Three-dimensional transient cooling simulations of a portable electronic device using PCM in multi-fin heat sink
Yi-Hsien Wang , Yue-TzuYang
Department of Mechanical Engineering
National Cheng Kung University, Tainan, 70101, Taiwan
Corresponding author. Tel.: +886-6-2757575 ext. 62172; Fax: +886-6- 2352973.
E-mail address: ytyang@mail.ncku.edu.tw
Abstract
Transient three-dimensional heat transfer numerical simulations were conducted to investigate a hybrid PCM (phase change materials) based multi-fin heat sink. Numerical computation was conducted with different amounts of fins (0 fin, 3 fins and 6 fins), various heating power level (2W, 3W and 4W), different orientation tests (vertical/horizontal/slanted), and charge and discharge modes. Calculating time step (0.03s, 0.05s, and 0.07s) size was discussed for transient accuracy as well. The theoretical model developed is validated by comparing numerical predictions with the available experimental data in the literature. The results showed that the transient surface temperatures are predicted with a maximum discrepancy within 10.2%. The operation temperature can be controlled well by the attendance of phase change material and the longer melting time can be conducted by using a multi-fin hybrid heat sink respectively.
Keywords: Phase change material, Electronic cooling, Numerical simulation
Source:Energy, Vol. 51, No. 4, pp. 320 -330 Year of Publication:2011
ISSN:0360-5442 Publisher:Elsevier
DOI :10.1016/j.energy.2011.06.023 © 2011 Elsevier Ltd. All rights reserved
Nomenclature
A, B, C Constant
b depth between heater to PCM (m) p
C specific heat (J/Kg K)
F melting volume fraction of PCM
g gravity (
m/s
2)H height of heat sink (m) specific enthalpy (J/kg)
h height of PCM (m)
he length of heater (m)
a b
L , L , Lc length of heat sink (m)
PCM
L length of PCM (m)
k thermal conductivity (W/m K)
P pressure (pa)
q wall heat flux (W/m2)
i S source term T temperature (K) t time step (s) t time (s) i j u ,u velocity (m/s) W width (m) We width of heater (m) Wf width of fin (m) Wpb width of PCM in case B (m) Wpc width of PCM in case C (m) , i j x x Coordinates (m) Greek symbols n
volume fraction in nth phase
thermal expansion coefficient
liquid fraction dynamic viscosity (kg/m s) density (kg/m2)
Constant Subscripts , i j component L Liquidm Melting
N nth phase
PCM phase change materials S Solid
1. Introduction
Sensible and latent heat storages are the physical phenomena for thermal energy storage which can be applied to different thermal applications, such as electronic cooling and hot water insulation. A latent heat storage system requires lower weights and fewer volume changes of material compared to conventional sensible heat energy storage systems for a given amount of energy.
Reviewed the PCM experimental study, Setoh et al. [1] examined the cooling of mobile phones using a phase change material (PCM). The result showed that using suitable usage of PCM could keep the mobile phone under a stable temperature. Ho and Viskanta [2] reported the heat transfer data during melting of n-octadecane from an isothermal vertical wall of a rectangular cavity. The result showed that except in the very early stages of melting, the rates of melting and of heat transfer were greatly affected by the buoyancy driven convection in the liquid. LAfdi et al. [3] studied the potential of using foam structures impregnated with phase change materials as heat sinks for cooling of electronic devices. Humphries and Griggs [4] investigated the heat transfer characteristics associated with the design and use of PCM thermal capacitors. Hongbo et al. [5] investigated the cold storage with liquid/solid phase change of water based on the cold energy recovery of Liquefied Natural Gas (LNG) refrigerated vehicles. Water was adapted as the phase change material. Chan and Tan [6] reported the findings of the solidification of an n-hexadecane inside a spherical enclosure. The results showed that the solidification phase front progressed concentrically inwards from the colder outer surface of the sphere.
The thermal management of battery modules with phase change materials (PCMs) is investigated experimentally by Duan and Naterer [7]. PCM cylinder surrounding the heater, and PCM jackets wrapping the heater are presented.
