Thermal performance analysis of heat pipe using response surface methdology

Abstract

Keywords: Heat Pipe; Nanofluids; Thermal Performance; Response Surface Methodology

Introduction

Heat Pipes (HPs) are the specific class of the heat exchangers. They are widely used in electronics cooling, spacecrafts, energy conservation, snow melting-deicing, energy storage, solar-thermal applications, cooling of gas turbine blades and domestic warm air heaters (USA). HP works on phase change phenomenon. Heat supplied to the evaporator section is used to vaporize the working fluid. Vapors of the working fluid move towards condenser section (due to pressure difference) and finally gets condensed

after rejecting heat to the cooling media of the condenser section. Now condensed liquid comes back towards the evaporator section through mesh wick structure [1] There are various operating limitations of heat pipes like sonic limit, entrainment limit, capillary limit, boiling limit and viscous limit [1]. Operating limitations are considered in design stage for the successful working of HP in varying and prolonged working conditions. Selection of operating parameters like heat load, orientation, volume, type of

*Corresponding author. *E-mail address: naveen.gupta@gla.ac.in This paper was recommended for publication in revised form by Regional Editor Younes MENNI Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

working fluid and vacuum pressure, depend on operating limitations. Figure 1 shows the various design/operating parameters considered by researchers in last 10 years. Researchers are already working on design parameters like shapes of HP [2] and mesh type [3][4][5] from last many years. Researchers noticed the superior thermophysical properties of nanofluids [6]. Superior thermo-physical properties make them futuristic class of thermofluids. Choi et al [7] introduced nano-fluid as the suspension of nanoparticles (size<100nm) in base fluids. He presented the NFs as the potential thermo-fluids for future endeavors. Thermal performance of heat pipe (TPHP) depends on the thermophysical properties of working fluid like density, wettability, dynamic viscosity, thermal diffusivity etc. [8]. Superior thermo-physical properties of working fluids enhance the TPHP. Poplaski et al. [9] studied the TPHP using nanofluids (like Al2O3, CuO and TiO2) as working fluid. Authors claimed that higher concentration of NFs reduced the convection currents, therefore, deteriorated the TPHP. In the era of nanotechnology, researchers used nanoparticles of highly conductive materials in various thermal applications in order to obtain the desired results [10]. Thermal diffusivity is the most important characteristic of NFs which plays an important role in heat transfer processes [11]. Therefore, nanoparticles of highly diffusive metals are considered to prepare NFs. Other properties like density, specific heat, surface characteristic etc. also have their own impact on thermal characteristics. Researchers have both positive and negative opinion regarding the application of NFs as working fluids in HPs. Some researchers claimed that NFs enhance the TPHP [11,12,13,14]. Qu et al [11] studied the oscillating heat pipe (OHP) using Al2O3-water NF.

Researchers showed that alumina NF enhanced the thermal performance of OHP. Deposited nanoparticles create convection current and improve the wettability of the evaporator surface. Qu and Wu [15] analyzed the TPHP using SiO2/water and Al2O3/water NF respectively. Results showed that Al2O3/water NF increased the TPHP while SiO2/water NF decreased the same. The main cause of the enhancement was the improved surface condition of HP. Xue et al. [16] conducted an experimental study on the TPHP using carbon nanotube suspension and found significant deterioration in thermal performance. Addition of carbon nanotube, changes the solid-liquid-vapor interfacial properties, and deteriorate the boiling heat transfer rate. Das et al. [17] investigated the variation in thermal conductivity with temperature. Authors claimed that thermal conductivity of NFs depends on the size of nanoparticles. Thermal conductivity of NF increases with the decrease in size of nanoparticles. Mahdavi et al [18] studied the heat transfer characteristics of HP. Authors performed numerical as well as experimental investigations and found good agreement between the results. Authors concluded that superior thermal conductivity of NF is the major cause of the enhancement in TPHP. The other major causes are extended surface area, reduction in bubble formations, enhanced wettability, higher conductivity of interfacial layer etc. Gupta et al [19] studied the application of CeO2/H2O nanofluid in HP. Authors observed good agreements between experimental and numerical data. Researchers [20] presented the review on nanofluids application in heat pipes and concluded that maximum thermal performance of heat pipe is obtained for suitable value of nanoparticles concentration.

