Design, cfd analysis and comparison of tapered heat pipe

. A heat pipe is a form of heat exchanger that is used to transmit heat from one end to another end. By incorporating an evaporation-condensation system cycle, a Tapered heat pipe can transport heat by capillary action. Heat pipe is comprised of three segments: Adiabatic, Evaporator, and Condenser. Condenser section (D) diameter is bigger than evaporator section (d) diameter in a tapered heat pipe design, allowing for an increase in vapor volume. The investigation deals with the design and CFD analysis of Tapered heat pipe will be performed. From the existing experimental data, the numerical analysis on tapered heat pipe is performed. In this numerical analysis the different D/d ratios are considered i.e., 1,2,3 and 4. Heat input values considered are 20 Watt and 50 Watt for all the D/d ratios. On investigating the tapered heat pipe for different D/d ratios we observed approximately 12% variation between existing experimental results and numerical results. A large variation in heat transfer coefficient in higher D/d ratios at higher temperatures are observed. At lower temperatures the variation of heat transfer coefficient along the D/d ratios is neglectable. These higher heat transfer coefficients of the tapered heat pipe are best suitable for cooling electrical components such as CPUs, circuit boards and transistors. In the present world of electric vehicles, the tapered heat pipe can also be used battery thermal management systems.


Introduction
Heat pipes are closed evaporator-condenser systems made of copper, water, ethanol, or other fluid-friendly materials.High-vapor-pressure working fluid saturates the wick's pores at the appropriate operating temperature.The heat pipe evaporates the liquid in the wick.Heat is absorbed at the evaporator end of the heat pipe and discharged at the condenser end when vapour condenses into a liquid to cool the device.The condenser end of the heat pipe receives heat and releases it at the evaporator end.*Corresponding author: bulipechinanookaraju@gmail.comThis aerospace-tested technology conducts thermal energy 100 times faster and has a superior energy-to-weight ratio than most effective solid conductors.Many applications employ heat pipes, which are approximately 70 years old.Heat pipes, two-phase heat transfer devices, transmit heat with little temperature loss.Thus, heat pipes are used in avionics, electronics cooling, design, medicine, transportation, and more.
In this numerical investigation, a new design of tapered form along the length of the heat pipe with small evaporator section diameter and bigger condenser section diameter is investigated.This is done to assist the significant volume growth of liquid water when it evaporates.Wider heat transfer area and larger diameter of the condenser section result in greater condensing heat transfer.The numerical investigation attempts to examine how the performance of a tapered heat pipe can be improved by varying the ratio between the diameters of the condenser and evaporator and the heat input.With the results obtained from the investigation heat transfer coefficient is evaluated as follows: Where, Te = Temperature of the Evaporator (0C).
Tc= Temperature of the Condenser(0C).As = Surface area of the heat pipe(m2) Qin = Heat Input(W).and 45o for copper nanofluid [10].Stéphane Lips et.al performed an experiment determines heat pipe thermal resistance and limitations.This experiment is a generalization of a recent analytical solution for a flat plate heat pipe entirely insulated on one face, and this work focuses on capillary-covered heat pipes.The experiment predicts thermal and hydrodynamic heat pipe performance, capillary structural parameters, and operating limitations using experimental findings.The thermal resistance and maximal heat transmission capabilities of these heat pipes make it impossible to compare them.Despite these limitations, the model may be utilized to build a heat pipe or simulate its behavior in a practical application, according to this article.It may also optimize heat sources and heat sinks on an electronic card and predict capillary structure essential characteristics using experimental data [12].

Numerical Formulation
To conduct numerical analysis for tapered heat pipe with Ansys Fluent.A multiphase flow process is included which has two combination of phases i.e. phase 1 is considered as waterliquid and phase-2 is considered as water-vapour.

Meshing
In Ansys Fluent meshing is the process of dividing the whole body into a small linear cubes or tetrahedral shapes.These smaller cubes or tetrahedral shapes are easy to solve with the Navier strokes equation.In this tapered heat pipe, geometry is divide into linear cubes, tetrahedral and hexagonal shapes as shown in the figure 3.Each of the sliced sections are named as evaporator section, adiabatic section and condenser section.The fluid region is named as fluid zone.

