Advances in Heat Transfer (eBook)

VI Design of Microgrooved Heat Pipes

There are many factors to be considered while designing an MHP. For a working fluid, the compatibility, thermal stability, wettability, vapor pressure, high latent heat, high conductivity, low viscosity, high surface tension, and accepted freezing point have to be considered. A criterion for the selection of a coolant liquid were given in Faghri [12], Dunn and Reay [9], and Heine and Groll [151]. Dunn and Reay [9] defined merit number (Me) for the coolant liquid selection:

=ρlσlλlμl

For a sealed container, the compatibility, thermal conductivity, wettability, strength, porosity, and fabrication have to be considered. In addition to these characteristics, which are primarily concerned with the internal effects, the container material must often be resistant to corrosion (resulting from interaction with the environment) and malleable (to be formed into the appropriate size and shape). Apart from these considerations, operating temperature range, diameter, power limitations, thermal resistances, and operating orientation should also be considered. Sugumar et al. [152] reported that an MHP operated effectively by achieving its maximum possible heat transport capacity only if it was to operate at a specific temperature. In reality, an MHP might be required to operate at temperatures different from that temperature. In the study of Sugumar et al. [152], the heat transport capacity of an equilateral triangle MHP was investigated. The MHP was filled optimally with working fluid for a specific design temperature and operated at different operating temperatures. For this purpose, water, pentane, and acetone were selected as the working fluids. The optimal charge level of the MHP was dependent on the operating temperature. Furthermore, the results also showed that if the MHP was to be operated at temperatures other than its design temperature, its heat transport capacity was limited by the occurrence of flooding at the condenser section or dry out at the evaporator section, depending on the operating temperature and type of working fluid. When the MHP was operated at a higher temperature than its design temperature, the heat transport capacity increases, but it was limited by the onset of dry out at the evaporator section. However, the heat transport capacity decreased if it was to be operated at lower temperatures than its design temperature due to the occurrence of flooding at the condenser end. However, the design issues were reduced to two major considerations by limiting the selection to copper/water heat pipes for cooling electronics. These considerations were the amount of power the heat pipe was capable of carrying and its effective thermal resistance.

A conventional heat pipe, which operates on a closed two-phase cycle, consists of a sealed container lined with a wicking material. The container of the heat pipe can be constructed from metals, ceramics, composite materials, or glass. In all applications, careful consideration must be given to the material type, thermophysical properties, and compatibility. For example, the container material must be compatible with the working fluid, strong enough to withstand pressures associated with the saturation temperatures encountered during heat addition and have a high thermal conductivity.

A LIMITATIONS TO HEAT TRANSPORT

The most important heat pipe design consideration is the amount of power that a heat pipe is capable of transferring. Heat pipes can be designed to carry a few watts or several kilowatts depending upon the application. Heat pipes can transfer much higher power for a given temperature gradient than even the best metallic conductors. If driven beyond its capacity, the effective thermal conductivity of the heat pipe was significantly reduced. Therefore, it is important to ensure that the heat pipe is designed to safely transport the required heat load.

The maximum heat transport capability of a heat pipe is governed by several limiting factors which must be addressed while designing a heat pipe. There are eight heat transport limitations of a heat pipe. These heat transport limits, which are a function of a heat pipe operating temperature, include viscous, sonic, capillary pumping, entrainment or flooding, boiling, condenser, vapor continuum, and frozen start-up. A typical heat pipe limit is presented in Fig. 18. It is possible to ensure that the heat pipe can transport the required thermal load, improve the design and material selection process, and provide a heat pipe that can function within a specific operating temperature range both effectively and reliably. For effective cooling, a heat pipe must operate within its limits [40].

1 Capillary Limit

The capillary action is caused at the evaporator due to the concave meniscus with higher pressure in the vapor than liquid. The higher liquid pressure is communicated to the condenser where liquid and vapor pressures are nearly equal. This drives the liquid from the condenser to the evaporator. The capillary pressure is responsible for the fluid circulation in a heat pipe. It is the limitation of fluid flow for a given capillary pressure difference generated, when this difference is exactly met by the pressure required for the flow of fluid. The heat input corresponding to this is called the critical heat input. Any higher value of heat input generates a dry spot in a heat pipe, and the length of the dry region is called the dry-out length. Therefore, at the critical heat input, we have zero dry-out length and for any higher heat input it increases. For a safe operation of a heat pipe, the capillary pumping head developed should be greater than the required pressure drop for the fluid flow.

The capillary limit for an MHP was investigated. Ma and Peterson [153] presented a mathematical model for predicting the capillary limit of an MHP. In this model, a method for determining the effect of the vapor–liquid frictional interaction on the liquid flow was included. A 2D model for the vapor flow friction factor was developed to obtain the friction factor for the vapor channel with an irregular shape. A control volume technique was employed to determining the flow characteristics of the liquid flow in the MHP. The results indicated that the contributions of the vapor–liquid frictional interaction were very important in determining the maximum heat transport capability, and depend on the operating temperature.

a Critical Heat Input

The critical heat input for an MHP, where the flow is sustained by capillary pumping, is defined as the heat input when the flow resulting from the curvature change is not able to meet the flow requirement due to higher rates of evaporation. For such a case, the radius of curvature of the liquid meniscus at the hot end reaches a value very close to zero and the device approaches its operating limit. This limit is called the capillary limit and it reaches first in many practical applications. From the Young–Laplace equation, it is clear that for the device to operate properly (no generation of dry spot) the radius of curvature should decrease monotonically from the cold to the hot end (R∗/dX∗should be always positive according to the coordinate system used herein). The value of R∗ at the hot end or the gradient of R∗ can also predict the operating limit of a heat pipe, that is, the critical heat input for a system controlled by capillary pumping. There are many methods to calculate the critical heat input. Some of them have been discussed below.

Numerical Method for Critical Heat Input Calculation

Numerical method to calculate the critical heat input was presented in Suman et al. [29]. They numerically found out the value of heat input so that the value of the radius of curvature at the end of the evaporative section is close to zero. That heat input was termed as the critical heat input.

Analytical Expressions for Critical Heat Input

The analytical expression of the critical heat input in the absence of gravity was derived in Suman and Kumar [32]. For constant heat fluxes in the evaporative and condensing regions Qc′=Q/f1WbLandQe′=Q/[(1−f2)WbL]), the expression for the critical heat input of an MHP in the absence of gravity can be given as

cr=2B1σlρlλlRo33B2L{1+f2−f1}

B1=[{cot (α+γ)−φ/2}+cot (α+γ)cos(α+γ)sinγsinα]

when

c′=Q(m+1)Wb(f1L)m+1(f1−X∗)mandQe′=Q(m+1)Wb(L(1−f2))m+1(X∗−f2)m

the expression for the critical heat input of an MHP without gravity is obtained as

cr=σlρlλlB1(Ro)33B2L(f2−f1)+3B2L(1−f2+f1)Lm(m+1m+2)

From the analytical expression we infer the following:

a. Qcr increases with an increase in the latent heat of vaporization.

b. Qcr increases with an increase in the surface tension of a coolant liquid.

c. Qcr increases with an increase in the density of a coolant liquid.

d. Qcr increases with...