Enhancement in thermal performance is obtained due to the increment in number of nucleation sites and superior thermal conductivity of nanofluids. Ahmadi et al [21] presented model for pulsating heat pipe, by applying GMDH (group method of data handling) neural network. Model predicted the value of thermal resistance and effective thermal conductivity with good accuracy. Maddah et al [22] presented numerical investigation for boiler efficiency. Researchers used response surface method to optimize the thermal efficiency for the variable mass flow rates and steam temperatures. In recent years research is going on the effect of nanoparticles coated mesh surface on thermal performance of HP. Researchers [23] used Al2O3 and TiO2 nanoparticles coated wick surface in their experimental study. In nanofluid applications, stability plays an important role. Due to sedimentation and agglomeration of nanoparticles, thermophysical properties of nanofluids deteriorate in prolonged working conditions. Therefore, TPHP also changes [24]. In nanoparticles coating, detachment of nanoparticles from the parent surface also causes deterioration in TPHP. But this deterioration is negligible as compared to the deterioration in case of nanofluids (due to sedimentation and agglomeration of nanoparticles)[25]. In last 20 years, researchers noticed that NF applications enhance the TPHP [26],[27]. Suspended nanoparticles reduced the bubble generation rate at the solid-liquid surface and leading to the reduction in thermal resistance. In available research articles, limited research on parametric optimization has been done [28]. The Optimization work on HP using nanofluids is available in very limited cases [29]. Limited research articles focus on the basic mechanisms and physics of NF application on TPHP. Therefore, in present work authors made an attempt to analyze the thermal

performance of heat pipe using Al2O3/water. Authors identified and highlighted the mechanism responsible for the change in thermal performance. RSM is an effective tool for optimization purpose.

Method And Materials

Al2O3 nanoparticles were purchased from Nano Research Lab (Jharkhand, India). Nanoparticles were stirred into D.I water as per the requirement. D.I water was prepared by distillation-based water purification system in chemistry lab of GLA University, Mathura (India). Mixture of D.I. water and nanoparticles were stirred for 4 hours. Table 1 show the description of nanoparticles. There are two types of methods to prepare the NFs: single step and double step. In present study double step method was chosen to prepare the NFs. To ensure the good stability of NF, it was sonicated for 5 hours and allowed to Table 1. Description of nanoparticles S.N. Nanoparticles

Figure 2. Sedimentation test for Al2O3/H2O nanofluid, before and after 10 days.

Figure 3. Size distribution of nanoparticles in nanofluid by DLS technique.

Figure 4. Experimental set-up. settle down. Figure 2 shows the sedimentation test of nanofluid for 10 days. After 10 days no sedimentation or agglomeration was noticed. To ensure the stability, diffraction light scattering (DLS) test was performed. Figure 3 shows the DLS analysis of NF. DLS analysis shows the slight agglomeration of nanoparticles. The agglomerated size is known as secondary size of nanoparticles. Generally secondary size (Size of nanoparticle in liquid form) is higher as compared to primary size (size of nanoparticle in powdered form) due to slight agglomeration.

Experimental Setup

In present work, authors investigated the TPHP using Al2O3/water NF as working fluid. Figure 4 shows the experimental set up. Figure 5 shows the schematic of the experimental set up. At evaporator section, circumferential heater is used. Control switch is used to regulate the power supply. Cooling water jacket is attached at the condenser section. K-type thermocouples are attached to the wall surface of HP. For recording the temperatures, all the thermocouples are attached to data logger. Vacuum pump with stabilizer is attached to the HP. Fluid filling arrangement is also attached to the HP. Evaporator section is wrapped with glass wool to reduce the heat loss. An orientation adjustment stand is also attached to the HP. The temperature of cooling water is maintained with the help of an isothermal cooling bath. All

Figure 5. Schematic of the experimental setup. the temperatures were recorded after achieving the steady state of the set- up. The HP details and the uncertainties involved in experimentation are shown in Table 2 & Table 3 respectively. Uncertainty Analysis Uncertainty analysis is an inevitable step of the experimental studies and it provides the assurance of experimental results. Assessment of uncertainty involve the systematic analysis of all kinds of errors related to measuring instruments and procedures also. Moffat R.J. [30] described the detailed and structured procedure to analyze the uncertainty. The uncertainties concerned to heat supply, thermal resistance and thermal efficiency were evaluated according to the following relations. 1

