energies Article
A Numerical Study on Natural Convection Heat Transfer of Handheld Projectors with a Fin Array Jin-Cherng Shyu *, Tsuni Chang and Shun-Ching Lee Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 80778, Taiwan;
[email protected] (T.C.);
[email protected] (S.-C.L.) * Correspondence:
[email protected]; Tel.: +886-7-3814526 (ext. 5343) Academic Editor: Kamel Hooman Received: 8 December 2016; Accepted: 20 February 2017; Published: 23 February 2017
Abstract: This study numerically investigates the effects of the number of bottom openings and the fin spacing on both the natural convection heat transfer and airflow field of the handheld projector with various orientations. The horizontally-oriented 120 mm × 53 mm × 19 mm handheld projector, which had 11 bottom openings and was installed with either 7 plate fins or 13 rows of square pin, was considered as the primary case. The fin number varied from 6 plates to 13 plates or from 7 pin rows to 16 pin rows, while the bottom openings varied from 11 to 15 in this study with handheld projector held at a specified inclination ranging from −90◦ to 90◦ . The results showed that the heat transfer coefficient of a specific surface of the plate-fin array installed in the primary handheld projector increased from 6 to 7 W/m2 ·K as the heating power increased from 2 W to 7 W. The optimal fin spacing in the handheld projector possessing 11 bottom openings was 2.875 mm and 3.375 mm for the plate-fin and pin-fin, respectively, at a heating power of 7 W. Although the velocity magnitude of the airflow between fins increased as the bottom opening increased, it was not able to offset the reduction of the airflow velocity resulting from the fin spacing reduction. Keywords: natural convection; fin array; openings; fin spacing; thermal resistance
1. Introduction Cooling hot electronic chips in an enclosure under natural convection condition is sometimes favorable because of numerous advantages that active cooling technique using blowers cannot achieve, such as noiseless, energy-saving and cost reduction. Handheld projectors, also named pico projectors, which are devices capable of projecting the information displayed on the mobile phone screen onto a larger surface to share with audience are highly demanded and consequently are expected to become a built-in device in every mobile phone in the near future. No matter what type of light source is used for the light engine in a handheld projector, the light engine generates a considerable amount of heat [1,2] within the handheld projector. Because maintaining the light engine at a comparatively low temperature is crucial for excellent and stable display quality, to efficiently dissipate the heat from the light engine to the ambient is of great importance. An isolated surface which excludes the interaction between the airflow induced by adjoining extended surfaces can be considered as the most simplified configuration of a fin array. Numerous heat transfer correlations on the natural convection of an isolated surface with various inclinations in form of Nu = CRan have been proposed [3–8]. To some degree, those heat transfer studies on an isolated surface formed the foundation of numerous following studies which investigated various effects on the natural convection heat transfer of a fin array in an infinite, still medium [9–18]. The results of those studies revealed that the fin material, fin pattern, and the spacing between fins, as well as the fin thickness affect the thermal performance of the fin array. Because the airflow of free convection is induced by buoyancy, the orientation of the fin array also plays an important role in heat transfer Energies 2017, 10, 266; doi:10.3390/en10030266
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under natural convection condition. In addition, some of those studies proposed empirical correlations which are applicable to predict the heat transfer coefficient and the optimum fin spacing [13,14,16] of a fin array in an infinite, still medium. Milnes et al. [19,20] examined the turbulence models to predict the variation of steady-state heat transfer coefficients throughout the Hypervapotron using computational fluid dynamics software. Drikakis et al. [21] investigated the formation of spurious vortical structures in incompressible flow simulations employing Godunov-type methods. However, the situation which a fin array is arranged in an enclosure, for example, the handheld projector, is much harsher than the situation stated in the previous paragraph, since the induced airflow for cooling the fin array is restricted by both the openings position and the dimensions of the case, and the clearance between the fin array and the shield in the vicinity as well. Shyu and Chan [22] measured the thermal resistance and the temperature distribution of the case surface of handheld projectors possessing a fin array. Three different handheld projector designs having two different types of fin arrays were tested. They also proposed a thermal resistance network of the handheld projectors to investigate the heat transfer coefficient of those combinations based on the measured temperature and thermal resistance. In order to enhance the heat transfer of the handheld projector, Shyu and Tsai [23] installed a piezoelectric fan that had a Mylar blade vibrating at several specific frequencies at 110 V in the handheld projector. The effects of both the operating frequency of the piezoelectric fan and the heating power on the vibrating amplitude of the piezoelectric fan, and the thermal performance of the handheld projector were investigated in this study. Since it could be expensive and time-consuming to experimentally investigate various effects of handheld projector on both the airflow field and heat transfer of the handheld projector in detail, this study aims to numerically investigate the thermal characteristics of a 120 mm × 53 mm × 19 mm handheld projector equipped with either a plate-fin array or a pin-fin array under natural convection condition. The effects of both fin dimensions of the plate and pin fin arrays and the openings on the lower case of the projector, and the handheld projector orientation as well, on the airflow in the projector and thermal resistance of the projector will be numerically investigated in this study. 2. Computational Methods and Boundary Conditions A 120 mm × 53 mm × 19 mm acrylic housing having several openings which is similar to a commercially available handheld projector (DIGI-EYE MP101, Inventec Besta, Taipei, Taiwan) was employed for the present numerical simulation as shown in Figure 1a,b. The heat-dissipating light engine in a practical handheld projector was transformed as an assembly of a 10 mm × 10 mm heater and a 47.5 × 33.5 mm × 12 mm insulation block of 0.687 W/m·K in thermal conductivity. A heat sink which is made of Al 6061 and consists of a plate-fin or pin-fin array, a rectangular fin array base and a heat sink plate extending from the fin array base as shown in Figure 2 tightly attached to the heater. Please refer to [22,23] for more detailed description of the dimension and material of all parts in the handheld projector. The numerical simulation with a handheld projector being centrally located in an 840 mm × 371 mm × 209 mm computational domain as shown in Figure 1b was performed in this study using commercially available software, COMSOL 5.1. The 3-dimensional numerical simulation was performed based on the following assumptions and boundary conditions:
• • • • • • •
Both heat transfer and airflow in the simulation are steady. Airflow is incompressible and laminar. Radiation heat transfer is negligible. All properties of air are functions of temperature obtained from COMSOL database. The thermal conductivity of all solids in the computational domain is constant as listed in Table 1. Ambient temperature is constant at 303 K. All boundaries of the computational domain in Figure 1b were regarded as walls on which airflow velocity is zero and the temperature is constant at 303 K.