Wei et al. [8] reported a thermal energy storage system employing the phase change material (PCM) FNP-0090 (product of NipponSeiro Co. Ltd.) for a rapid heat discharge. The experimental study of PCM cooling application was studied by Fok et al. [9]. The result indicated that PCM-based heat sinks with internal fins could be viable for cooling hand-held electronic devices. A Phase Change Slurry (PCS) test is conducted by Huang et al. [10]. The results indicated that the paraffin/water emulsion containing a paraffin weight fraction of 30–50 wt.% is an attractive candidate. Mario et al. [11] studied a new type of wall panel which is called phase change material
structural insulated panel (PCMSIP). Pal and Joshi [12] carried out an experimental and computational study of melting in a tall enclosure by a constant heat flux source and adiabatic boundaries which focus on the effect of natural convection. Mettawee and Assassa [13] investigated the performance of a compact phase change material (PCM) solar collector based on latent heat storage. The experimental results showed that in the charging process, the average heat transfer coefficient increases sharply with the increasing molten layer thickness, as the natural convection grows stronger.
Numerical simulation study have been discussed and predicted as following. Shatikian et al. [14] carried out the transient three- and tow-dimensional simulations using Fluent 6.0 software. Results showed that the transient phase-change process, expressed in terms of the volume melt fraction of the PCM, depends on the thermal and geometrical parameters of the system. The numerical study of melting natural convection in a rectangular enclosure heated by three discreet protruding electronic chips has been conducted by Faraji et al. [15]. The result presented that the working time required by chips to reach the critical temperature depends closely on the substrate thickness. Kandasamy et al. [16] studied various parameters with PCM. Results showed that increased power input increased the melting rate. P. Lamberg and Siren [17] presented a simplified analytical model to predict the solid–liquid interface location and temperature distribution of the fin in the melting process with a constant imposed end-wall temperature. The result was consistent with the numerical data. Akhilesh et al.[18] presented a thermal design procedure for proper sizing of composite heat sinks to get the maximizing energy storage and the longer melting period in a given range of heat flux and height. Gong and Mujumdar [19] developed a novel storage unit of multiple phase change materials. The finite element model has been adapted to simulate the model involved as a result of alternating melting and freezing processes. Huang et al. [20] found that 2D model prediction was compared well with those of the 3D model under appropriate boundary conditions. Wang and Mujumdar [21] studied the effect of orientation of heat sink on the thermal performance. Brent et al. [22] used an enthalpy-porosity approach to model the melting of pure gallium in a rectangular cavity with combined convection-diffusion phase change. It showed that the method converges rapidly and is capable of accurately predicting both the position and morphology of the melt front at various time with relatively modest computational requirements.
Nayak et al. [23] studied the numerical model for heat sinks with phase change materials and thermal conductivity enhancers. Kim et al. [24] conducted the feasibility of using a novel cooling strategy that utilized the heat load averaging capabilities of a phase change material (PCM). Vargas and Bejan [25] studied the optimum thermodynamic match between two streams at different temperatures which
is determined by maximizing the power generation. Ravi et al. [26] studied the heat transfer behavior of phase change material fluid (PCM) under laminar flow conditions in circular tubes and internally longitudinal finned tubes.
Hao and Tao [27] studied the simulation of the laminar hydrodynamic and heat transfer characteristics of suspension flow with micro-nano-size phase-change material (PCM) particles in a microchannel. Saha and Dutta [28] studied the characterization of melting process in a Phase Change Material (PCM)-based heat sink with plate fin type thermal conductivity enhancers (TCEs). He et al. [29] combined phase equilibrium considerations with DSC measurements, a reliable design method to incorporate both the heat of phase change and the temperature range.
The present study simulates the cooling technologies of portable hand-held electronic devices with a constant and uniform volumetric heat generation using the phase change material. Dimensions and conditions of the test model referred to the experimental data reported by Fok et al. [9]. Correlations are developed for secured working time and the corresponding surface temperature.
