J. Cent. South Univ. Technol. (2011) 18: 580-586

DOI: 10.1007/s11771-011-0734-2

Effects of bending on heat transfer performance of axial micro-grooved heat pipe

JIANG Le-lun(蒋乐伦), TANG Yong(汤勇), PAN Min-qiang(潘敏强)

School of Mechanical and Automotive Engineering,

South China University of Technology, Guangzhou 510640, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2011

Abstract: Heat pipe is always bent in the typical application of electronic heat dissipation at high heat flux, which greatly affects its heat transfer performance. The capillary limit of heat transport in the bent micro-grooved heat pipes was analyzed in the vapor pressure drop, the liquid pressure drop and the interaction of the vapor with wick fluid. The bent heat pipes were fabricated and tested from the bending angle, the bending position and the bending radius. The results show that temperature difference and thermal resistance increase while the heat transfer capacity of the heat pipe decreases, with the increase of the bending angles and the bending position closer to the vapor section. However, the effects of bending radius can be ignored. The result agrees well with the predicted equations.

Key words: electronics cooling system; axial micro-grooved heat pipe; bending; heat transfer performance

1 Introduction

Heat pipe is a highly efficient heat transfer component, and is widely used in electronics cooling, such as the CPU of desktop and laptop [1-2]. With higher integration of electronic components, heat pipe always needs to be bent in the thermal structure design of electronic cooling system because of the restriction of the geometrical structure and its limited space. So far, many researchers have investigated on the heat transfer performance of bent heat pipe. BLISS et al [3] designed a flexible heat pipe and found that bending little influenced the heat transfer performance. MERRIGAN  et al [4] tested the heat pipe with bending angles of 0°, 90° and 180°, and found that the distribution of axial temperature was associated with bending but the heat pipe could work normally after being bent by 180°. SHAUBACH and GERNERT [5] made comparisons on the heat transfer performances of sintered felt heat pipe, mesh heat pipe and V-grooved heat pipe before and after bending. The results indicated that the heat transfer limit of sintered wick is the best while the thermal resistance of V-grooved heat pipe is the least. DHANANJAY and DANIEL [6] theoretically analyzed and tested mini bent sintered heat pipe, and found that with bending angle increasing, temperature became different between the evaporator and condenser, and the heat transfer capacity decreased. TAO et al [7] found that the heat transfer limit of axial grooved heat pipes after bending by 90° is lower than that of the straight one. WANG et al [8] researched the start-up performance of different bending angles in axial grooved heat pipes and found that the bending heat pipe was more sensitive to the inclination.

A lot of work about bending heat pipe have been done in the 1970s and 1980s [9-10], but little research has been completely made on the heat transfer performance of the axial micro-grooved heat pipe at different bending position and bending radius. In this work, the capillary limit of the bent axial micro-grooved heat pipes was analyzed. Then the bent heat pipes were fabricated and an experimental platform was set. Finally, the experimental data were analyzed and discussed based on the bending angle, the bending position and the bending radius. These results can also be used as the basic data of bent heat pipe to guide the thermal structure design of electronic cooling system.

2 Theory analysis

The heat pipe has several performance limits, such as sonic limit, boiling limit, entrainment limit and capillary limit. However, it is bent at the adiabatic section, so only the capillary limit is affected [11]. Therefore, only the effects of bending on capillary limit were discussed in this work.

Three simple hypotheses were set before the analysis of the bent axial micro-grooved bending pipe:

1) Steady fluid flow and heat transfer,

2) The vapor phase and fluid phase in the state of laminar flow, and

3) Constant fluid properties.

According to the hydrodynamics, the impact force equation of the vapor to the wall and the wick fluid in the adiabatic section as shown in Fig.1 can be deduced as

where ρ_v represents the vapor density of fluid (kg/m³),  represents the vapor velocity of fluid (m/s), A_v represents the vapor cross section of heat pipe (m²) and α represents the bending angle.

Fig.1 Impact force from vapor to fluid

The vapor pressure drop in the bending section can be expressed as

where K_b can be calculated as

According to the Cotter theory, the vapor pressure drop inside the bent heat pipe is

where Q represents the total input heat transfer rate, μ_v represents the vapor viscosity, l_a represents the length of adiabatic section, r_v represents the radius of vapor section and h_fg represents the fluid latent heat of vaporization.

