Electronics Guide

The Heat Pipe Cycle

The complete thermodynamic cycle consists of four distinct transport processes occurring simultaneously in different regions of the device. At the evaporator interface, heat conducted through the container wall evaporates the working fluid, with the wick structure supplying liquid to the heated surface. The resulting vapor flows through the vapor space toward the condenser, driven by the slight pressure difference between hot and cold ends.

At the condenser, vapor contacts the cooler wick structure and container wall, condensing and releasing latent heat that conducts through the wall to the heat sink. The capillary pressure generated by the wick structure's curved liquid-vapor interfaces pumps the condensate back through the wick to the evaporator, overcoming viscous flow resistance and any adverse gravitational effects.

This cycle continues automatically as long as heat input occurs at the evaporator and heat rejection occurs at the condenser. The system self-regulates through pressure and temperature equilibrium, with operating temperature determined by the working fluid's vapor pressure curve at the prevailing system pressure.

Performance Limits

Several fundamental limits constrain heat pipe performance, determining maximum heat transport capability under various operating conditions. The capillary limit represents the most common constraint, occurring when capillary pumping pressure cannot overcome the sum of liquid flow resistance, vapor pressure drop, and gravitational head. Exceeding the capillary limit causes wick dryout at the evaporator, resulting in dramatic temperature rise.

The sonic limit applies at startup or low temperatures when vapor velocity approaches sonic conditions at the evaporator exit, creating a choked flow condition that limits heat transport. The entrainment limit occurs at high heat fluxes when high-velocity vapor flow shears liquid droplets from the wick surface, carrying them to the condenser and starving the evaporator of working fluid.

The boiling limit results when nucleate boiling within the wick creates vapor bubbles that block liquid return flow, causing local dryout. The viscous limit dominates at very low temperatures when high fluid viscosity prevents adequate liquid or vapor flow. Operating heat pipes within these limits ensures reliable performance and prevents thermal failure.

Sintered Powder Wicks

Sintered metal powder wicks, formed by heating metal particles until they bond through solid-state diffusion, provide excellent capillary performance with moderate permeability. The sintering process creates a porous structure with interconnected pores whose size depends on particle diameter, sintering temperature, and pressure. Copper powder wicks commonly use particle sizes ranging from 50 to 200 micrometers, producing effective pore radii of 10 to 50 micrometers.

These wicks generate high capillary pressures due to small pore radii, enabling operation against gravity and high heat fluxes. The uniform pore structure provides consistent performance, while the rigid, mechanically robust structure simplifies manufacturing and handling. Sintered wicks offer good thermal contact with the container wall, minimizing evaporator thermal resistance.

Graded porosity designs optimize performance by using fine powder near the vapor space for high capillary pressure and coarser powder near the container wall for lower flow resistance. Multiple sintered layers can create composite structures balancing capillary and permeability requirements. Sintered powder wicks dominate in high-performance applications requiring maximum heat transport capability.

Grooved Wicks

Axial grooves machined or formed into the inner container wall provide simple, low-cost wick structures with high permeability but limited capillary pressure. Rectangular, triangular, or trapezoidal groove profiles create capillary channels along the heat pipe length, with liquid return occurring through these grooves while vapor flows through the central space.

Grooved wicks offer minimal flow resistance due to large flow cross-sections, enabling high liquid flow rates and long transport lengths. The absence of porous media eliminates viscous drag within the wick structure. However, the relatively large hydraulic radius of grooves produces limited capillary pressure, restricting operation against gravity and maximum heat flux capability.

These wicks excel in horizontal or favorable gravity orientations where high heat transport capability and long transport distances are required. Manufacturing simplicity and low cost make grooved wicks attractive for moderate performance applications. Micro-grooved designs with dimensions below 100 micrometers improve capillary performance while maintaining good permeability.

Mesh and Screen Wicks

Woven metal screens wrapped around a mandrel and inserted into the heat pipe container provide intermediate performance between sintered powder and grooved wicks. Multiple screen layers create the wick thickness, with the weave pattern determining pore size and permeability. Common mesh sizes range from 100 to 400 mesh (150 to 40 micrometer openings).