2. Mathematical formulation 2.1. Governing equations
The schematic diagram of the three-dimensional physical models is shown in Fig.1. The system is designed based on the average dimensions of typical portable hand-held electronic devices and all dimensions of the computational domain refer to the experimental study by Fok et al. [9]. Dimensions of simulation for case A, B and C are listed in Table.1. The PCM is based on the properties of N-eicosane as listed in Table 2. The PCM base heat sink is composed by a solid aluminum block with a cavity that contains with 44 mL phase change material inside each case, and the height of air gap in each case is setting by 1 mm.
The following assumptions are made to model the PCM based heat sink heat transfer problem:
(1) three-dimensional, (2) laminar flow, (3) unsteady state,
(4) constant fluid properties, (5) neglect radiation heat transfer.
The governing equations for the conservation of mass, momentum and energy for this hybrid system can be written as
0 n n i i u t x (1) (2) momentum equation 2 , ( ) ( ) n i j i n i n n i n i j j j i u u u p u t x x x x g S (2) (3) Energy equation n ( n ) ( n i ) (k i i T u t x x xi) (3) wherenis the nth fluid’s volume fraction in the computational cells. For air phase, the density depends on its temperature as shown in Table 1. For the aluminum solid phase, constant thermo physical properties are specified. For the PCM phase, considering computational continuity during phase change, the density can be expressed as L PCM m (T-T )+1 (4) Where is the density of PCM at the melting temperature L Tmand is the thermal
expansion coefficient. is the dynamic viscosity of liquid PCM which is given by B
0.001 exp(A ) T
(5) Where A = and B = 1790 which is reported by Humphries and Griggs [4],
is the velocity component an is the specific enthalpy. 4.25
i
u d is the liquid
fraction during the phase change which occurs over a range of temperature s T Tl,
defined by the following rel
T ations: .T Ts, 0, a b. T Tl, 1, . , s s l l s T T T T T T T , c (6) The source term Siin the momentum equation is given by
2 3 C(1 ) i S ui (7) where C(13 )2
is the mimic ‘‘porosity function’’ defined by Brent et al. [22], so that the source term will be active while the liquid fraction is larger than zero to take the computational balance in momentum equation. The value of C is a mushy zone constant reflecting the behavior of melting phase-change materials. The value of
C = 105 has been used in the present study. The constant = 0.001 is a constant to avoid zero in the number.
2.2. Boundary conditions
Initial and boundary conditions follow the experimental setup by Fok et al. [9]. The entire initial calculation domain is setting the temperature at 25°C besides the base area of heater. The bottom wall of the heater (25 50 mm in x-z plane) in each case is set at a constant heating power with 3 W. The boundary condition in each side of the wall is setting adiabatic. The symmetry boundary condition in half domain is used to reduce the calculation time as shown in Fig.2. The appliance of symmetry verification is also discussed by Fok et al. [9]. The following initial and boundary conditions are applied to solve the governing equations:
1. Initial condition: (given in case A, B and C) 25
Tinitial °C, ui 0
2. Heat flux supplied from the bottom heater:
Case A '' 11~36 , s 0 , 17.5~67.5 k x mm y mm z mm T q y , Case B '' 11~36 , s 0 , 20.5~70.5 k x mm y mm z mm T q y , Case C '' 11~36 , s 0 , 23.5~73.5 k x mm y mm z mm T q y .