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Table 1. Thermal conductivity of all solids in the computational domain. Item
Projector Case
Heat Sink
Heater
Insulation Block
Material Thermal conductivity Energies 2017, 10, 266
PMMA 0.22 W/m·K
Al 6061 167 W/m·K
Kapton 0.12 W/m·K
phlogopite 0.687 W/m K 3 of·17
Table 1. Thermal conductivity of all solids in the computational domain
The set of governing equations including continuity equation, momentum equation and energy Item Projector Case Sink Heater Insulation Block equation of air flow in the computational domainHeat in three-dimensional Cartesian coordinates are listed Material PMMA Al 6061 Kapton as Equations (1)–(3), respectively, subject to the aforementioned assumptions.phlogopite Thermal conductivity
0.22 W/m·K
167 W/m·K 0.12 W/m·K 0.687 W/m·K → · V = 0 equation, momentum equation and energy The set of governing equations including∇continuity equation of air flow in the computational domain in three-dimensional Cartesian coordinates are → → * * listed as Equations (1)–(3), respectively, subject to the aforementioned assumptions. 2
ρ0 V · ∇ V
= −∇ p + µ∇ V + ρ g ∇ ⋅V = 0
(2)
(1)
→ ·∇ T = ∇ · ( k ∇T ) ρC p V ρ 0 V ⋅ ∇V = −∇p + μ∇ 2V + ρg
(1)
(
)
→
(2)
(3)
where ρ0 , ρ, V, p, µ, T, Cp , and k are reference ) air, temperature-dependent ρC p (V ⋅ ∇ )density T = ∇ ⋅ (k∇Tof (3) density of air, velocity vector of the airflow, pressure, viscosity, temperature, specific heat, and the thermal where ρ 0 , ρ, V , p, μ, T, Cp, and k are reference density of air, temperature-dependent density of air, conductivity of air, respectively. In addition, the following heat diffusion equation was simultaneously velocity vector of the airflow, pressure, viscosity, temperature, specific heat, and the thermal employedconductivity to computeofthe in each solid,heat diffusion equation was air,temperature respectively. distribution In addition, the following simultaneously employed to compute the temperature distribution in each solid,
∇2 T2 = Q ∇ T =Q
(4)
(4)
where Q iswhere zero Q for the in computational domain heaterwhich which dissipates power of qs . is all zerosolids for all in solids the computational domainexcept except the the heater dissipates power of qs. Upper case Fin array base Heat sink plate
Side openings (left)
Heat sink consisted of a fin array, a fin array base and a heat sink plate Lower case Front openings Insulation block Bottom openings
Heater
Side openings (right)
Battery socket
(a)
Handheld projector
Computational domain The six faces of the computational domain were treated as walls at 303 K.
(b)
Figure 1. Schematic diagram of (a) the handheld projector in this study; (b) the computational domain including the handheld projector, the surrounding air, and its mesh.
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(b)
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Energies 2017, 10, 266 domain including the handheld projector, the surrounding air, and its mesh
116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140
Numerical simulation of the governing equations performed by COMSOL is based on finite Numerical simulation of the governing equations performed by COMSOL is based on finite element method that subdivides the entire computational domain into simpler finite elements, and element method that subdivides the entire computational domain into simpler finite elements, and then uses variational methods to solve the problem by minimizing an associated error function then uses variational methods to solve the problem by minimizing an associated error function based based on Galerkin method of weighted residuals. The governing equations are transformed into a on Galerkin method of weighted residuals. The governing equations are transformed into a set of set of linear algebraic equations. These equations were solved using SIMPLE algorithm for the linear algebraic equations. These equations were solved using SIMPLE algorithm for the pressure pressure correction processes, and convective and diffusive terms in the governing equations are correction processes, and convective and diffusive terms in the governing equations are discretized discretized by upwind and central difference schemes, respectively. The maximum number of by upwind and central difference schemes, respectively. The maximum number of iteration was iteration was 200, while approximately 170,000 grids were established in the computational domain. 200, while approximately 170,000 grids were established in the computational domain. The number The number of grid was tested prior to the numerical study, and it was determined while the most of grid was tested prior to the numerical study, and it was determined while the most accurate accurate results were obtained based on the comparison between the values obtained from results were obtained based on the comparison between the values obtained from simulation and simulation and the measured values. The comparison of thermal resistance and surface temperature the measured values. The comparison of thermal resistance and surface temperature distribution distribution are shown in Figure 3(a) and Figure 3(b) based on the current number of grid. The are shown in Figure 3a,b based on the current number of grid. The feature size of the mesh in feature size of the mesh in the computational domain ranged from 0.35 mm to 80 mm as revealed in the computational domain ranged from 0.35 mm to 80 mm as revealed in Figure 1b. The residual Figure 1(b). The residual−reached 2×10-3 ~ 4×10-3 while finishing computation, which correspond to − 3 3 reached 2 × 10 ~4 × 10 while finishing computation, which correspond to approximately 2 h of approximately 2 hours of computation time per case on a Pentium processor (Intel Xeon E3-1230, 4 computation time per case on a Pentium processor (Intel Xeon E3-1230, 4 cores, 3.2 GHz) computer cores, 3.2 GHz) computer with 16.0 GB memory. with 16.0 GB memory. In order to assure the reliability of the simulation results, the airflow field and the temperature In order to assure the reliability of the simulation results, the airflow field and the temperature distribution within the computational domain where a horizontally-oriented handheld projector distribution within the computational domain where a horizontally-oriented handheld projector was was arranged in the center equipped with either a plate-fin array or a pin-fin array as illustrated arranged in the center equipped with either a plate-fin array or a pin-fin array as illustrated Figure 2 Figure 2 was first computed at several heating powers ranging from 2 W to 7 W, and then those was first computed at several heating powers ranging from 2 W to 7 W, and then those simulated data simulated data were compared with the experimental results reported in [22]. Note that the were compared with the experimental results reported in [22]. Note that the horizontally-oriented horizontally-oriented handheld projector having either a plate-fin array possessing 7 7-mm-wide, handheld projector having either a plate-fin array possessing 7 7 mm-wide, 10 mm-high and 2 mm-thick 10-mm-high and 2-mm-thick rectangular plates as shown in Figure 2(a), or a pin-fin array possessing rectangular plates as shown in Figure 2a, or a pin-fin array possessing 13 rows of square pin as shown 13 rows of square pin as shown in Figure 2(b), and 11 bottom openings was considered as the in Figure 2b, and 11 bottom openings was considered as the primary case. primary case.