Model Setup
The geometry here is the exact model of the heat pipe used for experimentation.The problem we are simulating is called a multi-phase problem.For the simulation of this type of problem we generally adopt the volume of fluid (VOF) method in two-phase modelling.For solving Pressure-Based solver is selected and the energy equation was ON.Because of varying volume fraction with time, transient condition was employed.The multi-phase model was ON and the VOF model is selected.The number of phases is selected as two because liquid and gas are present in the heat pipe making the liquid-water as the primary phase and watervapor as the secondary phase.The body force is taken as implicit because of gravity effect.Standard K-epsilon in the viscous model is taken, so the flow is turbulent, and the flow is far away from the wall.The mass transfer mechanism between the two phases is solely because of evaporation and condensation.Lee's model is taken as evaporation and condensation model.Evaporation and condensation frequency is taken as 10/s and 5/s respectively.The interaction between phase-1 and phase-2 in terms of surface tension is taken as 0.072N/m.For saturation properties, saturation temperature is taken as constant with value 300K.

Materials:
The Tapered heat pipe is made up of copper.In materials there are three phases solid, liquid and mixtures.Depending on the species material is allotted.The liquid phases considered are primary phase-1 is water-liquid and the secondary phase-2.

Steps and boundary conditions
Initial evaporator height fill ratio was unity.The evaporator liquid is patched as a unity since the fill ratio is 100%.Initial condenser and adiabatic section fill ratio is 0. Due to boiling and condensation, phase-1, water-liquid, becomes phase-2, steam (water-vapour).The literature review experiments determine the volume fraction in condenser and adiabatic.The solution uses water at saturation pressure.
Heat flux is considered as boundary condition at evaporator region for different heat input and different D/d ratios and at condenser section boundary condition is consider as a convective heat transfer coefficient for a constant water bath temperature of 297K. the adiabatic section boundary condition is given as heat flux 0 W/m2 because it is insulated wall.No-slip conditions are given to the walls as fluid has zero velocity compared to the boundary.Hence, velocity boundary condition will become Uwall = 0.

Solution
The Navier-Stokes equations are solved using SIMPLEC.QUICK, a higher-order differencing system with three-point upstream weighted interpolation for cell phase variables, is used to discretize momentum, volume fraction, and energy.All cases had a time step of 0.001s and a total time of 4500s.Time variation was also noticed.CFD simulations calculate heat pipe thermal resistance by obtaining fraction profile temperature and pressure.A comparison is made between existed experimental data and numerical boiling temperature for different diameter ratios (D/d) and different heat inputs (20w, 50w) is shown in the figure 16.It is also observed that in existed experimental data and numerical investigations, with increase in heat input, boiling temperature is increasing.However, the deviation between the existed experimental data and numerical values is approximately 12 to 15 % and is generally because in experimentation the temperature of the water being circulated at condenser end is not constant, where as in CFD a constant water batch temperature is used.A comparison is made between existed experimental data and numerical different diameter ratios (D/d) and different heat inputs (20w, 50w) with the heat transfer coefficient is shown in the figure 17.It is observed that in existed experimental data and numerical investigations, with increase in heat input, heat transfer coefficient is increasing.also be seen that increasing in diameter ratios the heat transfer coefficient is increasing.We concluded that, when compared with the conventional heat pipe, tapered heat pipe produces more heat transfer coefficient.For conventional heat pipe it is approximately 0.5 kW.m-2K but in tapered ratio 3 it's nearly 3.3 kW.m-2K.However, the deviation between the existed experimental data and numerical values is approximately 12 to 15 % and is generally because, in experimentation the temperature of the water being circulated at condenser end is not constant, where as in CFD a constant water batch temperature is used.

Conclusion
In the numerical analysis for different Heat inputs (20W, 50W) and D/d ratios (1,2,3) are analyzed and compared with the existed results.It found that Heat input increases the heat transfer coefficient raises and by changing D/d ratios heat transfer coefficient increases.On comparison with existed experimental results and CFD numerical results, there is a 10-12% deviation.
Hence, we concluded that Tapered Heat pipe with ratio: 2 and 3 are applicable for moderate and high temperature.

Figure 2 .
Figure 1.Geometry of Tapered heat pipe.Figure 2. CAD Model of Tapered heat pipe.

Figure 5 Figure 6 .Figure 7 .Figure 6
Figure 5 Depicts the heat pipe temperature distribution with a 50W heat input.At the evaporator end highest temperature is recorded as 341K and lowest temperature is 300.6Krecorded at condenser end.4.1.2Temperature Contour for D/d: 2

Figure 7
Figure 7 Depicts the heat pipe temperature distribution with a 50W heat input.At the evaporator end highest temperature is recorded as 354.4K and lowest temperature is 300.4Krecorded at condenser end.

Figure 9 1 Figure 10 .Figure 11 . 2 Figure 12 .Figure 13 . 3 Figure 14 .Figure 15 .Figure 16 .
Figure 9 Depicts the heat pipe temperature distribution with a 50W heat input.At the evaporator end highest temperature is recorded as 344.2K and lowest temperature is 300.3Krecorded at condenser end.4.2 Contours of pressure 4.2.1 Pressure Contour for D/d: 1