Mesh wicks offer moderate capillary pressure and permeability, with performance depending on wire diameter, mesh count, and number of layers. The fabrication process allows easy thickness adjustment by varying layer count. Screen wicks provide good conformability to container geometry and reasonable manufacturing cost.

Composite wick designs combine fine mesh layers near the vapor space for capillary pressure with coarse mesh or grooves near the wall for liquid distribution. The flexibility of screen wicks facilitates integration of structural features such as arteries or bypass channels for enhanced liquid transport.

Composite and Arterial Wicks

Advanced wick designs combine multiple structures to optimize different performance aspects. Arterial wicks incorporate large liquid flow channels (arteries) within or beneath the primary wick structure, separating the capillary pumping function from liquid transport. Arteries provide high-permeability flow paths that dramatically reduce liquid flow resistance while the fine-pore primary wick generates capillary pressure.

Tunnel-wick designs place arteries between the wick and container wall, creating circumferential and axial flow channels that distribute liquid with minimal resistance. Monogroove wicks use specialized groove geometries that maintain liquid flow through surface tension forces while accommodating large vapor spaces for low-resistance vapor flow.

These sophisticated wick structures enable heat transport capabilities far exceeding conventional designs, particularly for long transport distances or adverse orientations. The complexity and cost of composite wicks limit their use to demanding applications where conventional designs prove inadequate. Proper design requires detailed modeling of coupled capillary, viscous, and gravitational forces within the multi-component wick structure.

Fluid Properties and Selection Criteria

The merit number, a dimensionless parameter combining key thermophysical properties, provides a first-order metric for fluid selection: (ρ_l · h_fg · σ) / μ_l, where ρ_l is liquid density, h_fg is latent heat, σ is surface tension, and μ_l is liquid viscosity. Higher merit numbers indicate superior heat transport capability, though actual performance depends on the complete property suite and operating conditions.

Vapor pressure characteristics determine operating temperature range and container stress. At the intended operating temperature, vapor pressure should range from approximately 10 kPa to 2 MPa. Lower pressures reduce vapor density and increase sonic velocity constraints, while higher pressures require thick-walled containers and create material compatibility challenges.

High latent heat of vaporization enables large energy transport with minimal fluid circulation, directly increasing heat transport capability. Low liquid viscosity reduces flow resistance in the wick structure, improving capillary limit performance. High surface tension produces small contact angles and strong capillary forces, increasing maximum capillary pressure. Good thermal conductivity in both liquid and vapor phases minimizes temperature gradients within the working fluid.

Common Working Fluids

Water dominates electronics cooling applications for operating temperatures between 30°C and 150°C, offering exceptional thermophysical properties, safety, low cost, and environmental compatibility. Water's high latent heat (2,260 kJ/kg at 100°C), high surface tension, and low viscosity produce superior heat transport capability. Copper or stainless steel containers with appropriate cleaning and processing provide excellent compatibility.

Ammonia serves cryogenic and low-temperature applications from -60°C to 100°C, with latent heat and transport properties approaching water's performance. The high vapor pressure requires robust containers but enables high heat transport density. Material compatibility limitations and toxicity require careful system design. Ammonia heat pipes find application in spacecraft thermal control and electronics cooling for extreme environments.

Methanol and acetone cover intermediate temperature ranges from -30°C to 120°C, offering good performance with moderate vapor pressures. These organic fluids provide alternatives to water for sub-freezing applications and situations requiring lower operating pressures. Ethanol serves similar temperature ranges with different property trade-offs.

For high-temperature electronics applications (200°C to 450°C), various organic heat transfer fluids and refrigerants provide appropriate vapor pressure characteristics. Dowtherm A, HFE fluids, and specialty heat transfer fluids cover this range. For extreme high-temperature applications beyond 450°C, liquid metals such as sodium, potassium, and cesium offer the necessary thermal stability, though their use introduces significant material compatibility and safety considerations.

Material Compatibility

Long-term reliability requires chemical compatibility between working fluid, wick material, and container to prevent corrosion, gas generation, and performance degradation. Chemical reactions can generate non-condensable gases that accumulate in the condenser, creating a thermal resistance that progressively degrades performance. Proper material pairing and manufacturing processes prevent these compatibility issues.