Figure 1. Schematic diagram of (a) the handheld projector in this study, (b) the computational
, Sf
141 142 143
(a) Figure 2. Cont.
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, Sf
144 145
(b)
146 147
Figure 2. The detailed dimensions of the heat sink having (a) a plate-fin array, and (b) the pin-fin Figure 2. The detailed dimensions of the heat sink having (a) a plate-fin array; and (b) the pin-fin array array in the primary handheld projector in the primary handheld projector.
148 149
Besides, the thermal resistance of the handheld projector from the heater to the ambient was defined as Besides, the thermal resistance of the handheld projector from the heater to the ambient was defined as TT−TT R s s aa R= (5)(5) qqs s
Ta and qs areq the ambient temperature, 303 K, and the heating power of the heater, respectively, 150 where where Ta and s are the ambient temperature, 303 K, and the heating power of the heater, and Ts is the average temperature over the entire heater surface estimated by 151 respectively, and Ts is the average temperature over the entire heater surface estimated by 1 Ts =T 1 TT((x, dA x, yy))dA s A s A A sA Z
s
152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172
s
(6) (6)
3. Results and Discussion 3. Results and Discussion The comparison of both the thermal resistance and the temperature distribution on the handheld Thebetween comparison of both the thermal the temperature distribution thethe projector the data obtained from theresistance numericaland simulation of the primary designonand handheld projector between the data obtained from the numerical simulation of the primary design measured data reported in [22] are presented in Figure 3. It can be seen in Figure 3a that the thermal and the measured data reported in [22] are presented Figure It can becomes be seen inlower Figureas 3(a) that the resistance of the handheld projector equipped with in either fin3.array the heating thermal resistance of the handheld projector equipped with either fin array becomes lower as the power increases for both measured results and simulation results. Because the airflow velocity through power increases for bothplates measured and simulation results.which Because airflow theheating pins was less than that through in theresults primary handheld projector, will the be illustrated velocity through the pins was less than that through plates in the primary handheld projector, in Figure 5, the thermal resistance of the handheld projector having a pin-fin array was higher than the which will be illustrated in Figure 5, the thermal resistance of the handheld projector having a other as shown in Figure 3a. The maximum deviation of the thermal resistance between the measured pin-fin array was higher than the other as shown in Figure 3(a). The maximum deviation of the values and the simulation data was approximately 10% at 2 W with a pin-fin array. As the heating thermal resistance between the measured values and the simulation data was approximately 10% at power increases, the deviation between simulation values and the measured values [22] becomes 2 W with a pin-fin array. As the heating power increases, the deviation between simulation values insignificant as shown in Figure 3a. In addition, the comparison of the temperature at four specific and the measured values [22] becomes insignificant as shown in Figure 3(a). In addition, the positions on both the temperature upper and lower cases of thepositions handheld thelower measured [22] comparison of the at four specific onprojector both the between upper and cases data of the and the present simulation data with a heating power of 7 W is also shown in Figure 3b. The surface handheld projector between the measured data [22] and the present simulation data with a heating temperature on upper and3(b). lower cases are temperature depicted as black and red respectively. power of 7 distribution W is also shown in Figure The surface distribution oncurves, upper and lower Thecases sharp drop in surface temperature between the first two positions and the other two positions was are depicted as black and red curves, respectively. The sharp drop in surface temperature likely because sink plate wasother righttwo beneath the first measuring points as illustrated between the the firsthot twoheat positions and the positions was two likely because the hot heat sink plate in Figure 1a, the air in the first handheld projectorpoints heated the hot heat sink 1(a), platethe could warm up the top was right beneath two measuring asby illustrated in Figure air in the handheld surface across the tiny spacing, 1.5sink mm,plate between heatup sink and theacross upperthe case ofspacing, the handheld projector heated by the hot heat couldthe warm theplate top surface tiny 1.5 mm, between the heat sink and theheat upper case ofThe the measured handheld projector via convection and projector via convection and plate conduction transfer. temperature distribution and transfer. The measured temperature distribution and the simulated are inthe theconduction simulated heat values are in reasonable agreement except the first point, which might values result from
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Energies 266 6 of 17 1.5 2017, mm,10, between the heat sink plate and the upper case of the handheld projector via convection
and conduction heat transfer. The measured temperature distribution and the simulated values are in reasonable agreement except the first point, which might result from the inaccurate thermal inaccurate thermal conductivity of the solids listed in Table 1 and the neglected radiation effect in conductivity of the solids listed in Table 1 and the neglected radiation effect in the simulation. the simulation. Because the heater was sandwiched between the insulation block and the heat sink as Because the sandwiched between thethe insulation and the heat sink as illustrated in illustrated in heater Figure was 1a, the heat generated from heater, block to the surroundings q s , transferred
Figure 1a, the heat generated from the heater, qs , transferred to the surroundings outside the handheld outside the handheld projector via both the insulation block, qb , having thermal conductivity of projector via both the insulation block, qb , having thermal conductivity of 0.687 W/m·K, and the 0.687 W/m·K, and the aluminum heat sink, qhs . The heat flow through the former path depends aluminum heat sink, qhs . The heat flow through the former path depends mainly on the conduction mainly on the conduction across the insulation block and the bottom acrylic case of the handheld across the insulation block and the bottom acrylic case of the handheld projector, while the heat flow projector, while the heat flow through the latter path is associated with the convection and radiation through the latter path is associated with the convection and radiation over the heat sink. Since the over the heat sink. Since the objective of this study is to investigate the effect of the number of the fin objective of this study is to investigate the effect of the number of the fin and the case openings on and the case openings on the handheld projector on the thermal resistance of the handheld projector, the handheld projector onthe the thermal resistance the handheld projector, it is essential realize it is essential to realize percentage of the heat of generated by the heater is dissipated via thetoheat the percentage of primary the heat case generated the heater is dissipated via the heat sink. For the sink. For the of the by handheld projector, the simulation results shows thatprimary the casepercentage of the handheld projector, the simulation results shows that the percentage of the heating power of the heating power transferred through the insulation block, qb qs , and the heat sink, transferred through the insulation block, q /q , and the heat sink, q /q , is approximately 30% s s of the fin array and the and b hs type regardless of the qhs qs , is approximately 30% and 70%, respectively, 70%, respectively, regardless of the type of the fin array and the heating power as shown in Figure 4. heating power as shown in Figure 4. The percentage of the heat transfers to surroundings through The the percentage of is theable heattotransfers to surroundings through theofheat able case to beopenings increasedisonce heat sink be increased once the arrangement fin sink arrayis and the arrangement of fin array and case openings is improved. improved.