3. Symmetry boundary conditions at side: Case A 36 , 0~18 , 0~85 0 x mm y mm z mm T x , 36 , 0~18 , 0~85 0 i x mm y mm z mm u x Case B 36 , 0~18 , 0~91 0 x mm y mm z mm T x , 36 , 0~18 , 0~91 0 i x mm y mm z mm u x Case C 36 , 0~18 , 0~97 0 x mm y mm z mm T x , 36 , 0~18 , 0~97 0 i x mm y mm z mm u x
4. Insulation boundary condition: Case A 0 0 x mm T x , 0 , 18 0 y mm y mm T y
, (not including heater), 0 , 85 0 z mm z mm T z
Case B 0 0 x mm T x , 0 , 18 0 y mm y mm T y
, (not including heater), 0 , 91 0 z mm z mm T z Case C 0 0 x mm T x , 0 , 18 0 y mm y mm T y
, (not including heater), 0 , 97 0 z mm z mm T z 3. Numerical computations
The numerical solution has been solved using the Fluent 12.0 software. The half computational grid was built of 36 18 86
98
(55,728 cells) in case A,
(59,616 cells) in case B, (63,504 cells) in case C as shown in Fig.2. The grid test was compared to the experimental data results by Fok et al. [9]. After comparison to careful examination of grid refinement process, the grids are chosen to simulate the following cases. Compared to different calculating time step size, the transient temperature distribution of time step size
36 18 92 36 18
t
=0.05s shows a good alignment with the experimental data in Fig.3. The convergence criterion at each time step was checked under 104 for momentum equation and 106 for continuity and
energy equations.
The melting three-dimensional Navier-Stokes and energy equations are solved numerically by a finite-difference scheme, and an enthalpy-porosity approach equation is adapted to simulate the phase-change (melting) boundary. The PCM-air VOF model is implemented to solve the continuity equation and PCM-air gap boundary due to the phase change volume expansion. In the VOF model, the Geo-Reconstruct which is the volume fraction discretization scheme is used to calculate the transient moving boundary. If the transient temperature of calculation cell in the PCM domain is equal to or higher than the melting temperature, the continuity and momentum equation will be calculated in the system. A uniform grid system with a large concentration of nodes in regions of an even gradient is employed due to highly unstable melting process. The numerical method used in the present study is based on the SIMPLE algorithm of Patankar [30]. A comparison of theoretical predictions with the experimental data in the literature was used to assess the grid independence of the results.
Different sizes of meshes are employed to test the numerical model. The time step duration of calculation is also discussed in the literature for further precise prediction in Fig.4. The simulation result has been validated with the experimental data which was reported in Fok et al. [9]. Certain discrepancies between calculations and the available data by Fok et al. [9] may be caused by the round off and discretization or measurement errors. In addition, the three dimensionality of the power level may contribute to the discrepancy between model predictions and experimental data.
4. Results and discussion
The numerical simulation of different amount of fins in case A, B, C have been conducted with variable parameters including variations of power level (2W~4W), different orientation test (vertical/horizontal/slanted) and charge and discharge modes. The numerical algorithm and validation are evaluated in this study by comparing numerical predictions with available experimental data provided by Fok et al. [9].
4.1. Numerical validation
To verify the present numerical model, the prediction domain under the conditions power level of 3 W and the same geometry are compared with the available experimental results by Fok et al. [9] as shown in Fig.3. The result of theoretical predictions with the experimental data by Fok et al. [9] is used to assess the grid refinement.
Different meshes ( 30 16 80 , 36 18 86 and 42 22 88 ) in case A, ( 30 16 86 , 36 18 92 and 42 20 96
104 92
) in case B and in case C
( , and ) are employed in testing the numerical
models. The results of the grid sensitivity study show that the simulations based on the grid in case A,
30 16 92 36 36 18 18 98 86 42 20
36 18 in case B and 36 18 98 in case C provide satisfactory numerical accuracy and are essentially grid independent. The numerical results show that the transient surface temperatures are reasonably predicted within a maximum discrepancy within 10.2% in case A, 8.7% in case B and 8.3% in case C. Besides, the time step refinement is discussed for further precise calculation time step. Figure 4 shows that the time step size of 0.05 second in different cases have good approaches to experimental data. For saving computer time and avoid more round off errors, time step size of 0.05 second is chosen to simulate the relatively discussed cases. Further decrease the time step size to 0.03 second does not show any noticeable change in the instantaneous results for the transient temperature distributions.
