur in the wicking structure and bubbles may become trapped in the wick, blocking the liquid return and resulting in dry out in the evaporator. This phenomenon, referred to as the boiling limit, differs from the other limitations previously presented because it depends on the evaporator heat flux as opposed to the axial heat flux [29].

The boiling limit is found by examining the nucleate boiling theory. This involves two separate phenomena: bubble formation and the subsequent growth or collapse of the bubbles. The first phenomenon, bubble formation, is governed by the number and size of nucleation sites on a solid surface. The second one, bubble growth or collapse, depends on the liquid temperature and corresponding pressure caused by the vapor pressure and surface tension of the liquid. Utilizing a pressure balance on a bubble and applying the Clausius–Clapeyron equation to relate the temperature and pressure, an expression for heat flux, beyond which bubble growth will occur, can be developed, i.e., [31]

$q_{b, m} = (\frac{2 π L_{eff} k_{eff} T_{v}}{λ ρ_{v} 1 n (r_{i} / r_{v})}) (\frac{2 σ}{r_{n}} - Δ P_{c, m})$ $q_{b, m} = (\frac{2 π L_{eff} k_{eff} T_{v}}{λ ρ_{v} 1 n (r_{i} / r_{v})}) (\frac{2 σ}{r_{n}} - Δ P_{c, m})$

(7.20)

where k_eff is the effective thermal conductivity of the liquid–wick combination. Such values are provided in Table 7.3. r_i is the inner radius of the heat pipe wall and r_n is the nucleation site radius, which according to Dunn and Reay [35], can be assumed to range from 2.54 × 10⁻⁵ to 2.54 × 10⁻⁷ m for conventional heat pipes.

As the power level associated with each of the four mentioned limitations has been determined as a function of the maximum heat transport capacity, the operating envelope can be determined. Then it is a matter of selecting the lowest limitation for any given operating temperature to determine the heat transport limitation applicable for a prespecified set of conditions.

7.5. Design and Manufacturing Considerations for Heat Pipes

Several studies have focused on problems associated with the design and manufacturing of heat pipes. Among these are the works by Feldman [38], Brennan and Kroliczek [39], Peterson [29], and Faghri [30]. Besides factors such as cost, size, weight, reliability, working fluid, and construction and sealing techniques, the design and manufacturing of heat pipes are governed by three operational factors, namely, the effective operating temperature range (determined by the selection of the working fluid), the maximum power the heat pipe is capable of transporting (determined by the ultimate pumping capacity of the wick structure), and the maximum evaporator heat flux (determined by the position where nucleate boiling occurs).

Table 7.3

Effective Thermal Conductivity of Liquid-Saturated Wick Structures

Wick Structure	k_eff
Wick and liquid in series	$\frac{k_{l} k_{w}}{{εk}_{w} {+ k}_{l} (1 - ε)}$ $\frac{k_{l} k_{w}}{{εk}_{w} {+ k}_{l} (1 - ε)}$
Wick and liquid in parallel	εk_l + k_w(1 − ε)
Wrapped screen	$\frac{k_{l} [(k_{l} {+ k}_{w}) - (1 - ε) (k_{l} - k_{w})]}{[(k_{l} {+ k}_{w}) + (1 - ε) (k_{l} - k_{w})]}$ $\frac{k_{l} [(k_{l} {+ k}_{w}) - (1 - ε) (k_{l} - k_{w})]}{[(k_{l} {+ k}_{w}) + (1 - ε) (k_{l} - k_{w})]}$
Packed spheres	$\frac{k_{l} [({2 k}_{l} {+ k}_{w}) - 2 (1 - ε) (k_{l} - k_{w})]}{[({2 k}_{l} {+ k}_{w}) + (1 - ε) (k_{l} - k_{w})]}$ $\frac{k_{l} [({2 k}_{l} {+ k}_{w}) - 2 (1 - ε) (k_{l} - k_{w})]}{[({2 k}_{l} {+ k}_{w}) + (1 - ε) (k_{l} - k_{w})]}$
Rectangular grooves	$\frac{(ω_{f} k_{l} k_{w} δ) + {ωk}_{l} (0.815 ω_{f} k_{w} + {δk}_{l})}{(ω + ω_{f}) (0.815 ω_{f} k_{l} + {δk}_{l})}$ $\frac{(ω_{f} k_{l} k_{w} δ) + {ωk}_{l} (0.815 ω_{f} k_{w} + {δk}_{l})}{(ω + ω_{f}) (0.815 ω_{f} k_{l} + {δk}_{l})}$