(a)
(b) Figure 3. Comparison of the (a) thermal resistance at different heating powers; and (b) surface temperature distribution on both top and lower cases at 7 W, between the measured results and the simulation results.
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Figure Energies 2017, 10,3. 266Comparison of the (a) thermal resistance at different heating powers; and (b) surface
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Figure 3. Comparison of theon (a)both thermal resistance at different heating powers; and (b) surface temperature distribution top and lower cases at 7 W, between the measured results and the temperature distribution simulation results. on both top and lower cases at 7 W, between the measured results and the simulation Figure 5results. shows the temperature distribution on the entire heat sink surface and the airflow
Figure 5 shows temperature distribution onprojector. the entireThe heat sinktemperature surface andregion the airflow through the fins of the the primary case of the handheld high around Figure 5 shows the temperature distribution on the entire heat sink surface and the airflow through the fins of the primary case of the handheld projector. The high temperature region around the second plate in Figure 5a or the third row of the pin fin in Figure 5b on the right denotes the through the finsplate of the case of thethird handheld projector. Theinhigh temperature around the the second inprimary Figure 5a or the row the pin fin 5b ontemperature theregion right denotes heater position on the opposite surface of the finofarray base. TheFigure noticeable gradient on the heater secondposition plate inon Figure 5a or the third row of the pin fin in Figure 5b on the right denotes the the opposite surface ofdifference the fin array The noticeable gradient the heat sink plate shows a temperature of base. approximately 20 Ktemperature between the hotteston area heater position on the opposite surface of the fin array base. The noticeable temperature gradient onarea the heat sink plate shows a temperature difference of approximately 20 K between the hottest around the junction of the heat sink plate and the fin array base and the coldest region on the heat sink the heat sinkthe plate shows temperature difference of approximately 20 Kthe between the hottest areaheat around junction ofathe heat sink plate and the fin array and coldest region on the plate. Because the clearance between the lower edge of thebase plates and the bottom openings is only around junction of the sink plate and the the lower fin array base the coldest region on the heat is sinkthe plate. Because theheat clearance between edge of and the plates and the bottom openings 1.0 mm, the air intake through a few plates was blocked due to the inappropriate arrangement of the sinkonly plate. between theplates lowerwas edgeblocked of the plates the bottom openings is 1.0Because mm, thethe airclearance intake through a few due toand the inappropriate arrangement openings and the plate fins, and caused a nonuniform airflow indicated by the arrows between plates only 1.0 mm, the air intake through a few plates was blocked due to the inappropriate arrangement of the openings and the plate fins, and caused a nonuniform airflow indicated by the arrows Figure 5a. However, the airfins, inlet and velocity through each opening in Figure 5b isbymore uniform ofinthe openings and plate caused nonuniform airflow indicated the arrows5b than between plates in the Figure 5a. However, the air ainlet velocity through each opening in Figure is that in Figure 5a,Figure because ofHowever, the larger clearance between the lowereach edge of the lowest column the between in 5a.in air inlet velocity opening Figure 5b of is of more plates uniform than that Figure 5a,the because of the largerthrough clearance between theinlower edge the pins and the bottom openings, 2.0 mm. In addition, the airflow velocity between two adjacent plates, more uniform than that in Figure 5a, the because of the larger clearance the lower edge ofvelocity the lowest column of the pins and bottom openings, 2.0 mm. between In addition, the airflow which is 4.5 mm apart, in Figure 5a is higher than that between pins in Figure 5b because the more lowest column of the pins and the bottom openings, 2.0 mm. In addition, the airflow velocity between two adjacent plates, which is 4.5 mm apart, in Figure 5a is higher than that between pins in densely distributed 1.75 mm,isimpose drag on airflow. The than lower airflow velocity through between two plates, which 4.5distributed mmhigher apart,pins, in Figure 5a is higher that between pins in Figure 5b adjacent because pins, the more densely 1.75 mm, impose higher drag on airflow. The pin-fin attributes to densely athrough higherdistributed thermal the handheld projector a pin-fin array Figure 5barray because the more pins,attributes 1.75ofmm, impose higher drag having onresistance airflow. The lower airflow velocity pin-fin resistance array to a higher thermal of the lower airflow velocity through pin-fin array attributes to a higher thermal resistance of the as handheld exhibitedprojector in Figurehaving 3a. a pin-fin array as exhibited in Figure 3a. handheld projector having a pin-fin array as exhibited in Figure 3a.
insulation block qb qhs heat sink insulation block qb qheater hs heat sink heater
Figure 4. The percentage of the heat transfer rate through both the insulation block and the heat sink Figure 4. The percentage of the heat transfer rate through both the insulation block and the heat sink Figure The percentage of thehandheld heat transfer rate through both the insulation of a4.horizontally-oriented projector at various heating powers. block and the heat sink of a horizontally-oriented handheld projector at various heating powers. of a horizontally-oriented handheld projector at various heating powers.
S S
Units: K Units: K
S S (a) (a) Figure 5. Cont.
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S
Units: K
S (b)
Figure 5. The temperature distribution on the entire heat sink surface and on an arbitrary slice, S, as Figure 5. The temperature distribution on the entire heat sink surface and on an arbitrary slice, S, as well as the airflow over the fin array in the primary case which has (a) 7 plates; or (b) 13 rows of pin, well as the airflow over the fin array in the primary case which has (a) 7 plates; or (b) 13 rows of pin, and 11 bottom openings on the horizontally-oriented handheld projector at a heating power of 7 W. and 11 bottom openings on the horizontally-oriented handheld projector at a heating power of 7 W.