The uncertainty associated with evaporator section was 3.7%. The uncertainty present in the measurement of heat loss was 4.1%. Uncertainty in heat supply, TRHP and TEHP were 3.5%, 3.87% and 4.1% respectively. Governing Equations For evaporator and condenser sections, thermal resistance is evaluated by the following expressions [31]: The total TRHP (R) = (TE –TC)/Qout

The Overall thermal conductivity (effective) of HP is evaluated by the following relation: Keff = Leff / (AxR)

RSM Methdology RSM mathematical modelling is used to determine the optimum results of any real-life application. RSM is used to find the most suitable combination of operating parameters to obtain the optimum results after performing minimum number of experiments. In present work, RSM architecture has four factors and five level for each. Heating power, orientation, filling ratio and nano fluid concentrations are treated as input parameters. The thermal resistance and thermal efficiency of HP are considered as the system responses. Table 4 shows the values of various factors and their levels considered in present study. Table 5 show the experimental results according to the CCRD structure. According to architecture matrix, experiments were conducted. Analysis of variance (ANOVA) for the above experimentation work provided the quantitative results for the p-value. Null hypothesis was rejected on the basis of p-value. The maximum acceptable p-value was 0.05. S values ensure the feasibility of the RSM model. For the above case S values were 0.565 and 3.451 respectively. R2 values were 97.35% and 96.35% respectively. R2 (adj) values were 96.23% and 96.6%.

Result And Discussion

Effects of Operating Parameters on Thermal Resistance The effects of operating parameters on thermal resistance of heat pipe (TRHP) are shown in Figure 6 (a-h). The Table 3. Measurements related uncertainties S.N.

TRHP depends on evaporator and conduction thermal resistances. Figure 6 (a) shows the dependence of TRHP on the increase in power and inclination angle (other parameters remain constant). Fig. 6(a) shows that the TR is inversely proportional to the power from 100Watt to 185 Watt, after that it depends directly on the power supply

(up to 200 Watt). The Brownian motion of the suspended nanoparticles depend directly on the power input. The thermal conductivity of NF is the function of temperature. The TRHP decreases up to the most favorable inclination angle (i.e. 60° angle) after that it increases. TRHP is determined on the basis of the wall temperature.

Figure 6. Parametric analysis for thermal resistance. Figure 6 (b) shows that the most favorable power supply and inclination angle are 185 Watt and 60° respectively for the minimum TR (less than 0.4°C/Watt). Figure 6 (c) displays the trend of TR for various inclination angles and concentrations. Orientation of HP has more impact on TR, minimum TR was found at 60° angle. TR continuously decreased initially with concentration and after 1.0%, increased slightly. Figure 6(d) shows that minimum TR (less than 0.4°C/Watt) was noticed at inclination angle of 60o and nanofluid concentration of

Conclusion

After conducting the experimental investigation, authors have drawn the following conclusions: • Nanofluids have the potential to enhance the thermal performance of heat pipe. Although stability issues restricted their use in prolonged working conditions. • The optimum value of thermal resistance and thermal efficiency are 0.3994 oC/Watt and 68.44% respectively. • Most suitable operating parameters for the maximum thermal performance in present investigation are as: 185.85 W Power, 60.09o inclination angle, 50.7% filling ratio and 1.05 % nanofluid concentration. • The predicted values by RSM model and experimental results validate each other. The nanofluids application in heat pipe improves the thermal performance. It involves more numbers of factors at mini, micro and nano level. Controlling of parameters simultaneously in order to obtain the maximum possible thermal performance at the aforesaid level is a challenging task. To explore the analysis at higher level of precision, advanced statistical tools and precise equipment are need to be developed.

Nomenclature

Nanofluid Thermal Resistance Central composite rotating design Wall temperature in °C Heat supplied Current supply Voltage Heat flux Length of evaporator section Length of adiabatic section Length of condenser section Heat Pipe Response surface methodology

Watt Thermal Resistance (°C/W) Thermal performance of heat pipe Surface area Effective thermal conductivity of the heat pipe Effective length of the heat pipe Cross-sectional (inner) area of heat pipe Thermal resistance of heat pipe Filling ratio (%) Concentration of nanofluid (vol. %) Input power (Watts)

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

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