Water requires copper, stainless steel, or specially treated aluminum containers with rigorous cleaning to remove contaminants and passivate surfaces. Ammonia pairs with aluminum or stainless steel but corrodes copper. Organic fluids generally offer broad compatibility but require evaluation for specific material combinations. High-temperature liquid metal working fluids demand specialized refractory metals or ceramics.

Manufacturing procedures significantly impact compatibility through surface preparation, cleaning protocols, and charging procedures. Vacuum baking removes absorbed gases and moisture from wick structures. Proper evacuation and purging sequences eliminate air and non-condensable gases before working fluid charging. Sealed heat pipes undergo quality testing to verify proper charging and absence of non-condensable gases.

Operating Principles and Structure

A vapor chamber consists of two thin metal plates sealed at the perimeter, with wick structure attached to the inner surfaces and a small working fluid charge contained within the evacuated cavity. Heat entering through the evaporator plate vaporizes working fluid in the wick structure, with the resulting vapor spreading two-dimensionally across the vapor space. Condensation occurs across the entire condenser surface area, releasing heat uniformly to an attached heat sink or spreader.

The two-dimensional vapor spreading provides isothermalizing performance far superior to solid metal plates of equivalent thickness. While copper plates exhibit significant temperature gradients when conducting heat laterally from a concentrated source, vapor chambers maintain near-uniform temperature across their entire surface area. This spreading action enables efficient coupling of small, high-power heat sources to large heat sink areas.

Typical vapor chamber thicknesses range from 1 mm to 10 mm, with larger areas requiring greater thickness to accommodate wick structure and vapor space. The challenge in vapor chamber design lies in maintaining adequate wick thickness for liquid return while minimizing overall device thickness. Advanced manufacturing techniques such as chemical etching, electroforming, and micro-machining create thin, high-performance wick structures.

Performance Characteristics

Vapor chambers achieve effective in-plane thermal conductivities of 5,000 to 20,000 W/m·K, dramatically exceeding copper's 400 W/m·K. This performance stems from parallel heat paths throughout the device rather than series conduction through bulk material. The spreading resistance from a concentrated heat source to a distributed sink decreases significantly compared to solid metal spreaders of equivalent size and thickness.

Thermal resistance of vapor chambers includes several components: evaporator contact resistance, evaporator wick resistance, vapor space resistance (typically negligible), condenser wick resistance, and condenser contact resistance. Total resistance typically ranges from 0.01 to 0.1 K/W depending on size, power level, and wick design. Properly designed vapor chambers add minimal thermal resistance while providing superior heat spreading.

Maximum heat flux capability depends on wick design and working fluid properties, with typical limits ranging from 10 to 100 W/cm² for water-based devices. The distributed nature of vapor chambers means that total power capacity can reach hundreds of watts while maintaining heat flux within acceptable limits. Orientation sensitivity generally proves less severe than for conventional heat pipes due to shorter liquid return distances.

Manufacturing and Integration

Vapor chamber manufacturing involves precise fabrication, assembly, and charging processes to achieve reliable performance. The container plates, typically copper or aluminum, undergo cleaning and wick attachment through sintering, bonding, or integrated formation techniques. Micro-grooves, posts, or screen structures provide the wick, with design optimized for the specific application requirements.

Sealing methods include brazing, welding, or epoxy bonding depending on materials, operating temperature, and pressure requirements. A small fill tube or port allows evacuation and working fluid charging before final sealing. Quality control procedures verify proper sealing, adequate fluid charge, and absence of non-condensable gases that would degrade performance.

Integration into thermal systems requires attention to mounting, thermal interface materials, and mechanical design. Flat surfaces facilitate direct contact with heat sources and heat sinks, though thermal interface materials remain necessary to accommodate surface roughness and flatness variations. Mounting pressure must be sufficient to minimize contact resistance without deforming the vapor chamber structure. Flexible thermal interfaces or compliant mounting systems accommodate coefficient of thermal expansion mismatches between vapor chambers and surrounding components.