4.2. Power level test
The effect of different heating power level (2W~4W) on the performance of heat sink with different fins (0~6fins) within PCM inside is examined in Fig.5. The results show that the higher power level transferred into the system, the earlier melting process will occur. The higher power source leads the earlier time from melting temperature (36°C). This phenomenon indicates the end of PCM melting function and no more temperature control ability after the melting temperature jumps. In each case, the power level of 2W in present calculation is still an undergoing phase change process after 150 min. The result of 2W predicts similar phase change process time period with 3W power level of reference data [9]. The results of 3W in each case are
much more matched than other power level tests with the 4W test in reference data [9]. The discrepancy may be caused by the round off error and discretization or measurement error. Considering these factors, the overall comparison with numerical test data is satisfactory with experimental one. The results of the grid sensitivity study and power level test showed that the simulations based on the grid provide satisfactory predictions.
4.3. Transient performance of charge and discharge modes
Fig.6 shows the comparisons of the transient surface temperature distributions of charge and discharge modes with the present numerical study and experimental result of Fok et al. [9]. The heating period is 4W on for 30 minutes, 0W off for 10 minutes, 4 W on for 30 minutes and 0W off for last 100 minutes. Total test time is 170 minutes to compare with available data Fok et al. [9]. Under the charging stage, the numerical result of peak temperature using PCM base heat sink model are 41.5°C in case A, 39.3°C in case B and 37.4 °C in case C. Due to the discrepancy of different fin numbers, the case C has a better temperature control than other cases. Under high power heating and high flux energy diffusion, 6 fin in case C has a lower temperature jump and smooth operation temperature distribution. In the same trying stage, the multi-fin heat sink with PCM inside presented powerful temperature control and maintained the system under a stable temperature gradient. Such temperature control will provide better system performance and prolong products life time.
4.4. Effect of orientation on PCM-based heat sink performance
The effect of multi-orientation is an important test for the PCM based heat sink
cooling technique to validate the thermal performance. Fig.7 indicates three different orientations which are vertical, horizontal and slanted (at45 ). In the front stage before melting process, the result shows no difference in three different tests. After the melting process, the temperature difference of orientation effect in the present study is less than 2°C. This test shows that orientation has a limited effect on the transient thermal performance in the hybrid cooling system. The results are similar to the references which are reported by Fok et al. [9], and Wang et al. [21].
4.5. Flow characteristics and heat transfer performance
Fig.8 to 10 illustrates the different stages in the melting process with the melting fraction of 0.1 to 1 and transient time of 3001.2s to 10480s. The morphology of the melting front is parallel to the vertical fin in fraction of 0.1 in each case. Similar melting front is discussed by Shatikian et al. [14]. Due to gravity effect and lower density, the air will keep on the top edge and the volume will change with the melting
fraction of PCM. The distribution of the each melting front is relatively matched with the melting temperature distribution. From Fig.8, the more influence of gravity effect is accompanied with the growth of melting area in fraction F = 0.3 and F = 0.6 in each case. At the same melting fraction stage, the fraction F = 0.1 in case A is 3001.2, 2401 and 3202 in case B and C. During the very early stage, heat transfer is dominated by conduction and the latent heat absorption of n-eicosane phase change will be accompanied. Therefore the temperature of each case are almost the same under melting temperature. In the melting fraction of F = 0.6 in each cases, case A has a higher temperature distribution ( = 308.6K) than case B ( =308.2K) although the melting time of case A is longer than case B. In case C, F = 0.9 has a smooth heat distribution and much longer melting time than others. After these results it can be realized that the overall temperature will be increased by the decreasing of melting fraction and PCM shows the powerful dominant of temperature control using a hybrid heat sink with PCM inside which is consistent with Kandasamy et al. [16].
min
T Tmin
4.6. PCM exploitation
Based on Fok et al. [9] experimental study and present numerical study, the usage of PCM with 6 fins prolonged the melting stage and provided stable and lower temperature in the exam module. Compared to case A, B and case C in Fig.8 to 10, the melting stage of case A was finished at 8201.2 seconds, case B was finished at 8187.0 seconds and case C was finished at 10480.0 seconds. Case B provided more stable temperature distribution than case A as shown in Fig.8 and Fig.9. From case C in Fig.10, the suitable fins arrangements can provide the system heat dissipation status which help to explore new hybrid efficiently cooling system under same operation temperature. Therefore present results could provide future exploitation based on same geometric and heat source.