From Peterson GP. An Introduction to heat pipes: modeling, testing and applications. Washington (DC): J. Wiley & Sons, Inc.; 1994; Chi SW, Heat pipe theory and practice, New York: McGraw-Hill Publishing Company; 1976.

7.5.1. Selection of Working Fluid

Because heat pipes rely on vaporization and condensation to transfer heat, selection of a suitable working fluid is an important factor. For most moderate temperature applications, working fluids with boiling temperatures between 250 and 375K are required. Possible fluids are ammonia, Freon-11 (trichlorofluoromethane) or Freon-113 (trichlorotrifluoroethane), acetone, methanol, and water. For a capillary-wick-limited heat pipe, the characteristics of a good working fluid are high latent heat of vaporization, high surface tension, high liquid density, and low liquid viscosity. Chi [31] combined these properties into a parameter, N_l, referred to as the liquid transport factor or figure of merit, defined as

$N_{l} = \frac{ρ_{l} σλ}{μ_{l}}$ $N_{l} = \frac{ρ_{l} σλ}{μ_{l}}$

(7.21)

This parameter can be used to evaluate various working fluids at specific operating temperatures. The concept of a single parameter for evaluating working fluids was extended by Gosse [40], who demonstrated that the thermophysical properties of the liquid–vapor equilibrium state could be reduced to three independent parameters.

Along with the importance of the thermophysical properties of the working fluid, consideration must be given to the ability of the working fluid to wet the wick and wall materials, as discussed by Peterson [29]. Other important criteria in the selection of the working fluid were presented by Heine and Groll [41].

7.5.2. Importance of the Wicking Structures

In addition to providing the pumping of the liquid from the condenser to the evaporator, the wicking structure ensures that the working fluid is evenly distributed over the evaporator surface. To provide a flow path with low flow resistance through which the liquid can be returned from the condenser to the evaporator, an open porous structure with high permeability is required. However, to increase the capillary pumping pressure, a small pore size is necessary. To manage these contradictory effects, a nonhomogeneous wick made of several different materials or a composite wicking structure might be used. Udell and Jennings [42] proposed and formulated a model for a heat pipe with a wick consisting of a porous media of two different permeabilities oriented parallel to the direction of the heat flux. This wick structure provided a large pore size in the center of the wick for liquid flow and a smaller pore size for capillary pressure.

Composite wicking structures accomplish a similar effect, as the capillary pumping and axial fluid transport are handled independently. In addition to fulfilling this dual purpose, several wick structures physically separate the liquid and vapor flow. This results from an attempt to eliminate the viscous shear force that occurs during countercurrent liquid and vapor flows.

7.5.3. Compatibility of Materials

Formation of noncondensable gases (NCGs) through chemical reactions between the working fluid and the wall or wicking structure, or decomposition of the working fluid, may cause problems in the operation of the heat pipe. For these reasons, careful consideration must be given to the selection of working fluids and wicking and wall materials to prevent the occurrence of such problems during the operational life time of the heat pipe. The formation of NCG may result in either decreased performance or total failure. Corrosion problems can lead to physical degradation of the wicking structure because solid particles carried to the evaporator wick and deposited there will most likely reduce the wick permeability [43].

Basiulis et al. [44] conducted extensive compatibility tests with several combinations of working fluids and wicking structures. The findings are summarized in Table 7.4 together with investigations by Busse et al. [45]. Other investigations have also been performed by, e.g., Zaho et al. [46], in which the compatibility of water and mild steel heat pipes was evaluated; Roesler et al. [47], who evaluated stainless steel, aluminum, and ammonia combinations; and Murakami and Arai [48], who developed a statistical predictive technique for evaluating the long-term reliability of copper–water heat pipes. These studies provided additional insight into the compatibility of various liquid–material combinations. Most of the data available are based on accelerated lifetime tests.