Design and Operation

Unlike conventional heat pipes where liquid returns through the wick structure surrounding the vapor core, loop heat pipes employ separate liquid and vapor transport lines forming a closed loop. The evaporator contains a fine-pore wick structure that generates capillary pressure, while vapor and liquid flow through dedicated tubes or channels. This separation eliminates the interference between counter-flowing liquid and vapor that limits conventional heat pipe performance.

The system consists of an evaporator containing the wick structure and compensation chamber, a condenser where vapor releases heat, and vapor and liquid return lines connecting these components. Heat applied to the evaporator vaporizes working fluid in the wick, creating a pressure differential that drives vapor through the vapor line to the condenser. Condensed liquid returns through the liquid line to the compensation chamber, which stores excess fluid and accommodates system volume changes with temperature.

The compensation chamber serves critical functions beyond liquid storage. It maintains the evaporator wick in a two-phase state, preventing flooding or dryout. The chamber temperature, typically slightly below evaporator temperature, determines system operating pressure through vapor-liquid equilibrium. Proper compensation chamber design and thermal control significantly influence loop heat pipe performance and stability.

Performance and Applications

Loop heat pipes achieve heat transport capabilities of kilowatts over distances of several meters with minimal temperature drops. The separated flow paths eliminate entrainment and viscous interaction limits affecting conventional heat pipes. Maximum transport distance depends on working fluid properties, tube diameters, and acceptable pressure drop, but commercially available systems transport heat 10 meters or more.

The flexible routing enabled by separate vapor and liquid lines allows LHPs to navigate complex geometries and connect multiple heat sources to multiple heat sinks. Systems can incorporate multiple evaporators sharing common condenser and transport lines, or distribute heat from one evaporator to multiple condensers. This flexibility makes LHPs attractive for satellite thermal control, avionics cooling, and telecommunications equipment thermal management.

Orientation tolerance represents a significant advantage, with proper design enabling operation in any orientation including adverse gravity. The capillary pressure generated by the evaporator wick overcomes gravitational head in the liquid return line. Loop configuration and compensation chamber placement affect orientation sensitivity, but well-designed systems operate reliably regardless of orientation.

Design Considerations

Loop heat pipe design requires careful analysis of coupled fluid dynamic, heat transfer, and capillary phenomena. The evaporator wick must generate sufficient capillary pressure to overcome pressure drops in the vapor line, condenser, liquid line, and any adverse gravitational head. Wick pore size, thickness, and permeability must be optimized for the anticipated heat load and working fluid.

Transport line sizing balances pressure drop against size and weight constraints. Larger diameter lines reduce pressure drop but increase system volume, weight, and working fluid inventory. Condenser design must provide adequate heat rejection area while maintaining acceptable pressure drop. The compensation chamber requires sufficient volume to accommodate fluid redistribution over the operating temperature range while maintaining proper thermal coupling to control system pressure.

Startup transients and flow stability require attention in LHP design. The system must establish proper vapor and liquid distribution from an isothermal initial state. Parasitic heat leaks between evaporator and compensation chamber influence operating temperature and can cause temperature oscillations if improperly managed. Advanced designs incorporate thermal control elements such as variable conductance devices or actively controlled parasitic heat loads to maintain stable operation across varying heat loads and sink temperatures.

Operating Mechanism

A pulsating heat pipe consists of a serpentine capillary tube with one end (evaporator) exposed to a heat source and the other end (condenser) coupled to a heat sink. The tube is evacuated and partially filled with working fluid, creating a series of liquid plugs and vapor bubbles distributed along the tube length. Unlike conventional heat pipes, PHPs contain no wick structure and operate at higher internal pressures.

Heat input at the evaporator causes vapor bubbles to expand, increasing pressure and pushing liquid plugs toward the condenser. At the condenser, vapor bubbles collapse as they cool, decreasing pressure and creating reverse flow. This process occurs asynchronously in multiple parallel channels, creating oscillating flow that transports heat through sensible heating of liquid plugs and latent heat transfer during evaporation and condensation.