An arbitrary slice, S, which shows both the air temperature between the horizontal heat sink Anthe arbitrary S, which shows both the airand temperature between the horizontal heat sink plate plate and upper slice, case of the handheld projector, the air temperature around the insulation and the upper case of the handheld projector, and the air temperature around the insulation block, is block, is also presented in Figure 5 with different temperature legend. The simulation results also presented in Figure 5 with different temperature legend. results exhibited exhibited that the air within the spacing between the horizontal heatThe sinksimulation plate and the upper case of that air within the spacing the horizontal heat of sink the upper case of the handheld thethe handheld projector was between almost stationary because theplate tinyand spacing, 1.5 mm. Therefore, projector became was almost stationary because mode of theas tiny mm. Therefore, conduction became conduction the major heat transfer thespacing, hot heat1.5 sink plate transferred heat across major heat transfer modecase, as the hot heatinsink platetemperature transferred heat across thecase thinsurface air layer thethe thin air layer to the upper resulting a peak on the upper into the upper Figure 3b.case, resulting in a peak temperature on the upper case surface in Figure 3b. heat transfer coefficient of one surface of plates, the plates, which erected the heater TheThe heat transfer coefficient of one surface of the which was was erected aboveabove the heater and was indicated a arrow red arrow the illustration in Figure 6, primary in the primary handheld projector and was indicated by aby red in theinillustration in Figure 6, in the handheld projector at various heating powers was estimated basedbased on itson average surface temperature and heat at various heating powers was estimated its average surface temperature and transfer heat transfer rate obtained from thethe simulated results. In addition, the heat transfer coefficient of a surface with with rate obtained from simulated results. In addition, the heat transfer coefficient of a surface identical surface temperature and and dimensions to thetoaforementioned surfacesurface in the plate-fin array in array identical surface temperature dimensions the aforementioned in the plate-fin theinstudy was also estimated usingusing several selected correlations. ThoseThose selected correlations are are the study was also estimated several selected correlations. selected correlations applicable for the estimation of the heat transfer coefficient of either a vertical, single plate [3,4,6] or or a applicable for the estimation of the heat transfer coefficient of either a vertical, single plate [3,4,6] a plate-fin array [9,11,18] in an infinite, still medium. Figure 6 demonstrates the comparison of the plate-fin array [9,11,18] in an infinite, still medium. Figure 6 demonstrates the comparison of the heat heat transfer coefficient among those data. It shows that heat transfer coefficients a single, transfer coefficient among those data. It shows that thethe heat transfer coefficients of of a single, vertical vertical plate estimated by the correlations [3,4,6], which are presented as orange curves, were plate estimated by the correlations [3,4,6], which are presented as orange curves, were higher than higher those of thearray plate-fin array placed in an infinitewhich medium, are as presented as green thosethan of the plate-fin placed in an infinite medium, are which presented green curves, because curves, because of the boundary layer interference between two adjoining fins of the plate-fin array. of the boundary layer interference between two adjoining fins of the plate-fin array. However, the heat However, the heat transfer coefficient the plate-fin installed in the primary handheld transfer coefficient of the plate-fin arrayofinstalled in the array primary handheld projector, which ranges from projector, 2which ranges 2from 6 W/m2·K to 7 W/m2·K, is even lower than that of the plate-fin array 6 W/m ·K to 7 W/m ·K, is even lower than that of the plate-fin array placed in an infinite medium. placed in an infinite medium. The deviation between the value predicted by the correlation [18] and The deviation between the value predicted by the correlation [18] and the present data continuously the present data continuously rises from 10% at 2 W to 26% at 7 W as show in Figure 6. The rises from 10% at 2 W to 26% at 7 W as show in Figure 6. The significant difference is likely because significant difference is likely because the case of the handheld projector and the complicated layout the case of the handheld projector and the complicated layout in the handheld projector prevent in the handheld projector prevent the warm air around the fin array inside the handheld projector the warm air around the fin array inside the handheld projector from discharging. Note that the from discharging. Note that the selected correlations used for estimating the heat transfer selected correlations used for estimating the heat transfer coefficient of a plate-fin array is applicable coefficient of a plate-fin array is applicable to the condition that the plate-fin array has to be placed to the condition that the plate-fin array has to be placed in an infinite, still medium. Such negative in an infinite, still medium. Such negative effect on the airflow would be more pronounced as the effect on the airflow would be more pronounced as the heating power increases because the air of heating power increases because the air of extremely high temperature accumulates around the fin extremely high temperature accumulates around the plate-fin fin array. array Therefore, thehandheld heat transfer coefficient array. Therefore, the heat transfer coefficient of the in the projector of the plate-fin array in than the handheld projector increased in a slower rate 6than those predicted increased in a slower rate those predicted by the correlations in Figure as the heating powerby the correlations in Figure 6 as the heating power increased. In fact, the heat transfer coefficient increased. In fact, the heat transfer coefficient estimated by those correlations can be regarded asestimated the by those correlations cantransfer be regarded as the valuearray that in thethe heat transferprojector coefficient upmost value that the heat coefficient ofupmost the plate-fin handheld canof the plate-fin the handheld can achieve. A betterachieves thermal slighter design ofdifference the handheld projector achieve. A array betterinthermal designprojector of the handheld projector in heat
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achieves slighter difference in heat transfer coefficient between the value predicted by correlations and the actual heat transfer coefficient in the handheld projector.
Figure 6. Comparison of the heat transfer coefficient of the plate fin between the present simulation results for the case of plate-fin array (blue curve) in the primary handheld projector and the values estimated by the published correlations for an isolated vertical rectangular plate (orange curves) and a plate-fin array (green curves) with the same surface temperature as the simulated one.
Subsequently, the effect of number of fin on the thermal resistance of the primary handheld projector was tested by gradually reducing the transverse spacing between two adjacent plates or pin rows, Sf in Figure 2, while keeping both the dimensions and the longitudinal spacing of each plate and pin indicated in Figure 2 as constants. Note that handheld projector having a fin array of either 7 plates or 13 rows of square pin was considered as the primary case. Figure 7a shows that the thermal resistance of the handheld projector having a plate-fin array reduced slightly as the number of plate increased from 7. However, as the number of plate was 9 and the spacing between plates was 2.875 mm, the thermal resistance of the handheld projector reached a minimum. Once the number of plate exceeded 9, the thermal resistance rapidly increased as the number of plate increased. The reason that causes the concave thermal resistance curve is the existence of an optimal spacing for the fin array. Although heat transfer from each plate decreases with decreasing transverse spacing, the number of fins that may be placed in a prescribed volume increases. Hence, the optimal spacing maximizes heat transfer from the array by yielding a maximum for the product of heat transfer coefficient and the total fin surface area. Figure 7a suggests that the optimal spacing between plates falls around 2.875 mm in the present plate-fin array of nonuniform temperature as the heating power is 7 W. Based on the heater temperature that the simulation results yielded at 7 W for the primary handheld projector having plate-fin array, the optimal fin spacing for the plate-fin array would be 3.3 mm and 4.3 mm, estimated by the correlation proposed in [11,14], respectively. The larger optimal spacing that the correlation predicted was because the ambient temperature was defined as the air temperature outside the projector, 303 K, which caused an overestimated Ra number used in both correlations [11,14] since the actual air temperature surrounding the fin array would be considerably higher than 303 K. Similar variation trend of the thermal resistance to the abovementioned case also occurred as the handheld projector was equipped with a pin-fin array as shown in Figure 7a. The thermal resistance slightly reduced as the row of pin fin increased from 7 to 9, which yielded a lowest thermal resistance
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with the spacing Energies 2017, 10, 266 between pins of 3.375 mm, and then gradually increased as the pin row further 10 of 17 increased. Although the trend of the thermal resistance variation in Figure 7 between two different handheld projectors was similar, it illustrates in Figureresistance 7 that theof thermal resistance of the handheld was similar, it illustrates in Figure 7 that the thermal the handheld projector having a projector having a plate-fin array was more sensitive to the transverse spacing between fins. Figure 7a plate-fin array was more sensitive to the transverse spacing between fins. Figure 7a also reveals that also reveals that the pin-fin array in a shrouded and narrow environment like the present handheld the pin-fin array in a shrouded and narrow environment like the present handheld projector projector demanded a larger transverse spacing that of a plate-fin array toa obtain a comparable demanded a larger transverse spacing than that than of a plate-fin array to obtain comparable thermal thermal resistance, as the natural convection was the major heat transfer mode. resistance, as the natural convection was the major heat transfer mode.