5. Conclusions
Various transient three-dimensional heat transfer investigations of hybrid PCM based different fin amount heat sink numerical cooling technique are carried out in this study. Markedly flow field and heat transfer characteristics are found with variations of different power level (2W-4W), different orientation tests (vertical/horizontal/slanted), and charge or discharge modes. The theoretical model developed using laminar Navier-Stokes equations of motion, energy equation, porosity like source term and VOF model, is capable of predicting the flow and heat transfer characteristics correctly for a PCM based heat sink system. The numerical results show that the transient surface temperatures are reasonably predicted with a maximum discrepancy within 10.2%. Through this study, the finding indicated that
the use of PCM in the aluminum heat sink would give electronic packages a more stable operation temperature. The heat transfer performance of case C with 6 fins provides more stable temperature control, better cooling ability and lower maximum operation temperature than case B and case C. The orientation tests for various fins heat sink show the limited effect on the phase change performance of the system in each case. The results show that the operation temperature can be controlled well by the attendance of phase change material and the longer melting time can be conducted by using a multi-fin hybrid heat sink respectively.
Acknowledgements
The authors would like to sincerely thank Professor F. L. Tan, School of Mechanical Engineering and Aerospace, Nanyang Technological University for his providing the detailed dimensions and valuable experimental data for us to complete the numerical validations.
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Table Captions Table 1
Geometric parameters in the present numerical study. Table 2
Table 1
Geometric parameters in the present numerical study. Case A W(mm) La(mm) H(mm) b(mm) h(mm) he(mm) We(mm) Lpcm(mm) Wpcm(mm) 72 85 18 3 14 50 50 63 50 Case B W(mm) Lb(mm) H(mm) b(mm) h(mm) he(mm) We(mm) Wb(mm) Wf(mm) Wpb(mm) 72 91 18 3 14 50 50 50 2 15.75 Case C W(mm) Lc(mm) H(mm) b(mm) h(mm) he(mm) We(mm) Wpcm(mm) Wf(mm) Wpc(mm) 72 97 18 3 14 50 50 50 2 9
Table 2
Properties of PCM, aluminum and air used in the numerical calculation. Material k(W/m K) (kg/m3) p C (J/kg K) Tm(0C) (g m/s) (J/kg) N-eicosane 0.15 785 0.001(T-308)+1 2460 35-37 1790 exp( 4.25 ) T 247300 Aluminum 202.4 2719 871 660.4 __ __ Air 0.0242 1.2 10 5 20.01134 3.498 T T 1006.4 __ __ __
Figure Captions Fig. 1. The physical model.
Fig. 2. Computational grid distributions of half domain.
(a) case A (without fin) (b) case B (3fins) (c) case C (6fins)
Fig. 3. Effect of grid refinement on temperature distributions in the present study.
Fig. 4. Effect of time step refinement on the temperature distributions in the present study.
Fig. 5. Comparison of three different powers in the present study. (a) case A (without fin) (b) case B (3fins) (c) case C (6fins) Fig. 6. Effect of charge and discharge on the temperature distributions. Fig. 7. Effect of orientation on the temperature distributions at 3W.
