ISTP-16, 2005, PRAGUE 16 TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA MOLECULAR DYNAMICS SIMULATION ON TOTAL THERMAL RESISTANCE OF NANO TRIANGULAR PIPE C.S. Wang* J.S. Chen* and S. Maruyama** * Department of Mechanical Engineering, National Taipei University of Technology **Department of Mechanical Engineering, The University of Tokyo Corresponding author: cswang@ntut.edu.tw Keywords: Molecular dynamics, Total Thermal Resistance, Surface Potential Energy Abstract This article studied the non-equilibrium heat transfer behavior in the nano triangular pipe. Molecular Dynamic simulation generates two controllable isothermal phantom boundary condition to compule internal temperature filled. The phantom work form, the change of integrating surface potential energy and the total thermal resistance can be computed by the temperature distribution along the axial direction. Results reveal that the total thermal resistance which included the solid-liquid resistance (evaporation and condensation region) and liquid-vapor resistance (adiabatic region). The total thermal resistance shows near parabolic type curve with respective to surface potential energy. By increasing the surface energy produce the more dense argon atoms aggregate in bottom and top lays which will be more heat transfer generated by phantom Pt molecular. But, as the surface energy larger than the optimal surface energy, argon atoms are absorpted and condensated over the surrounding which will decrease the rate of heat transfer and produce larger thermal resistance. 1 Introduction The article [1] reveals that the thermal resistance is the more important property not only in the marco size but also the micro or nano scale, previously. On the other hand, the resistance of the very small liquid-solid interface may be significant at some small system size with the reduction of the system size. The Molecular Dynamic(MD) method is a very useful technique to simulate the nano heat transfer in the microscopic scale [1]. For example, studies of basic mechanisms of heat transfer such as in phase change heat transfer demand the microscopic understanding of liquid-solid phenomena. Maruyama[2] discovered liquid molecular condenses argon in the solid surface under different temperature and different surface energy inside a periodic nano boundary condition. The thermal resistance in the interface of liquid-solid was also measured by MD simulation. They proposed that the thermal resistance was equivalent to 5~20nm thickness of liquid heat conduction layer, and was strongly dependent on the wettability. It was demonstrated that a thermal resistance cannot be neglected over a solid-liquid interface. The MD studied the thermal resistance of Lennard-Jones solid crystals in the nonequilibrium system by Matsumoto et al [3]. Inside fcc crystal, one-dimensional steady heat conduction was realized by using a pair of temperature controlling heat baths. They found the temperature profile of the interface would be not continuous when the crystal is with different size parameter as the extended of a jump temperature. Moreover Ohara et al[4]. have analyzed the possible explanation of the thermal boundary resistance based on their intermolecular energy transfer concept developed by the detailed studies of heat conduction in liquid phase water [5] and Lennard- Jones fluid[6]. Lee [7] said when the system size is microscopic as in thin film 1
Chin-Shu Wang, Jong-Shun Chen, Shigeo Maruyama composites, the small thermal resistance due to molecular level ordering in noticeable even for the prefer solid-solid. Even though many authors researched about the thermal resistance in the nano-scale, but no ones talked about the shape effects of the pipe before. In the macro heat transfer, we can use the hydraulic radius to calculate the pipe s cross section shape area, and also consider the surface energy of the surrounding boundary which play an important role in this nano scale heat transfer. In addition the resultant of force (surface tension) will be depended on the angle of the corner, the surface energy[8] and the solid temperature. The paper will explore the results of nano triangular pipe affect the thermal resistance and the dynamic behavior of the fluid. 