The two problems, i.e., NCG generation and corrosion, are only two of the factors to be considered when selecting heat pipe wicks and working fluids. Other problems include wettability of the fluid–wick combination, strength-to-weight ratio, thermal conductivity and stability, and fabrication costs.

7.5.4. Sizes and Shapes of Heat Pipes

Heat pipes vary in both size and shape, ranging from a 15-m-long monogroove heat pipe developed by Alario et al. [49] for spacecraft heat rejection to a 10-mm-long expandable bellows type heat pipe developed by Peterson [50] for the thermal control of semiconductor devices. The cross-sectional areas of the vapor and liquid flows also vary significantly from those encountered in flat-plate heat pipes, which have very large flow areas, to commercially available heat pipes with a cross-sectional area of less than 0.30 mm². Heat pipes may be fixed or variable in length and either rigid or flexible for situations in which relative motion or vibration is concerned.

Table 7.4

Working Fluid, Wick, and Container Compatibility Data

Material	Water	Acetone	Ammonia	Methanol
Copper	RU	RU	NU	RU
Aluminum	GNC	RL	RU	NR
Stainless steel	GNT	PC	RU	GNT
Nickel	PC	PC	RU	RL
Refrasil	RU	RU	RU	RU
Material	Dow-A	Dow-E	Freon-11	Freon-113
Copper	RU	RU	RU	RU
Aluminum	UK	NR	RU	RU
Stainless steel	RU	RU	RU	RU
Nickel	RU	RL	UK	UK
Refrasil	RU		UK	UK

7.5.5. Reliability and Lifetime Tests

Peterson [29] presented an extensive review of life testing and reliability. The review indicated that many of the early investigations, e.g., those conducted by Basiulis and Filler [51] and Busse et al. [45], focused on the reliability of various types of material combinations in the intermediate operating temperature range. Long-duration life tests on copper–water heat pipes have been performed by numerous investigators. Among them, Kreed et al. [52] indicated that this combination, with proper cleaning and charging procedures, can produce heat pipes with an expected lifetime of decades. Other tests reported in Ref. [35] have indicated similar results for copper–acetone and copper–methanol combinations. However, these tests also stated that care must be taken to ensure the purity of the working fluid, wick structure, and case materials. Table 7.4 presented a summary of compatibility data obtained from various investigations.

In addition to the use of compatible materials, long-term reliability can be ensured by careful inspection and preparation processes such as

• laboratory inspection to ensure that material of high purity is used for the case, end caps, and fill tubes,

• appropriate inspection procedures to ensure that the wicking material is made from high-quality substances,

• inspection and distillation procedures to ensure that the working fluid is of high purity,

• fabrication in a clean environment to ensure or eliminate the presence of oils, vapors, etc.,

• use of clean solvents during the rinse process [53].

The effects of long-term exposure to elevated temperatures and repeated thermal cycling on heat pipes can be estimated by using a model developed by Baker [54]. This model utilizes the Arrhenius expression to predict the response parameter F,

$F = C e^{- A/kT}$ $F = C e^{- A/kT}$

(7.22)

where C is a constant; A, the reaction activation energy; k, the Boltzmann constant; and T, the absolute temperature.

This model utilizes experimental results obtained from the Jet Propulsion Laboratory in the United States to predict the rate and amount of hydrogen gas generated over a 20-year lifetime for a stainless steel heat pipe, with water as the working fluid. With this model, the generated mass of hydrogen can be predicted as a function of time.

Experiences with a wide variety of applications ranging from consumer electronics to industrial equipment have demonstrated that mechanical cleaning of the case and wicking structure with an appropriate solvent, combined with an acidic etch and vacuum bake out at elevated temperatures, can make heat pipes free of contaminants, thus enabling negligible performance degradation (less than 5%) over a product lifetime of 10 years [53].