(a) Heat sink
Battery socket
(b) Figure 7. (a) Number of plates or pin rows vs. thermal resistance of the handheld projector having Figure 7. (a) Number of plates or pin rows vs. thermal resistance of the handheld projector having 11 bottom openings and the transverse spacing between adjacent plates or pin rows (Sf); and (b) 11 bottom openings and the transverse spacing between adjacent plates or pin rows (Sf ); and (b) number number bottom vs. openings thermal resistance the mass flow rate air entering the of bottomofopenings thermal vs. resistance and the mass and flow rate of air entering theofhandheld projector handheld projector having either 7 plates or 13 rows of pin at a heating power of 7 W. having either 7 plates or 13 rows of pin at a heating power of 7 W.
As the number of bottom openings of the primary handheld projector increased by reducing the As the number of bottom openings of the primary handheld projector increased by reducing spacing between openings, Sop in Figure 7b, while keeping the first bottom opening at the fixed the spacing between openings, S in Figure 7b, while keeping the first bottom opening at the fixed position, the related variation ofopboth the thermal resistance and the total mass flow rate of air position, the related variation of both the thermal resistance and the total mass flow rate of air entering entering the handheld projector through all bottom openings at a heating power of 7 W were shown in Figure 7b. Note that the mass flow rate of the airflow was estimated by integrating the inner product of ρV and the area, A , over the entire surface of the lower case. It can be observed that
( )
the total mass flow rate of the air through those bottom openings substantially increased as the
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the handheld projector through all bottom openings at a heating power of 7 W were shown in Figure 7b. →
Note that the mass flow rate of the airflow was estimated by integrating the inner product of (ρ V ) and →
2017, 10, 266 of 17of the Energies area, A, over the entire surface of the lower case. It can be observed that the total mass flow11rate the air through those bottom openings substantially increased as the number of bottom openings began number of bottom openings began to increase, and then reached a plateau, irrespectively of the fin to increase, and then reached a plateau, irrespectively of the fin type. A significant drop and inflection type. A significant drop and inflection of the mass flow rate occurred as the number of bottom of the mass flow rate occurred as the number of bottom openings was 13 on the handheld projector openings was 13 on the handheld projector having a plate-fin array. It suggests that a few openings having a plate-fin array. It suggests that a few openings were blocked because of the inappropriate were blocked because of the inappropriate arrangement of the plate fin and the bottom openings, arrangement of the plate fin and the bottom openings, similarsuch to the phenomenon Figure similar to the phenomenon revealed in Figure 5. However, concave shape ofrevealed the mass in flow rate 5. However, shape of the mass flowhaving rate did not occur the other handheld projector did not such occurconcave in the other handheld projector pin-fin array in because of the larger clearance having pin-fin array because of the larger clearance between the lower edge of the lowest column between the lower edge of the lowest column of the pins and the bottom openings as mentioned inof the Figure pins and the bottom openings as mentioned in of Figure 5. Figure 7b also shows that the variation 5. Figure 7b also shows that the variation the thermal resistance of the handheld projectorof the exactly thermaldepends resistance thevariation handheld depends on the of air mass flow rate, onof the of projector air mass exactly flow rate, regardless of variation the fin type in the handheld regardless of the fin type in the handheld projector. projector. Figure 8 shows thethe airflow velocity sections in inthe thehandheld handheldprojector projector Figure 8 shows airflow velocitycontour contouron onfour four different different sections which different configurationsofofthe thefin finarray arrayand andopenings. openings. It can which hashas different configurations can be be observed observedininFigure Figure8 8that that velocity magnitude the airflowbetween betweenfins finsreduced reduced as as the number the the velocity magnitude ofof the airflow numberof offin finincreased, increased,while whilethe the velocity magnitude of the airflow increased as the number of bottom openings increased, regardless velocity magnitude of the airflow increased as the number of bottom openings increased, regardless of the type. However, the increaseofofbottom bottomopenings openings was was not not able of the fin fin type. However, the increase able to to offset offsetthe thereduction reductionofofthe the airflow velocity resulting from the increase of the number of fin as shown in Figure In airflow velocity resulting from the increase of the number of fin as shown in Figure 8a,c,d,f.8a,c,d,f. In addition, the pink rectangles marked in Figure reveal that the inappropriate arrangement of the addition, pink rectangles marked in Figure 8a,c,f reveal 8a,c,f that the inappropriate arrangement of the fins and the fins and the bottom openings blocked the air from entering the interfin region and reduced the the bottom openings blocked the air from entering the interfin region and reduced the airflow velocity. airflow velocity.
(a)
(b)
(c) Figure 8. Cont.