According to Darcy’s law, the liquid pressure drop can be calculated as

where m represents the mass flow rate of fluid, μ_l represents the liquid viscosity, l_eff represents the effective length of heat pipe, ρ_l represents the liquid density of fluid, k represents the liquid permeability of wick and A_w represents the cross section of wick.

Considering the effect from the vapor impact force and gravity, the equation of the liquid pressure drop is

where ε (ε<1) represents a geometrical parameter concerned with the wick structure in the heat pipe and l_hp represents the length of heat pipe.

CHI [12] proposed the pressure balance equation in the heat pipe:

Δp_cap≥?p_v+?p_l±?p_g                            

where Δp_cap represents the maximum capillary pumping press and ?p_g represents the hydrostatic pressure due to gravity.

Ignoring the vapor pressure drop of the straight pipe, the calculating equation of capillary limitation can be expressed as

where σ represents the surface tension of wick, r_e represents the capillary radius of the evaporator, φ represents the angle between the heat pipe and the horizontal plane, f_l represents the liquid friction coefficient and f_v is the vapor friction coefficient.

Considering F_x and ?p_b, Eq.(9) can be modified as

The capillary limitation of the heat pipe in this experiment was tested in the horizontal orientation, therefore, the influence from its gravity on the heat transfer performance can be ignored, and Eq.(10) can be simplified as

3 Experimental

3.1 Fabrication of bent heat pipes

The rectangular grooves in the axial micro-grooved heat pipe were fabricated by oil-filled high-speed spin forming process [13-15]. This fabrication method has the advantages of high depth to width ratio of the grooves, adjustable tear number and different pipe radii. The experimental heat pipes were cylindrical ones with a length l_hp=350 mm, an outside radius R_w=3 mm, a groove height h=0.26 mm, and a groove width w₂=0.18 mm, as shown in Fig.2. Heat pipes were charged with 0.91 mL of the purified water as the working fluid.

Fig.2 SEM image of wick structure

The bending position (S) can be expressed as

where l_b represents the length from the heating end.

The heat pipes could be identified by the bending position (30%, 50%, 70%) and bending radius (R15.0, R17.5, R20.0), as shown in Table 1, and every sample could be bent from 0° to 135° with increment of 45° at each testing.

Table 1 Bending parameters of heat pipes

3.2 Experimental setup

An experimental setup was designed for testing heat transfer performance of bent heat pipes, as shown in Fig.3. It was mainly composed of heating module, cooling module and data collecting module. The experimental setup was placed on a horizontal platform with ambient temperature 25 °C, and the adiabatic section of the heat pipe was exposed in the air.

The heating module was used to heat the heat pipe as the vapor section at different input power, while the cooling module was designed to cool as the condenser section of heat pipe at a constant temperature. The data collecting module consisted of five pieces of thermal resistor Pt100, data collecting module (NI Compact DAQ and data collecting card USB-9217), and NI labview data acquisition program. The position of thermal resistor was marked in Fig.3. T₁ and T₂ were located at the two ends of the heating section, T₄ and T₅ at two ends of the cooling section, and T₃ at the adiabatic section, which were all pressed tightly to the heat pipe wall with spring force and insulated from environment.

Fig.3 Schematic diagram of experimental setup (mm)

3.3 Experimental procedure

The experimental test was performed to investigate the heat performance of the bent heat pipes. The constant temperature bath was adjusted at (50±0.5) °C and the flux of glass rotameter at (200±1.5) L/h to keep the working temperature of heat pipe at 60-70 °C, which was a reliable temperature value for general electronic components. Load power was varied from 25 W with increment of 5 W, and the test would be stopped when the temperature at the evaporator end cap increased drastically due to dryout. The wall temperature of the heat pipe was recorded at the steady state by each thermal load step. The results of the test included the errors in the measurement, such as tolerance of the input power (±0.5 W) and temperature fluctuation error   (±0.1 °C).

4 Results and discussion

4.1 Effects of bending angle

When the input power reaches a value Q_in, a smaller input power increase, ?Q_in, will make the temperature at the evaporator end abruptly increased compared with other temperatures at the evaporator. The input power Q_in can be defined as the heat transfer limit [16].