7.6. Various Types of Heat Pipes

A heat pipe must possess vapor–liquid equilibrium with the saturated liquid and its vapor (gas phase). The saturated liquid vaporizes and moves to the condenser, where it is cooled and transferred to saturated liquid again. In a conventional heat pipe, the condensate is returned to the evaporator using a wick structure exerting a capillary action on the liquid phase of the working fluid. Various types of wick structures are used in heat pipes, including sintered metal powder, screen, and grooved wicks, which have a series of grooves parallel to the pipe axis. The performance of the heat pipes also depends on the selection of a container, a wick, and welding materials compatible with one another and with the working fluid of interest. Performance can be degraded and failures can occur in the container wall if the constituents are not compatible. For example, the constituents can react chemically or set up a galvanic cell within the heat pipe. Additionally, the container material may be soluble in the working fluid or may catalyze the decomposition of the working fluid on reaching a particular temperature limit of the working fluid. Faghri [55] provided up-to-date information on the compatibility of metals with the working fluids, which is summarized in Table 7.5. High-quality arterial grooved heat pipes are preferred for thermal stabilization of satellites. Various configurations of heat pipes are available in the market for a variety of applications [56]. Most heat pipes are generally circular cylinders. Other shapes such as rectangular (vapor chamber), conical [rotating heat pipes (RHPs)], triangular (micro heat pipes), and nose cap geometries (leading edge cooling) have also been studied.

7.6.1. Heat Pipes with Variable Conductance

A VCHP is a capillary-driven heat pipe in which an NCG is supplied to the heat pipe, in addition to the working fluid. When the VCHP is operating, the NCG is swept toward the condenser end of the heat pipe by the flow of the working fluid vapor condensing in the condenser. The NCG then blocks the working fluid from reaching a portion of the condenser. The VCHP works by variation of the portion of the condenser being available for the working fluid. As the evaporator temperature increases, the vapor temperature (and pressure) rises, the NCG is compressed, and the condenser is more exposed to the working fluid. This increases the conductivity of the heat pipe and decreases the temperature of the evaporator. Conversely, if the evaporator is cooled, the vapor pressure drops and the NCG expands. This reduces the portion of the condenser available for condensation and thus the heat pipe conductivity is decreased, which helps maintain the evaporator temperature. The first application of the VCHP to communication technology satellite was reported in [57].

Many models have been developed based on a flat front model [58], steady diffusive interface models [59–61], and a transient diffusive interface model [62] of the interface between the vapor and the NCG. The diffusive interface model assumes transient one-dimensional mass diffusion across the vapor–gas interface, with constant properties. Although the model is simplified by ignoring the compressibility in the vapor flow, it may well predict the transient operation of the VCHP. Two studies [63,64] presented a CFD model for unsteady two-dimensional heat and mass transfer in the vapor–gas region of a gas-loaded heat pipe to predict the behavior of the startup transient in the vapor–gas region. Two-dimensional transient operation of a VCHP was studied in [65].

Table 7.5

Materials Relative to Working Fluid

Working Fluid	Compatible Material	Incompatible Material
Water	Stainless steel, copper, silica, nickel, titanium	Aluminum, Inconel
Ammonia	Aluminum, stainless steel, iron,
Ammonia	nickel, cold rolled steel
Methanol	Stainless steel, iron, copper, brass, silica, nickel	Aluminum
Acetone	Aluminum, stainless steel, copper, brass, silica
Freon-11	Aluminum
Freon-21 (dichlorofluoromethane)	Aluminum, iron
Freon-113	Aluminum
Heptane	Aluminum
Dowtherm	Stainless steel, copper, silica
Lithium	Tungsten, Tantalum, molybdenum, niobium	Stainless steel, nickel, Inconel, titanium
Sodium	Stainless steel, nickel, Inconel, niobium	Titanium
Cesium	Titanium, niobium, stainless steel
Mercury	Stainless steel	Molybdenum, Inconel, nickel, tantalum, titanium, niobium
Lead	Tungsten, tantalum	Stainless steel, nickel, Inconel, titanium,
Lead	Tungsten, tantalum	niobium
Silver	Tungsten, tantalum	Rhenium

From Faghri A. Heat pipes, review, opportunities and challenges. Front Heat Pipes (FHP), 5, 1–48, 2014.http://dx.doi.org/10.5098/fhp.5.1.