Fig. 8. Evolution of melting process and temperature contour of the case A: (a) F= 0.1, t = 3001.2 s, (b) F= 0.6, t = 5601.2 s
(c) F= 0.9, t = 6801.2 s, (d) F= 1, t = 8201.2 s
Fig. 9. Evolution of melting process and temperature contour of the case B: (a) F= 0.1, t = 3001.2 s, (b) F= 0.6, t = 5601.2 s
(c) F= 0.9, t = 6801.2 s, (d) F= 1, t = 8201.2 s
Fig. 10. Evolution of melting process and temperature contour of the case C: (a) F= 0.1, t = 3001.2 s, (b) F= 0.6, t = 5601.2 s
Lb Heater PCM Heat sink w Wf Wpb he b h Wf Wpc he b h Lc w Heater PCM Heat sink (A) (C) (E) (B) (D) (F) b Lpcm h w Heater PCM Heat sink he Air gap H x z Y z Y g La g wpcm wpcm wpcm H H
(a) case A (without fin) (b) case B (3fins) (c) case C (6fins) Fig.2. Computational grid distributions of half domain.
0 20 40 60 80 100 120 140 160 20 40 60 80 30 50 70 T e m p eratur e ( 0C) Grid test
Exp. of Fok et al. [9] of case A 36x18x86 of case A Exp. of Fok et al. [9] of case B 36x18x92 of case B Exp. of Fok et al. [9] of case C 36x18x98 of case C
Time (min)
0 20 40 60 80 100 120 140 160 20 40 60 80 30 50 70 T e m p eratur e ( 0C)
Time step test
Exp. of Fok et al. [9] of case A t=0.05s of case A
Exp. of Fok et al. [9] of case B t=0.05s of case B
Exp. of Fok et al. [9] of case C t=0.05s of case C
Time (min)
(a) case A (without fin) 0 20 40 60 80 100 120 140 160 0 20 40 60 80 10 30 50 70 Tem p era ture( 0C)
Power test of case A Exp. of 4W of Fok et al. [9] Simulation of 2W Simulation of 3W Simulation of 4W Time (min) 0 20 40 -10 10 30 50 er r o f 3W p red ic ti on t o e x p. ( % ) (b) case B (3fins) 0 20 40 60 80 100 120 140 160 0 20 40 60 80 10 30 50 70 Temper ature( 0C)
Power test of case B Exp. of 4W of Fok et al. [9] Simulation of 2W Simulation of 3W Simulation of 4W Time (min) 0 20 40 -10 10 30 50 er r of 3 W pr edicti on to exp. (%) (c) case C (6fins) 0 20 40 60 80 100 120 140 160 0 20 40 60 10 30 50 Temper ature( 0C)
Power test of case C Exp. of 4W of Fok et al. [9] Simulation of 2W Simulation of 3W Simulation of 4W Time (min) 0 20 40 -10 10 30 50 er r of 3 W pr edicti on to exp. (%)
0 20 40 60 Time (min)80 100 120 140 160 180 10 20 30 40 50 60 15 25 35 45 55 Te mp era tu re( 0c)
Effect of charge and discharge usage Numerical prediction of case A Numerical prediction of case B Numerical prediction of case C Exp. of Fok et al. [9] for case A
0 20 40 60 80 100 120 140 160 20 40 60 80 30 50 70 Tempera tu re ( 0C) Orientation effect
Present result (vertical) of case A Present result (horizontal) of case A Present result (slanted at 450
) of case A Present result (vertical) of case B Present result (horizontal) of case B Present result (slanted at 450
) of case B Present result (vertical) of case C Present result (horizontal) of case C Present result (slanted at 450
) of case C
Time (min)
(a) F = 0.1, t = 3001.2 s (b) F = 0.6, t = 5601.2 s
(c) F = 0.9, t = 6801.2 s (d) F = 1, t = 8201.2 s.
Fig.8. Evolution of melting process and temperature contour of the PCM (Case A).
(a) F = 0.1, t = 2401.0 s (b) F = 0.6, t = 4302.0 s
(c) F = 0.9, t = 5298.0 s (d) F = 1, t = 8187.0 s.
Fig.9. Evolution of melting process and temperature contour of the PCM (Case B).
(a) F = 0.1, t= 3202.0 s (b) F = 0.6, t= 7191.0 s
(c) F = 0.9, t= 9183.0 s (d) F = 1, t= 10480.0 s.
Fig.10. Evolution of melting process and temperature contour of the PCM (Case C).