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(d)
(d)
(e)
(e)
(f) Figure 8. The airflow velocity contour on four sections in the fin array in the handheld projector at a
Figure 8. The airflow velocity contour on four sections in the fin array in the handheld projector at heating power of 7 W, with different configurations including (a) 7-Plate, 11-Opening; (b) 7-Plate, (f) including (a) 7-Plate, 11-Opening; (b) 7-Plate, a heating power of 7 W, with different configurations 14-Opening; (c) 11-Plate, 14-Opening; (d) 9-Row, 11-Opening; (e) 9-Row, 14-Opening; (f) 13-Row, 14-Opening; (d) 11-Opening; (e) 9-Row, 14-Opening; (f)at 13-Row, Figure(c) 8. 11-Plate, The airflow velocity contour on9-Row, four sections in the fin array in the handheld projector a 14-Opening, units: m/s.14-Opening; 14-Opening, units: m/s. heating power of 7 W, with different configurations including (a) 7-Plate, 11-Opening; (b) 7-Plate, (c) 11-Plate, 14-Opening; (d) 9-Row, (e) 9-Row, The14-Opening; velocity vector of the airflow within the11-Opening; pink rectangles in 14-Opening; Figure 8a,f (f) are13-Row, enlarged in 14-Opening, units: m/s. Figure 9a,b, respectively. In Figure 9a,b show that the airflow can not flow straight after passes in The velocity vector of the airflow within the pink rectangles in Figure 8a,f are itenlarged through the bottom openings because the fin shading the openings forms a barrier that causes air to Figure 9a,b, The respectively. In Figure 9a,b show that airflow caninnot flow8a,f straight after itinpasses velocity vector of the airflow within thethe pink rectangles Figure are enlarged deflect before it enters the passage between fins. Such airflow deflection would reduce the airflow through Figure the bottom openings because shading the openings forms barrierafter thatit causes 9a,b, respectively. In Figurethe 9a,bfin show that the airflow can not flow astraight passes air to rate through the passage between fins because the airflow at the inlet has an angle with respect to throughitthe bottom openings because the fin shading the openings forms a barrier that causes air deflect before enters the passage between fins. Such airflow deflection would reduce thetoairflow the centerline of the passage. deflect before it enters the passage between the fins.airflow Such airflow reduce the respect airflow to the rate through the passage between fins because at thedeflection inlet haswould an angle with rate through the passage between fins because the airflow at the inlet has an angle with respect to centerline of the passage. the centerline of the passage.
(a) (a)
(b) (b)
Figure 9. The enlarged picture to show the velocity vector of the airflow in the pink rectangle in (a) Figure 8a; and (b) Figure 8f.
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Figure 9 The enlarged picture to show the velocity vector of the airflow in the pink rectangle in (a) Figure and (b) Figure 8f. Energies 2017, 8a; 10, 266
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Figure 10 shows the orientation effect on the thermal resistance of the handheld projector with Figure 10 shows the orientation effect onincluding the thermal of thedenoted handheld various combinations of fins and openings, the resistance primary cases as projector “7-Plate, with various combinations of fins and openings, including the primary cases denoted “7-Plate, 11-Openings” and “13-Row, 11-Openings”, and the improved designs denoted asas “7-Plate, 11-Openings” and and “9-Row, “13-Row,14-Openings”, 11-Openings”, and the improved as “7-Plate, 14-Openings” as well. It can be seen designs in Figuredenoted 9 that the thermal 14-Openings” and “9-Row, 14-Openings”, as well. It can be seen in Figure 9 that the thermal resistance resistance of the handheld projector having either a plate-fin array or a pin-fin array significantly of the handheld projector either a plate-fin or a pin-fin its reduced as its tilted anglehaving increased, and reached array a minimum at θ array = 60°.significantly As the tiltedreduced angle ofasthe ◦ tilted angleprojector increased, and reached a minimum = 60 As the tilted angle increased. of the handheld projector handheld further increased toward θat= θ90°, its.thermal resistance Moreover, the ◦ , its thermal resistance increased. Moreover, the thermal resistance further increased toward θ = 90 thermal resistance variation was almost symmetric with respect to θ = 0°. The thermal resistance of variation was almost symmetric respect to θwas = 0◦ .lower The thermal resistance the handheld the handheld projector having awith plate-fin array than that having aofpin-fin array atprojector a tilted ◦ , while having a plate-fin array was lower than that having a pin-fin array at a tilted angle less than 30 angle less than 30°, while contrary results revealed at a tilted angle of the handheld projector ◦ and 90◦ . The reasons contrary 60° results a tiltedthat angle of the projector between between andrevealed 90°. The at reasons cause thehandheld thermal resistance variation60with the orientation of that cause the thermal resistance variation with the orientation of the handheld projector the handheld projector are associated with the arrangement of airflow direction and are the associated openings with the arrangement of airflow direction and the openings on the handheld projector case. airflow on the handheld projector case. The airflow field will be elucidated in Figures 11 and 12The at various field will be elucidated in Figures 11 and 12 at various orientations of the handheld projector. orientations of the handheld projector.
g
θ
Figure Figure 10. 10. The The thermal thermal resistance resistance of of the the handheld handheld projector projector with with various various configurations configurations at at various various tilted angles at a heating power of 7 W. tilted angles at a heating power of 7 W.