The oscillation frequency typically ranges from 0.1 to 10 Hz depending on tube diameter, working fluid, fill ratio, and heat input. Multiple parallel channels enhance performance through statistical averaging of local oscillations and provide flow redundancy. The number of turns and channel arrangement significantly influence transport capability and thermal resistance.

Design Parameters

Tube diameter must remain small enough to prevent gravity stratification of liquid and vapor phases while large enough to avoid excessive flow resistance. Typical inner diameters range from 0.5 mm to 3 mm, with smaller diameters generally providing better performance for gravity-opposing orientations but higher flow resistance. The tube diameter should remain below the critical diameter where buoyancy forces overcome surface tension forces.

Fill ratio, the fraction of tube volume occupied by liquid, critically affects performance. Too little liquid results in insufficient heat transport capacity and potential local dryout, while excessive liquid reduces vapor volume and dampens oscillations. Optimal fill ratios typically range from 40% to 70% depending on tube geometry, working fluid, and operating conditions. The fill ratio may require adjustment for specific applications through experimental optimization.

The number of parallel channels and turns influences both heat transport capability and thermal resistance. More channels increase redundancy and statistical averaging of oscillations, improving reliability and reducing thermal resistance variations. Additional turns increase effective heat transport distance but also increase flow resistance. Typical designs employ 5 to 20 turns with 2 to 10 parallel channels.

Advantages and Limitations

Pulsating heat pipes offer compelling advantages for certain applications. Manufacturing simplicity eliminates wick fabrication, reducing cost and enabling innovative geometries. The wickless structure permits easy miniaturization and planar configurations formed by chemical etching or micro-machining. PHPs tolerate partial dryout better than conventional heat pipes since liquid remains distributed throughout the system rather than concentrated in a wick structure.

However, several limitations constrain PHP application. Thermal resistance typically exceeds conventional heat pipes by factors of 2 to 10 due to intermittent contact between working fluid and heat transfer surfaces. Temperature oscillations at the evaporator, resulting from the pulsating flow mechanism, may prove unacceptable for temperature-sensitive components. Minimum heat input requirements exist to initiate and maintain oscillations, limiting low-power applications.

Orientation sensitivity depends on tube diameter and working fluid properties. Small-diameter tubes minimize gravity effects, enabling multi-orientation operation. Performance typically improves with the evaporator below the condenser (gravity-assisted) and degrades with adverse orientation, though properly designed PHPs operate in all orientations. The stochastic nature of pulsating flow can result in performance variations between nominally identical devices.

Corner Flow Mechanism

Micro heat pipes typically employ polygonal cross-sections (triangular, square, or star-shaped) where acute corner angles create capillary channels for liquid return. Surface tension pulls liquid into these corners, forming curved menisci that generate capillary pressure. As evaporation occurs at the liquid-vapor interface, capillary forces continuously supply liquid to the evaporator region while vapor flows through the central channel toward the condenser.

This corner flow mechanism eliminates the need for traditional wick structures, simplifying fabrication and enabling integration with micro-fabrication processes. The capillary pressure generated by corner menisci depends on corner angle, surface properties, and working fluid characteristics. Sharper corner angles produce higher capillary pressures but also increase liquid flow resistance.

The absence of a wick structure means that evaporation occurs directly from the liquid-vapor interface in the corners rather than through a porous structure. This direct evaporation reduces thermal resistance compared to conventional heat pipes with thick wick structures. However, the limited liquid flow area in corners constrains maximum heat transport capability compared to larger heat pipes with sophisticated wick designs.

Fabrication Methods

Micro heat pipe fabrication leverages semiconductor manufacturing techniques and precision machining. Silicon micro-machining creates channels through anisotropic etching, deep reactive ion etching (DRIE), or laser ablation. Silicon's excellent thermal conductivity and well-established processing methods make it attractive for micro heat pipe applications, despite chemical compatibility challenges with some working fluids.

Metal micro heat pipes use precision machining, wire electrical discharge machining (EDM), or micro-extrusion to form channels. Copper provides excellent thermal properties and compatibility with water, the preferred working fluid for electronics cooling. Aluminum offers lower weight and adequate performance for many applications. Composite fabrication methods bond machined plates or use drawn metal tubes with shaped cross-sections.