7.6.2. Rotating Heat Pipes

In [66], a two-phase heat transfer device designed to cool machinery by removing heat through a rotating shaft was reported. The device was called an RHP. The heat input to the evaporator vaporizes the working fluid. As in ordinary heat pipes, the vapor travels down the heat pipe to the condenser, where heat is removed as the vapor condenses. In contrast to a normal heat pipe using a wick to return the condensate, an RHP uses the centrifugal force. A copper–water RHP with a copper screen mesh wick at various heat loads was tested in [67]. An experimental test rig with a water-cooled condenser section was built to study the heat transfer in the RHP for various heat loads and various rotational speeds ranging from 1000 to 2000 rpm.

7.6.3. Cryogenic Heat Pipes

The continuous growth of space-based communications and sensors, along with the evolution of aerospace and avionics, increases the demands for thermal control and heat removal in low-temperature environments. An early review of the application of cryogenic heat pipes in spacecraft was presented in [68]. Charlton and Bowman [69] developed a mathematic model to predict the performance of cryogenic heat pipes under transverse vibration. Supercritical startup behavior of cryogenic heat pipes was studied in [70]. Bughy et al. [71] discussed the thermal switching cryogenic heat pipes for thermal management of CCD cameras used in the NASA space interferometry mission.

7.6.4. Vapor Chamber

The vapor chamber is a capillary-driven planar (flat-plate heat pipe) design with a small aspect ratio. The main advantage of the vapor chamber is that it can be placed directly beneath the heat-generating avionics components without adding additional thermal resistance. There are two main applications for vapor chambers [72–74]. One application is that they are used when high powers and heat fluxes are applied to a relatively small evaporator. Heat input to the evaporator vaporizes the liquid, which flows in two dimensions to the condenser surface. After the vapor has condensed on the condenser surface, capillary forces in the wick return the condensate to the evaporator. Note that most vapor chambers are insensitive to gravity and will still operate when inverted, with the evaporator above the condenser. Another application is that compared to a one-dimensional tubular heat pipe, the width of a two-dimensional heat pipe allows an adequate cross section for heat flow, even with a very thin device.

7.6.5. Loop Heat Pipes

LHPs are two-phase heat transfer devices using capillary action to remove heat from a source and to passively move it to a condenser or radiator [75]. LHPs are similar to heat pipes but have the advantages of providing reliable operation over long distances and having the ability to operate against gravity. A large heat load can be transported over a long distance with a small temperature difference. The main components of LHPs are an evaporator, a condenser, a vapor line, a liquid line and a hydroaccumulator. A wick is required only in the evaporator and hydroaccumulator. The rest of the loop is made of smooth walled tubing. The hydroaccumulator is usually called a compensation chamber. The principle of LHPs is that the liquid in the evaporator evaporates by the applied heat load and a meniscus is formed in the liquid–vapor interface in the wick. A pressure gradient is developed by the surface tension that moves the vapor toward the condenser where it condenses. The liquid is pushed back to the evaporator by the same surface tension. The compensation chamber is connected to the evaporator by a secondary wick. With a slight variation in the placement of the compensation chamber wherein it is located remotely from the evaporator, a different version of the LHP is named as a capillary pumped loop (CPL). In a CPL, the compensation chamber is known as a reservoir and is outside the path of the fluid circulation. Ku [76] presented operating characteristics of an LHP. The heat transfer mechanism in the evaporator of an LHP was investigated in [77] and [78]. Shukla [79] studied the thermofluid dynamics of LHP operation. Different designs of LHPs ranging from powerful, large-sized LHPs to miniature LHPs (micro LHPs) have been developed and employed in a variety of applications, both in ground-based and space applications [80–82]. LHPs operating with ammonia as the working fluid are popular thermal control devices for high-powered telecommunication satellites.