Figures 11 and 12 show the airflow velocity around the fin array in the primary handheld projector Figures 11 and 12 show the airflow velocity around the fin array in the primary handheld with various orientations at a heating power of 7 W. The upper case of the handheld projector, the projector with various orientations at a heating power of 7 W. The upper case of the handheld location of the bottom openings and the front openings are denoted with UC, BO and FO, respectively, projector, the location of the bottom openings and the front openings are denoted with UC, BO and in these figures for clear illustration. The white blocks, color and the arrows in these figures represent FO, respectively, in these figures for clear illustration. The white blocks, color and the arrows in the fins, velocity magnitude and the airflow direction, respectively. As the orientation of the handheld these figures represent the fins, velocity magnitude and the airflow direction, respectively. As the projector was 0◦ , it can be observed in Figures 10 and 11 that the air entered the handheld projector orientation of the handheld projector was 0°, it can be observed in Figures 10 and 11 that the air from every bottom opening and the lower front openings, and then moved upward through the space entered the handheld projector from every bottom opening and the lower front openings, and then between fins, and finally left the handheld projector from both the side openings and front openings moved upward through the space between fins, and finally left the handheld projector from◦ both the◦ that were close to the upper case. As the tilted angles of the handheld projector were 30 and 60 , side openings and front openings that were close to the upper case. As the tilted angles of the both figures show that not only the front openings, but those side openings close to the upper case handheld projector were 30° and 60°, both figures show that not only the front openings, but those were outlets for the airflow induced by the hot fin array, while the major inlets for the outside air side openings close to the upper case were outlets for the airflow induced by the hot fin array, while were still the bottom openings. As the inclination of the handheld projector was 30◦ and 60◦ , after the the major inlets for the outside air were still the bottom openings. As the inclination of the handheld air crossed the fins, it was accelerated toward the front openings with a maximum velocity around projector was 30° and 60°, after the air crossed the fins, it was accelerated toward the front openings 0.15 m/s and 0.20 m/s, respectively, which was higher than the air velocity (0.08 m/s) within that with a maximum velocity around 0.15 m/s and 0.20 m/s, respectively, which was higher than the air region in a horizontal handheld projector. Therefore, this resulted in a lower thermal resistance of velocity (0.08 m/s) within that region in a horizontal handheld projector. Therefore, this resulted in a the slightly inclined handheld Becausehandheld the plateprojector. fins hindered the warm air fins fromhindered moving lower thermal resistance of the projector. slightly inclined Because the plate upward as the orientation of the handheld projector was upright (±90◦ ), the surrounding air flowed into the handheld projector through each bottom openings was immediately discharged from the same
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openings. Under such circumstance, relatively small amounts of air were allowed to flow through the space between plates. However, unlike the flow situation when the tilted angle of the handheld Energiesprojector 2016, 9, x was FORpositive, PEER REVIEW 14 of 17 the front openings became the inlets as the tilted angle of the handheld projector was negative. In addition, the air circulation adjacent to the fin located in the farthest position from gradually discharged the side openings, regardless of side the openings, orientation of the handheld the front openingsfrom would benearby gradually discharged from the nearby regardless of the projector. orientation of the handheld projector. The airflow around pin-finarray array inprimary the primary projector with various The airflow aroundthe the pin-fin in the handheldhandheld projector with various orientations was similar that intoFigure 10.Figure The major difference thebetween airflow presented in Figures 11 in orientations was to similar that in 10. The major between difference the airflow presented and 12 is that the air was not discharged from the bottom openings as the handheld projector was Figure 11 and Figure 12 is that the air was not discharged from the bottom openings as the handheld ◦ , because the held was upright, fin configuration allowed the warm air to rise through the spacing projector held±90 upright, because the pin fin configuration allowed the warm air to rise 90 0 , pin between fins, which led to a lower thermal resistance of the handheld projector having a pin-fin array through the◦spacing between fins, which led to a lower thermal resistance of the handheld projector at ±90 as shown in Figure0 10.
having a pin-fin array at 90 as shown in Figure 10.
= 00
UC
FO
g BO
421 422 = 300
FO
= 300
UC
UC
BO
BO FO
423 424 FO
= 600
= 600 UC
UC BO BO FO
425 426
FO
Figure 11. Cont.
= 900
BO
UC
= 900
UC
BO
BO BO Energies 2017, 10, 266
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FO
425 426
FO
= 900
BO
= 900
UC
UC
BO
FO
427 428 429
Figure 11. 11. TheThe airflow velocity around thethe plate-fin array in the primary handheld projector under Figure airflow velocity around plate-fin array in the primary handheld projector under 0 0 0 various orientations ( 30 ◦60 ◦90 at ◦a) heating power of 7 W various orientations (±,30 , ±,60 , ±) 90 at a heating power of 7 W. Energies 2016, 9, x FOR PEER REVIEW
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= 00
UC
FO
g BO
430 431 = 300
FO
= 300
UC
UC
BO
BO FO
432 433
FO
= 600
= 600 UC
UC BO BO
FO
434 435
FO
Figure 12. Cont.
= 900
BO
UC
= 900
UC
BO
UC BO BO
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FO
434 435
FO
= 900
BO
= 900
UC
UC
BO
FO
436 437 438 439 440 441 442 443 444
Figure 12.12. TheThe airflow velocity around thethe pin-fin array in in thethe primary handheld projector under Figure airflow velocity around pin-fin array primary handheld projector under 0, ◦ 600, ◦900) at◦ a heating power of 7 W various orientations ( 30 various orientations (±30 , ±60 , ±90 ) at a heating power of 7 W.
4. Conclusions 4. Conclusions This study numerically investigates the effects of the number of bottom openings and the fin This study numerically investigates the effects of the number of bottom openings and the fin spacing on the natural convection heat transfer and airflow field of the handheld projector with spacing on the natural convection heat transfer and airflow field of the handheld projector with various various orientations. The horizontally-oriented 120 mm × 53 mm × 19 mm handheld projector, which orientations. The horizontally-oriented 120 mm × 53 mm × 19 mm handheld projector, which had had 11 bottom openings and was installed with either 7 plate fins or 13 rows of square pin, was 11 bottom openings and was installed with either 7 plate fins or 13 rows of square pin, was considered considered as the primary case. The fin number varied from 6 plates to 13 plates or from 7 rows of as the primary case. The fin number varied from 6 plates to 13 plates or from 7 rows of pin to 16 rows of pin, while the number of the bottom openings varied from 11 to 15 in this study with handheld projector held at a specified inclination ranged from −90◦ to 90◦ . The simulation results showed that the heat transfer coefficient of a given surface of the plate fins installed in the primary handheld projector slowly increased from 6 to 7 W/m2 ·K as the heating power increased from 2 W to 7 W. With 11 bottom openings, the optimal fin spacing of the fin array in the handheld projector possessing 11 bottom openings was 2.875 mm and 3.375 mm for the plate fin and pin fin, respectively, at the heating power of 7 W. Although the velocity magnitude of the airflow between fins increased as the number of the bottom openings increased, it was not able to offset the reduction of the airflow velocity resulting from the reduction of fin spacing. The thermal resistance of the handheld projector having either a plate-fin array or a pin-fin array significantly reduced as its tilted angle increased, and reached a minimum at θ = 60◦ . The variation of the thermal resistance of the handheld projector with the alteration of inclination was almost symmetric with respect to θ = 0◦ . As the tilted angle of the handheld projector was 30◦ or 60◦ , the air was accelerated toward front openings after it crossed the fins, causing a thermal resistance lower than that of the horizontal handheld projector. Acknowledgments: The authors appreciate the financial support from the Ministry of Science and Technology of Taiwan under the contracts of MOST 104-2221-E-151-037 and MOST 105-2221-E-151-030. Author Contributions: Mr. Tsuni Chang performed all simulations in this study. Shun-Ching Lee contributed the numerical model. Jin-Cherng Shyu analyzed the simulation data, wrote the paper, and was responsible for revising the manuscript according to the reviewers’ comments. Conflicts of Interest: The authors declare no conflict of interest.
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