Arrays of micro heat pipes can be integrated into substrates or heat spreaders, creating distributed cooling structures. Parallel micro channels formed through micro-machining provide multiple independent heat transport paths, improving reliability and heat spreading capability. These arrays find application in high-power processor cooling, power electronics thermal management, and thermal control of photonic devices.

Performance Characteristics

Micro heat pipe performance scales with size, with smaller devices exhibiting lower maximum heat transport but potentially lower thermal resistance per unit length. Typical heat transport capabilities range from 1 to 50 watts for individual micro heat pipes, with thermal resistances from 0.1 to 10 K/W depending on size, length, and working fluid.

The scaling laws governing micro heat pipe performance differ from conventional heat pipes due to increased importance of interfacial phenomena at small scales. Surface tension forces dominate gravitational forces, improving orientation tolerance. However, viscous flow resistance increases with decreasing dimensions, limiting transport length and heat flux capability. Contact line dynamics and thin film evaporation become significant contributors to overall thermal resistance.

Startup behavior and operating stability require careful consideration in micro heat pipe design. Small fluid inventories mean that minor leaks or non-condensable gas generation significantly impact performance. Temperature overshoot during startup may occur due to liquid redistribution and vapor core formation. Proper filling procedures and quality control measures ensure reliable operation.

Gravity-Assisted Operation

When the evaporator is positioned below the condenser (thermosiphon or gravity-assisted orientation), gravity aids liquid return flow, reducing the capillary pressure requirement and increasing maximum heat transport capability. In this favorable orientation, heat pipes can operate with minimal or no wick structure, with gravity providing the liquid return mechanism. Performance typically improves by 20% to 100% compared to horizontal operation.

Thermosiphons exploit this principle, using simple wick structures or even bare tube walls with liquid return driven entirely by gravity. These devices achieve high heat transport rates with minimal complexity and cost. However, they require fixed orientation and cannot tolerate tilting that reduces the vertical height difference between evaporator and condenser.

The performance improvement in gravity-assisted operation stems from the reduced resistance to liquid flow and increased maximum capillary pressure available for vapor flow resistance and radial wick resistance. The liquid return path experiences assistance rather than opposition from gravity, allowing higher fluid circulation rates and heat transport capabilities.

Adverse Orientation

Operating with the evaporator above the condenser (gravity-opposing or adverse orientation) requires the wick structure to generate sufficient capillary pressure to overcome the gravitational head in addition to viscous flow resistances. This substantially reduces maximum heat transport capability, with performance degradation depending on wick design, working fluid, and elevation difference.

The gravitational pressure penalty equals ρ·g·h, where ρ is liquid density, g is gravitational acceleration, and h is the vertical height difference. For a 30 cm water heat pipe operating vertically against gravity, the gravitational penalty amounts to approximately 3 kPa, which must be overcome by wick capillary pressure. This represents a significant fraction of typical capillary pressures for moderate-performance wicks.

Heat pipes designed for adverse orientation require high-performance wick structures with small pore radii to generate adequate capillary pressure. Sintered powder wicks, fine mesh wicks, or composite arterial structures provide the necessary capillary performance. The design must ensure sufficient capillary pressure margin across the operating range to prevent liquid starvation and evaporator dryout.

Tilt and Horizontal Operation

Horizontal operation represents an intermediate case where gravity acts perpendicular to the heat pipe axis, creating neither assistance nor opposition to axial liquid flow. However, gravity can cause liquid pooling in the bottom portion of the pipe, potentially reducing effective wick area and vapor space. Properly designed heat pipes operate reliably in horizontal orientation with performance between gravity-assisted and adverse orientations.

Tilted orientations create partial gravitational assistance or opposition depending on angle. Small tilt angles from horizontal typically have minimal impact, while larger angles progressively approach fully vertical performance. The effective gravitational head equals h·sin(θ) where θ is the angle from horizontal. Design margins must account for anticipated orientation ranges and potential misalignment during installation.

Multi-orientation designs intended for operation in various positions require conservative wick design to ensure adequate performance in the worst-case (adverse) orientation. Performance testing should verify operation across the full orientation range to identify any unexpected degradation or stability issues. Applications requiring orientation independence may benefit from loop heat pipes or vapor chambers, which exhibit reduced orientation sensitivity compared to conventional heat pipes.