2 Molecular Dynamics Method Fig.1 shows the configuration 93.627 81.084 219.57Å θ=60 of triangular nano heat pipe which has both top and bottom solid phantom layer Pt and enclosed by Pt lateral surface. Liquid argons accumulate at top (condensation zone) and bottom (evaporation zone) surface, saturated argon vapor at the middle(adiabatic zone). The argon-argon interactive force is confined by Lennard-Jones potential form as σ 12 σ 6 φ( r) = 4ε[( ) ( ) ] (1) r r which use cut off distance 3.5σ and corresponding parameters as: σ Ar =3.4 Å, m Ar =6.036 10-26 kg and ε Ar =1.67 10-21 J. the harmonic oscillating FCC(1,1,1) crystacl structure there layer solid Pt wall has each layer 1156 Pt molecule at the top and down side and related Pt parameter as: m Pt =3.24 10-24 kg, σ s =2.77 Å(equilibrium distance) and k=46.8n/m(spring constant). It s noticed that the free electron transfer heat s effects are ignored in this solid wall. The Ar-Pt interactive force uses the one dimension integrated potential function. In FCC(1,1,1) surface as 4π 3 ε INT σ INT 10 σ INT 4 Φ ( Z ) = [2( ) 5( ) ] (2) 2 15 σ Z Z s which has the minimum potential value at Z=σ int as 4π 3 σ INT 2 ε surf = ( ) ε INT (3) 5 σ s where the σ int =(σ s+ σ Ar )/2=3.085 Å and ε int between 0.527 10-21 J to 1.169 10-21 J list in Table 2 of E2~E6 case. 3 Results and Discussion Fig. 2 shows the temperature field along the axial which the reveal that the discontinuity difference as T Evap = 5. K, T cond = 6. K for jump 59 jump 71 the E3 case. By using the conduction thermal resistance s definition R T =T jump /q w, the resistance can be computed as R Evap 6 2 = 0.124 10 m K W, p / R cond p / 6 2 = 0.145 10 m K W, also the thermal conductions coefficient can be calculated by the slope of temperature distribution ( T Z ) as Evap cond λ L = 0.164W / mk, λ L = 0.045W / mk. In order to interpret the physical meaning of thermal resistance, define a length scale of LR = λrrt which represent the effective thickness of thermal resistance. Results show the L R, L Evap = 10. nm, R 8 L cond R = 12. 6nm are coincident with Maruyama[2], 5~20nm thickness. The other E2~E6 case computed data list in Tab.1~Tab.3. Different surface potential energy affects the liquid vapor interface change. Fig. 3 shows the molecule distribution (E2~E6) at the front view of pipe which vary the surface potential. Results reveal the interface appear convex at E2, E3 case, E5, E6 case appear concave interface and E4 case appear flat interface. The above phenomena show that adhesion force is smaller than attractive force in E2, E3 case, but E5, E6 case show that adhesion force is larger than attractive force. The E4 case show the balance of adhesion force and attractive force. By comparison of the mass flow rate M of E2~E6 case in Tab.1 show that E2, E3 have larger mass value than E5, E6 and E4 case has M(678.4kg/m 2 s) maximum value which reveal 2
MOLECULAR DYNAMICS SIMULATION ON TOTAL THERMAL RESISTANCE OF NANO TRIANGULAR PIPE argon molecule in the flat liquid-vapor interface has the critical maximum mass evaporating rate. Different surface potential energy affects the number density contour change. Fig. 4 shows the number density contour which are averaged contour in the plotting to condensation, adiabatic and evaporation zone. At 1000ps, the argon there are not affects by temperature driving difference force and molecules are just confined by the Pt-Argon surface energy only. Fig. 4(a) shows uniform number density contour in the evaporation and condensation zone but Fig. 4(c) reveals molecular absorpted and concentrated inside the channel groove. As the surface potential increases form E2 to E6 case, obviously the quantum discredited number density profile inside the groove. At 5000ps, the argon there are affected by temperature driving difference ΔT larger than the surface potential energy. Obviously, Fig.4 (d) in the condensation zone, number density contour concentrated than Fig. 4(a) at 1000ps for E2, E4, E6 case. Reversibly, in the evaporation zone, Fig. 4(d) number density contour sparse than it at 1000ps for E2, E4, case. The driving temperature difference has much stronger effects on the E4 case but slowly in E6 case (as in Fig4. (f)). Different surface potential energy affects the total thermal resistance. Tab.3 show the total T evap cond thermal resistance ( R = R + R + R ) sys adi varies with surface potential E2~E6 case where the R is the thermal resistance in the adiabiatic adi zone, the R is the thermal resistance evap cond in the evaporation zone, the