Operation Principles of Heat Pipes
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| Historical Development of Heat Pipes
Operation Principles of Heat Pipes Working Fluids and Temperature Ranges of Heat Pipes Capillary Wick Designs and Structures in Heat Pipes Heat Transfer Limitations of Heat Pipes |
The operation of a heat pipe [1][2] is easily understood by using a cylindrical geometry, as shown in Fig. 1. However, heat pipes can be of any size or shape. The components of a heat pipe are a sealed container (pipe wall and end caps), a wick structure, and a small amount of working fluid which is in equilibrium with its own vapor. Different types of working fluids such as water, acetone, methanol, ammonia or sodium can be used in heat pipes based on the required operating temperature. The length of a heat pipe is divided into three parts: the evaporator section, adiabatic (transport) section and condenser section. A heat pipe may have multiple heat sources or sinks with or without adiabatic sections depending on specific applications and design. Heat applied externally to the evaporator section is conducted through the pipe wall and wick structure, where it vaporizes the working fluid. The resulting vapor pressure drives the vapor through the adiabatic section to the condenser, where the vapor condenses, releasing its latent heat of vaporization to the provided heat sink. The capillary pressure created by the menisci in the wick pumps the condensed fluid back to the evaporator section. Therefore, the heat pipe can continuously transport the latent heat of vaporization from the evaporator to the condenser section. This process will continue as long as there is a sufficient capillary pressure to drive the condensate back to the evaporator.
The menisci at the liquid-vapor interface are highly curved in the evaporator section due to the fact that the liquid recedes into the pores of the wick. On the other hand, during the condensation process, the menisci in the condenser section are nearly flat. A capillary pressure exists at the liquid-vapor interface due to the surface tension of the working fluid and the curved structure of the interface. The difference in the curvature of the menisci along the liquid-vapor interface causes the capillary pressure to change along the pipe. This capillary pressure gradient circulates the fluid against the liquid and vapor pressure losses, and adverse body forces such as gravity or acceleration.
The vapor pressure changes along the heat pipe are due to friction, inertia and blowing (evaporation) and suction (condensation) effects, while the liquid pressure changes mainly as a result of friction [2]. The liquid-vapor interface is flat near the condenser end cap corresponding to a zero local pressure gradient at very low vapor flow rates. A typical axial variation of the shape of the liquid-vapor interface and the liquid and vapor pressures for low vapor flow rates are shown in Figs. 2(a) and 2(b), respectively.
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The maximum local pressure difference occurs near the evaporator end cap. This maximum local capillary pressure should be equal to the sum of the pressure drops in the vapor and the liquid across the heat pipe in the absence of body forces. When body forces are present, such as an adverse gravitational force, the liquid pressure drop is greater, indicating that the capillary pressure must be higher in order to return the liquid to the evaporator for a given heat input. At moderate vapor flow rates, dynamic effects cause the vapor pressure drop and recovery along the condenser section, as shown in Fig. 3(b).
The local liquid-vapor pressure difference is small, but this pressure gradient approaches zero at the condenser end cap similar to the low vapor flow rate case. Again, the capillary pressure difference at the evaporator end cap should be balanced by the sum of the total pressure drop in the vapor and liquid across the heat pipe.
The general trend at high vapor flow rates with low liquid pressure drops is different from the other two cases. The vapor pressure drop can exceed the liquid pressure drop in the condenser section. In such a case, the liquid pressure would be higher than the vapor pressure in the condenser section if the pressure in the liquid and vapor are equal at the condenser end cap. In reality, the wet point is not situated at the condenser end cap as shown in Fig. 4(b), and the menisci at the liquid-vapor interface in the condenser are curved.
Traditionally, heat pipe theory consists of fundamental analyses related to hydrodynamic and heat transfer processes. Fluid mechanics theory is generally used to describe the axial liquid pressure drop in the wick structure, the maximum capillary pumping head and the vapor flow in the vapor channel. Heat transfer theory is used to model the transfer of heat into and out of the heat pipe. Phenomena such as conjugate heat conduction in the wall and wick, evaporation and condensation at the liquid-vapor interface, and forced convection in the vapor channel and wick structure are described. The various thermal resistances or elements in a conventional heat pipe are shown in Fig. 5. The thermal processes such as solidification and liquefaction, and those related to rarefied gases can play important roles in modeling transient heat pipe operation during startup from the frozen state.
Fundamentally, one expects to analyze the internal thermal processes of a heat pipe as a thermodynamic cycle subject to the first and second laws of thermodynamics [1][2]. Zuo and Faghri predicted the transient heat pipe performance by using a simple thermal resistance model similar to that of Fig 5. However, classical heat pipe theory does not consider a thermodynamic approach. The idealized cycle is shown in Fig. 6(a). A quantity of heat, Qin, is applied to the heat pipe system at an average evaporator temperature, Te. Under steady operation, the same quantity of heat is rejected at a lower average condenser temperature Tc. Work is produced inside the heat pipe, but is then completely used in overcoming the hydrodynamic losses of the system. The thermal energy is converted to mechanical energy due to phase change at the liquid-vapor interface by producing a pressure head.
The thermodynamic cycle of the heat pipe is shown in Fig. 6(b) [2]. The fluid enters the evaporator as a compressed liquid at temperature T1 and leaves at temperature T2 or T2′ as saturated or superheated vapor, respectively. The vapor flows through the vapor channel from the evaporator to condenser due to the vapor pressure differential in the evaporator and condenser sections (2-3, or 2-2′-3). The vapor enters the condenser section as a saturated vapor or mixture. The condensate enters the adiabatic section as a saturated liquid (4). Finally, the liquid leaves the adiabatic section to enter the evaporator as a compressed liquid to complete the cycle. The work done on the working fluid during its circulation through the heat pipe is the area enclosed by the temperature versus entropy diagram shown in Fig. 6(b). As expected from the second law of thermodynamics, the conversion of thermal energy to kinetic energy is associated with heat rejection at a temperature below the high temperature reservoir in the system with efficiency less than 100%. It should be noted that in most heat pipes, the end-to-end temperature difference is small compared to other conductive systems. Nevertheless, the most ideal heat pipe can never be completely isothermal because this would violate the second law of thermodynamics. The capability of the simple thermodynamic analysis is very limited. In most cases, the heat transfer and fluid mechanics methodologies are needed to solve a heat pipe problem, especially when a quantitative solution is required.
References
- ↑ Zuo, Z. J., Faghri, A., and Langston, L., 1998, "Numerical Analysis of Heat Pipe Turbine Vane Cooling," Journal of Engineering for Gas Turbines and Power, 120(4), 735-743.
- ↑ 2.0 2.1 Khalkhali, H., Faghri, A., and Zuo, Z. J., 1999, "Entropy Generation in a Heat Pipe System," Applied Thermal Engineering, 19(10), 1027-1043.