Resistance Components

Evaporator resistance includes the contact resistance between heat source and pipe wall, conduction through the pipe wall, and resistance through the liquid-saturated wick to the evaporation interface. Contact resistance depends on surface finish, interface materials, and mounting pressure, typically contributing 0.01 to 0.1 K/W. Wall conduction resistance usually proves negligible for thin-walled copper or aluminum pipes. Wick resistance depends on wick thickness, effective thermal conductivity of the liquid-saturated structure, and evaporation heat transfer coefficient.

Vapor core resistance typically proves negligible in properly designed heat pipes due to high vapor thermal conductivity and convective transport. Temperature drops in the vapor phase rarely exceed 0.1°C except in extremely long heat pipes or at very high power levels approaching sonic velocity limits. For thermal modeling purposes, the vapor core is often treated as isothermal.

Condenser resistance mirrors evaporator resistance in reverse: vapor condensation onto the wick, conduction through the saturated wick, conduction through the pipe wall, and contact resistance to the heat sink. The symmetry between evaporator and condenser means similar resistance magnitudes, though different areas or wick structures can create asymmetry.

Axial resistance along the pipe length results from vapor pressure drop and liquid pressure drop in the wick structure. In well-designed heat pipes, these axial resistances typically prove small compared to radial resistances at the evaporator and condenser. However, long transport distances, small diameters, or high power levels can make axial resistance significant.

Typical Resistance Values

Conventional cylindrical heat pipes with sintered powder wicks exhibit total thermal resistances ranging from 0.05 to 0.5 K/W depending on size, length, and power level. Small diameter pipes (3-6 mm) typically show higher resistance than larger pipes (8-12 mm) due to limited surface area and increased flow resistance. Operating below the capillary limit, resistance remains relatively constant with power level, increasing sharply as limits are approached.

Vapor chambers achieve lower areal thermal resistances, typically 0.01 to 0.1 K/cm² for the device itself, excluding interface resistances. The parallel heat flow paths and large surface areas enable low resistance despite thin profiles. Spreading resistance calculations must account for the two-dimensional heat flow and finite vapor chamber size.

Interface resistances between heat pipes and heat sources or sinks often dominate total system thermal resistance. Achieving low interface resistance requires flat surfaces, appropriate thermal interface materials, and adequate mounting pressure. The thermal designer must optimize the entire thermal path, as a low-resistance heat pipe provides little benefit if coupled through high-resistance interfaces.

Temperature Dependence

Heat pipe thermal resistance varies with operating temperature due to temperature-dependent working fluid properties. Higher temperatures generally reduce resistance through decreased fluid viscosity (reducing flow resistance) and increased vapor density (improving vapor transport). However, the relationship proves complex due to competing effects on surface tension, latent heat, and wick capillary performance.

Most heat pipes exhibit optimal performance over a specific temperature range determined by working fluid selection. Operating significantly below this range increases resistance due to high viscosity and low vapor pressure. Operating above the optimal range may decrease performance if approaching the working fluid's critical point or encountering material compatibility issues.

Transient thermal response and dynamic resistance characteristics matter for applications with time-varying heat loads. Heat pipes respond to load changes within seconds to minutes depending on size, thermal mass, and working fluid inventory. The effective thermal capacitance includes the container, wick, working fluid, and surrounding thermal interfaces. Accurate transient modeling requires consideration of both resistance and capacitance networks.

Mechanical Mounting

Heat pipe mounting must provide secure mechanical attachment while minimizing thermal interface resistance and accommodating differential thermal expansion. Common mounting methods include clamping, soldering, brazing, and adhesive bonding. The selection depends on operating temperature, required thermal performance, manufacturing processes, and serviceability requirements.

Clamping approaches use mechanical fasteners or spring-loaded mechanisms to press heat pipes against heat sources and sinks. This method enables disassembly for service and accommodates thermal expansion through compliant interfaces. Adequate clamping pressure (typically 50-200 kPa) minimizes contact resistance while avoiding heat pipe deformation. Thermal interface materials fill microscopic surface gaps.