R is the thermal resistance in the condensation zone. Fig. 3 shows both thermal resistance has well coincidence with Maruyama [2] paper which just consider the thermal resistance only. Fig. 3 shows the R T sys has a minimum optimal value near the E4 case which represents the phantoms (ΔT temperature difference effect) balance the Pt surface potential effect (absorption the argon inside the groove ) and also has a highest mass-flow rate M=6.78.4 Kg/m 2 s inside the nano heat pipe. 4. Conclusions The molecular dynamics applied in the triangular nano heat pipe get the following results as: 4.1 The number density profiles have the same quantum energy level location inside the triangular groove (σ int /Sin30 ) which respect to different Pt surface potential energy. 4.2 The thermal resistance decreases with the increasing a surface potential result of the decreasing temperature jump. 4.3 Consider the surface potential in the triangular heat pipe, the adiabatic zone need to compute the liquid, vapor and interface energy flux and the over saturated liquid in the condensation zone result in the backward inside the groove. 4.4 The optimal mass flow rate in E4 case which has the minimum optimal total thermal resistance and has a maximum mass flow rate which is the balance effects of exciting phantom molecule and absorpted surface Pt molecule. 5 Acknowledgements The authors gratefully acknowledge efforts of our student C.S. Chen during this study and the funding supported by NSC 92-2212-E027-012 References [1] S. Maruyama, "Molecular Dynamics Methods in Microscale Heat Transfer," Handbook of Heat Exchanger Update, (2002), pp. 2.13.7-1-2.13.7-33. [2] S. Maruyama and T. Kimura, A study on Thermal Resistance over a Solid-Liquid Interface by the Molcular Dynamics Method, Threm. Sci. Eng., Vol. 7, no.1, 1999. [3] M. Matsumoto, H. Wakabayashi and T. Makino, Thermal Resistance of Crystal Interface: Molecular Dynamics Simulation, Trans. JSME, Ser. B, vol.68, no. 671, pp. 1991-1925, 2002. [4] T. Ohara and D. Suzuli, Intermolecular Energy Transfer at a Solid-Liquid Interface, Micro. Thermophys. Eng., vol. 4, No. 3, pp. 189-196, 2000. [5] T. Ohara, Intermolecular Energy Transfer in Liquid Water and Its Contribution to Heat Conduction: An Molecular Dynamics Study, J. Chem. Phys., vol. 111, pp. 6492-6500, 1999. [6] T. Ohara and D. Suzuli, Intermolecular Energy Transfer to Heat conduction in a Simple Liquid, J. Chem. Phys., vol. 111, pp. 9667-9672, 1999. [7] Lee, S,-M., Matamis, G., Cahill, D. G, and Allen, W. P., Thin-Film Materials and Minimum Thermal Conductivity, Microscale Thermphys. Eng., vol.2, no.1, pp.31-36 1998. 3
Chin-Shu Wang, Jong-Shun Chen, Shigeo Maruyama 7. Table and Figure Tab. 1 Simulation conditions and measured values. See Fig. 12 and nomenclature. Tab. 2 Adiabatic energy flux for vapor, liquid, interface and adiabatic thermal resistance. ε int ( 10-21 J) Q v a (MW/m 2 ) Q L a (MW/m 2 ) Q I a (MW/m 2 ) Q t a (MW/m 2 ) Tadi jump (K) R adi (*10-6 m 2 K/W) E2 0.527 7.00 0.00 2.83 9.83 0.14 0.014 E3 0.688 9.89 0.00 17.32 27.21 0.23 0.008 E4 0.848 8.35 0.95 14.79 24.09 0.84 0.035 E5 1.009 6.18-2.80 14.13 17.51 2.76 0.158 E6 1.169 3.30-5.98 9.14 6.46 2.84 0.440 Tab. 3 Solid-liquid thermal resistance, adiabatic zone thermal resistance and system total resistance. ε int ( 10-21 J) R adi (*10-6 m 2 K/W) R Evap (*10-6 m 2 K/W) R Cond (*10-6 m 2 K/W) R T sys (*10-6 m 2 K/W) E2 0.527 0.014 0.247 0.212 0.473 E3 0.688 0.008 0.124 0.145 0.277 E4 0.848 0.035 0.099 0.093 0.227 E5 1.009 0.158 0.064 0.063 0.285 E6 1.169 0.440 0.061 0.048 0.549 4
MOLECULAR DYNAMICS SIMULATION ON TOTAL THERMAL RESISTANCE OF NANO TRIANGULAR PIPE Fig. 2 The temperature distribution along the axial direction at 3000 ps in E3 case Fig. 1 The configuration of nano triangular heat transfer system 5
Chin-Shu Wang, Jong-Shun Chen, Shigeo Maruyama convex convex flat concave concave E2 E3 E4 E5 E6 Fig. 3 The front view of triangular pipe molecular plotting at 3000ps, curve show the interface of liquid, vapor (convex, concave and flat curve). (a) (b) (c) (e) (f) (g) Fig. 4 The number of density contour plat show the different surface potential energy (E2~E6) with condensation, adiabatic and evaporation zone. 6
MOLECULAR DYNAMICS SIMULATION ON TOTAL THERMAL RESISTANCE OF NANO TRIANGULAR PIPE Fig. 5 The total thermal resistance R T very with the surface potential energy for E2~E6 case. 7