7.6.6. Micro Heat Pipes

Micro heat pipes for cooling electronic devices were proposed in [83]. A micro heat pipe is defined as a heat pipe in which the mean curvature of the liquid–vapor interface is comparable in magnitude to the reciprocal of the hydraulic radius of the total flow channel. Typically, micro heat pipes have convex but cusped cross sections (e.g., a polygon), with a hydraulic diameter in the range of 10–500 μm. A miniature heat pipe is defined as a heat pipe with a hydraulic diameter in the range of 0.5–5 mm. An overview of the development of micro heat pipes was presented in [84]. The fabrication and experimental data on the performance characteristics of the flat water–copper heat pipe with external dimensions 2 × 7 × 120 mm have been reported with radial heat fluxes of 90 and 150 W/cm² for horizontal and vertical applications, respectively [85]. Shukla [86] investigated the heat transfer limitations of micro heat pipes and found that the maximum heat transfer capacity of a micro heat pipe depends on the capillary and fluid continuum limits. It was found that methanol is a better suited working fluid for a micro heat pipe with triangular cross section. The capillary limit calculated in [86] was almost twice the value obtained in [87].

7.6.7. Nanofluids in Heat Pipe Applications

The working fluids in heat pipes can be helium and nitrogen for cryogenic temperatures (2–4 K) and liquid metals such as mercury (523–923 K), sodium (873–1473 K), and indium (2000–3000 K) for extremely high temperatures. The working fluid in a heat pipe is chosen according to the temperatures at which the heat pipe should operate. The vast majority of heat pipes for spacecraft and electronics cooling use ammonia (213–373 K), alcohols [such as methanol (283–403 K) or ethanol (273–403 K)], or water (298–573 K) as the working fluid. Copper–water heat pipes have a copper envelope, use water as the working fluid, and typically operate in the temperature range from 293 to 423 K. The working fluids have some limitations in the heat transfer rates of the heat pipe.

Development of nanofluids, i.e., fluids consisting of a conventional heat transfer base fluid with nanometer-sized oxide or metallic particles suspended within, offers the opportunities of increased heat transfer rates over conventional systems by more than 20%. Shukla et al. [88,89] reported a 30% increase in thermal conductivity by dispersing 0.1% copper particles in water. Significant improvement of heat transfer rates was found by dispersing copper, alumina, and silver colloid suspensions in water. Enhancement of thermal conductivity was also observed with copper oxide dispersed in water and ethylene glycol [90]. In addition to the heat transfer rates, the magnetic affinity of the solid particles in metallic suspensions allows for their manipulation by electromagnets, thereby eliminating the need for pumps and controls and may provide enhanced heat transfer. This has created interest in the application of a novel nanofluid-based actively controlled thermal management system for small satellite applications [91]. NASA has set a road map for the development of high-temperature heat pipes, which will be a solution for the high heat flux encountered during ascent and reentry of space vehicles [92]. The fluid with ultrafine suspended nanoparticles might be appropriate for satellite applications of heat pipes.

7.7. Concluding Remarks and Summary

This chapter presented a brief review of heat pipes in aerospace applications and also the basic principles of the operation of heat pipes. Thermal management in spacecraft is challenging because of the adverse environmental radiation. A variety of heat pipes for cryogenic and high-temperature applications have already been used in space applications. LHPs and CPLs with multiple evaporators and condensers have been found to be effective thermal management solutions for high-powered communication satellites. The macro and micro LHPs can play important roles in thermal solutions for small satellites. Heat pipes have emerged as appropriate and cost-effective responses to these challenges. Heat pipes used in thermal protection systems have been found superior to high-temperature materials, with the benefits of lightweight and a passive design. A wick having nanostructures, with a gradient along the length of the wick, can promote capillary fluid flow, and the use of nanofluids as working fluids can improve the heat transfer rates of heat pipes.

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Table of Contents for Chapter 7. Heat Pipes for Aerospace Application

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