Fig.4(a) presents the effect of bending angles on the wall temperature distribution along the longitudinal axis of pipe 2 with the input power of 30 W. The temperature difference is below 3 °C, which indicates that the heat pipe still has good isothermal characteristics with different bending angles. Fig.4(b) presents the effect of bending angles on the temperature difference with different input powers of pipe 2. When the input power is below heat transfer limit, the temperature difference is small, which means that the thermal equilibrium, namely isothermal property of the bending pipe from the evaporator to the condenser is well accomplished. However, the temperature difference is increased with the increase of the bending angle at the same input power. According to Eqs.(4), (5) and (7), the vapor pressure drop and liquid pressure drop increase as the bending angle increases, and the pressure drop may largely affect the temperature distribution of the heat pipe [17]. When the input power exceeds the limit of the bent heat pipe, temperature difference will increase dramatically. This is because the pressure drop balance, as presented in Eq.(8), is broken and the capillary force of working fluid is not enough to flow from the condenser to the evaporator. There is not enough working fluid to wet the top part of the vapor section, and the bent heat pipe is dry.

The thermal resistance of heat pipe is defined as

where T_e,ave represents the average temperature of the evaporator and T_c,ave is the average temperature of condenser.

Fig.4 Effect of bending angles on wall temperature distribution along longitudinal axis (a) and temperature difference with different input powers (b)

Fig.5 presents the effect of bending angles on the thermal resistance under different input powers of pipe 2. When the input power is below heat transfer limit, thermal resistance is 0.07-0.10 °C/W, which indicates that heat pipe works well at a relatively steady thermal resistance value with different bending angles. However, the thermal resistance increases with the increase of bending angle at the same input power. Pressure drop increases as the bending angle increases at the same heat flux, and the returned flow of the condensed liquid to evaporator decreases, therefore, the thermal resistance increases by a relatively thick liquid film of the condenser. When the input power exceeds the heat transfer limit, the thermal resistance abruptly increases, due to the fact that the end cap of the evaporator is dry, which means that the heat transfer of the heat pipe is only the heat conduction by the wall without high speed vapor.

Fig.5 Effect of bending angles on thermal resistance under different input powers

Fig.6 presents the effect of bending angle on the heat transfer limit of pipe 2. The heat transfer limit decreases greatly with the increase of the bending angle, and almost 30% at the bending angle of 45° compared with that of the straight heat pipe. However, heat transfer limit decreases especially fast at the bending angles between 0° and 45° and is slowed down above 45° with increasing the bending angle. According to Eq.(11), the capillary limit decreases as the bending angle increases, so Eq.(11) agrees with Fig.6. According to Eq.(2), the high-speed flowing vapor impacts the working fluid in the grooves and disperses part of working fluid in the bending section, which further affects the heat transfer limit of heat pipe.

Fig.6 Effect of bending angles on heat transfer limit

4.2 Effects of bending position

In the heat dissipation design of electronic products，the adiabatic section of heat pipe is not virtually adiabatic but always exposed to the air, so the adiabatic section in this experiment is placed in the air. Therefore, there is temperature difference between the adiabatic section and environment, so fluid condensation also happens in the adiabatic section and the vapor flow velocity in the adiabatic section is not a constant value but decreases with the increase of the length.

Fig.7(a) presents the effect of bending position on the wall temperature distribution along the longitudinal axis of pipes 4, 5 and 6 at the bending angle of 90° with input power of 30 W. The temperature difference is less than 2.5 °C, which indicates that heat pipes have good isothermal property with different bending positions. Fig.7(b) presents the effect of bending position on the temperature difference under different input powers at the bending angle of 90° of pipes 4, 5 and 6. When the input power is below heat transfer limit, temperature difference increases with the input power. This is due to the fact that the vapor flow velocity increases with increasing input power. According to Eq.(5), the vapor pressure drop also increases, therefore, the temperature difference increases [16]. The temperature difference generally increases as the bending position value, S, decreases at the same input power. It is because the vapor flow velocity and the vapor pressure drop at different bending positions are various. When the input power exceeds the limit of the heat pipes, the heat transfer performance is sharply deteriorated.