Soldering or brazing creates permanent joints with minimal thermal resistance. These methods require careful process control to avoid heat pipe damage from excessive processing temperatures. Fluxes must be compatible with heat pipe materials and thoroughly cleaned after joining. Solder joints provide excellent thermal contact but create rigid connections that may concentrate stress from thermal expansion mismatches.

Adhesive bonding using thermally conductive epoxies offers moderate thermal performance with simplified processing. Modern thermally enhanced adhesives achieve thermal conductivities of 3-5 W/m·K, providing adequate performance for many applications. Bond line thickness control proves critical, with thin, uniform bonds minimizing thermal resistance. Adhesives provide some compliance to accommodate thermal expansion.

Thermal Interface Management

Thermal interface materials (TIMs) fill air gaps between mating surfaces, dramatically reducing contact thermal resistance. Selecting appropriate TIMs requires balancing thermal performance, compliance, reliability, and cost. Common options include thermal greases, phase change materials, thermal pads, and metal foils, each offering distinct characteristics.

Thermal greases provide the lowest resistance (typically 0.1-0.5 K·cm²/W) due to low viscosity enabling thin bond lines and void elimination. However, greases can migrate over time, particularly at elevated temperatures or under vibration. Containment methods or periodic reapplication may be necessary for long-term reliability.

Phase change materials remain solid at room temperature but soften at operating temperature (typically 45-60°C), flowing to fill interface gaps while maintaining shape at lower temperatures. These materials combine grease-like performance during operation with the handling advantages of solid pads. The softening transition temperature must be appropriate for the application.

Thermal pads offer handling convenience and consistent bond line thickness but typically exhibit higher thermal resistance (0.5-2.0 K·cm²/W) than greases. Soft, conformable pads minimize the pressure required for good contact, making them suitable for applications with limited clamping force. Gap-filling pads accommodate surface non-flatness and component tolerance variations.

Stress and Reliability Considerations

Thermal expansion mismatches between heat pipes, heat sources, heat sinks, and mounting structures create mechanical stresses during temperature cycling. These stresses can damage components, degrade thermal interfaces, or compromise heat pipe integrity. Design approaches to manage thermal expansion include compliant mounting, stress relief features, and material matching.

Compliant thermal interfaces and mounting systems accommodate expansion while maintaining thermal contact. Spring-loaded fasteners maintain consistent pressure despite dimensional changes. Flexible heat pipe sections or bellows absorb differential expansion in long transport distances. Thermal interface materials with appropriate compliance prevent stress concentration at bond lines.

Vibration and shock environments require secure mechanical attachment and fatigue-resistant designs. Heat pipe mounting must prevent fretting wear while accommodating dynamic loads. Support locations should avoid high-stress regions of the heat pipe structure. Finite element analysis identifies stress concentrations requiring design modification or reinforcement.

Long-term reliability testing should encompass thermal cycling, vibration exposure, and extended operation at rated conditions. Degradation modes include working fluid loss through leakage, non-condensable gas generation, wick contamination, and mechanical fatigue. Accelerated life testing with elevated stress levels can identify potential failure modes, though correlation to field conditions requires careful validation.

System-Level Optimization

Heat pipes and vapor chambers function as components within complete thermal management systems. System-level optimization requires balancing heat pipe performance with heat sink effectiveness, airflow management, and spatial constraints. The benefit of low heat pipe thermal resistance diminishes if the overall system bottleneck lies elsewhere in the thermal path.

Thermal modeling encompassing all system components identifies limiting resistances and guides optimization efforts. Computational fluid dynamics (CFD) analysis reveals airflow patterns and convective heat transfer characteristics. Coupled thermal-structural analysis addresses expansion and stress concerns. Parametric studies explore design trade-offs and sensitivity to manufacturing variations.

Economic considerations balance thermal performance against cost, weight, and volume constraints. High-performance heat pipes with sophisticated wick structures may prove unnecessary if simpler solutions meet requirements. Conversely, investing in advanced thermal transport can enable compact system designs or higher power capabilities that create system-level value exceeding component cost.