Fig.7 Effect of bending position on wall temperature distribution along longitudinal axis (a) and temperature difference under different input powers (b)

Fig.8 presents the effect of bending positions on the thermal resistance under different input powers at bending angle of 90° of pipes 4, 5 and 6. When the input power is below the limit of the heat pipes, the thermal resistance increases with decreasing bending position value, S, and the thermal resistance is 0.067-0.11 °C/W. According to Eq.(7), the vapor flow velocity affects the liquid pressure drop at different bending positions, and thickness of the liquid film at the condenser changes, which causes the variety of thermal resistance.

Fig.8 Effect of bending position on thermal resistance under different input powers

Fig.9 presents the effect of bending position on the heat transfer limit of pipes 4, 5 and 6. The heat transfer limit of pipes 4, 5 and 6 is about 55 W in their straight state. However, compared with the straight heat pipe, the maximal decrease of heat transfer limit is about 40% at the bending position value of 30%, while the minimal decrease is about 15% at the bending position value of 70%. So the heat transfer limit is increased obviously with the increase of the bending position value, S. The vapor flow velocity in the adiabatic section decreases with the increase of the bending position value, S. In accordance with Eq.(11), the vapor flow velocity will decrease the capillary limit in the heat pipe by influencing the vapor pressure drop and fluid pressure drop.

Fig.9 Effect of bending positions on heat transfer limit

4.3 Effects of bending radius

Fig.10(a) presents the effect of bending radius on the wall temperature distribution along the longitudinal axis of pipes 1, 4 and 7 at the bending angle of 90° with the input power of 30 W. The temperature difference is less than 2.5 °C, so heat pipes have good isothermal property under different bending radius. Fig.10(b) presents the effect of bending radius on the temperature difference under different input powers at the bending angle of 90° of pipes 4, 5 and 6. The temperature difference is always less than 3 °C when the input power is below the heat transfer limit. As shown in Fig.10, the bending radius has little effect on the temperature difference. This is because the bending radius of the axial micro-grooved heat pipe is always larger than 15 mm due to the restriction of the bending technique, and large radius results in little influence on bending pressure loss, as a result, the effects of bending angle on the temperature difference can be ignored.

Fig.11 presents the effect of bending radius on the thermal resistance under different input powers at bending angle of 90° of pipes 1, 4 and 7. The thermal resistance is 0.067-0.085 °C/W and its fluctuation is little under different bending radius compared with the straight heat pipe. This indicates that bending radius shows little effect on thermal resistance of heat pipes.

Fig.10 Effect of bending radiuses on (a) wall temperature distribution along longitudinal axis; (b) temperature difference under different input powers

Fig.11 Effect of bending radiuses on thermal resistance under different input powers

Fig.12 presents the effect of bending radius on the heat transfer limit of pipes 1, 4 and 7. Fluctuation of the heat transfer limit is within 5 W under different bending radius. The possible reason lies in the fact that the bending has little damage to the grooves in the heat pipe, so the capillary force is almost the same at different bending radius. The vapor pressure drop at different bending radius can be ignored, so the capillary limit varies little.

Fig.12 Effect of bending radiuses on heat transfer limit

5 Conclusions

1) Heat pipe can still keep good isothermal property after being bent. But the temperature difference increases with increasing the bending angle and decreasing the bending position value, S. The bending radius shows little effect on the temperature difference.

2) The thermal resistance of the bending heat pipe keeps below 0.11 °C/W. The bending angle and bending position shows great influence on the thermal resistance, but the effect of the bending radius can be ignored.

3) The bending of the heat pipe has very great effect on the heat transfer limit. The overall heat transfer coefficient is decreased by almost 30% at the bending angle of 45° and by about 40% at the bending position of 30% compared with that of the straight heat pipe. However, the bending radius affects little on the heat transfer limit of the heat pipe.

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(Edited by LIU Hua-sen)

Foundation item: Project(U0834002) supported by the Joint Funds of the National Nature Science Foundation of China and Guangdong Province; Project (2009ZM0134) supported by the Foundational Research Funds for the Central Universities in China

Received date: 2010-03-29; Accepted date: 2010-06-29

Corresponding author: PAN Min-qiang, Associate Professor, PhD; Tel: +86-20-87114634; Fax: +86-20-87114634; E-mail: mqpan@scut.edu.cn