Thermal Science & Engineering Vol.15 No.3 (2007)

MEMS ᛛⴚࠍ↪޿ߡ૞⵾ߒߚੱᎿࠠࡖࡆ࠹ࠖઃ߈
વᾲ㕙ߦࠃࠆᩭᴣ㛛⃻⽎ߩታ㛎⊛⎇ⓥ૒⮮ 㓉⊓̐  ዊᴰ ቟㇢Á  ᄢ┻ ᶈ㕏ÁExperimental Study on Fundamental Phenomena of Nucleate-Boilingby Using Heat Transfer Surface with Artificial Cavities Createdby MEMS Technology
Takato SATO̐, Yasuo KOIZUMIÁ

andHiroyasu OHTAKEÁ

Abstract
Pool nucleate boiling heat transfer experiments were performed for water by using a well-controlled and -definedheat transfer surfaces in the range of the surface heat flux of ~ 4.54104 W/m2. One or three cavities were created ona mirror-finished silicon plate of 0.525 mm thickness by utilizing the Micro-Electro Mechanical Systems (MEMS)
technology. In present experiments, the cavities were arranged in a straight line. The silicon plate was placed facing up
at the bottom of the test container filled with distilled water. The back side of the silicon plate was irradiated by a laser
beam to heat up the test heat transfer surface. The back side temperature was measured with a radiation thermometer.
A boiling state was recorded with a high speed video camera. Thermal interaction between neighboring cavities
became weak as the cavity spacing became wide and it disappeared when S/Lc = 1.6 in present experimental range.
Four bubble coalescence patterns; vertical, horizontal and declining coalescence and vertical lift (no coalescence),
were confirmed. When S/Lc  1.6, horizontal and declining coalescence disappeared. When the cavity spacing was
narrow, hydraulic interaction between neighboring cavities played an important role in heat transfer. It became lessimportant as the cavity spacing became wide. When S/Lc  1.2, the hydraulic interaction between neighboring cavities
became negligible and phase change heat transfer took a main part.
Key Words: Nucleate boiling, Bubble behavior, MEMS, Artificial cavity

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ᐔⴧ⃿ᒻ᳇ᵃඨᓘ᷷ᐲᄌേߩᮡḰ஍Ꮕ࡟࡯ࠩ࡯ᾖ኿ඨᓘ
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ฃઃᣣ: 2007 ᐕ 3 ᦬ 20 ᣣ, ╙ 43 ࿁ᣣᧄવᾲࠪࡦࡐࠫ࠙ࡓࠃࠅฃઃ㧘ᜂᒰ㧦㐷಴᡽ೣᎿቇ㒮ᄢቇᄢቇ㒮 ᯏ᪾Ꮏቇኾ᡹ (‫ޥ‬192-0015 ᧲੩ㇺ౎₺ሶᏒਛ㊁↸ 2665-1)ÁᎿቇ㒮ᄢቇᎿቇㇱ (‫ޥ‬192-0015 ᧲੩ㇺ౎₺ሶᏒਛ㊁↸ 2665-1)
̐-1- - 101

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)

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㧝 ✜ ⸒ᴣ㛛વᾲߪ㜞޿ᾲવ㆐₸ࠍ᦭ߔࠆߚ߼㧘㜞᷷‛૕ߩല₸⦟޿಄ළᛛⴚߣߒߡᐢߊ೑↪ߐࠇߡ߈ߡ޿ࠆ㧚ߘߩߚ߼ᴣ㛛⃻⽎ߩ⎇ⓥߪᣣᧄࠍ฽߼਎⇇ฦ࿖ߢ
60㨪70 ᐕߩ㐳߈ߦࠊߚߞߡ⛯ߌࠄࠇߡ߈ߡ޿ࠆ㧚ߒ߆ߒߥ߇ࠄㅢᏱવᾲ㕙ߩᴣ㛛ߦߪ㧘⴫㕙☻ߐ㧘ࠠࡖࡆ࠹ࠖߩᒻ߿ࠨࠗ࠭ߥߤߩ⴫㕙⁁ᘒ㧘⴫㕙ߩỨࠇᕈ㧘ኻᵹ㧘ᾲવዉ㧘⋧ᄌൻ㧘᳇ᵃ᜼േߥߤߩ Fig. 1 ߦ␜ߔࠃ߁ߥ‛ℂ⊛․ᕈ߿ᾲ․ᕈߥߤ߇ᄢ߈ߥᓇ㗀ࠍᜬߜ㧘੕޿ߦ߆ࠄߺวߞߡ޿ࠆ㧚߹ߚ㧘ߘߩਛߦߪᒝ
޿㕖✢ᒻᕈࠍᜬߟ㔍⸃ߥ⃻⽎߽฽߹ࠇߡ޿ࠆ㧚ߘࠇࠁ߃㧘ᴣ㛛⃻⽎ߪ㕖Ᏹߦⶄ㔀ߢ޽ࠅ㧘ᄙߊߩᧂ⸃᣿
ߥㇱಽࠍᱷߒߡ޿ࠆ㧚
Kenning ࠄ [1]ߪ㧘વᾲ㕙ߦ 28.1 mm40.8 mm㧘
ෘߐ 0.13 mm ߩࠬ࠹ࡦ࡟ࠬ᧼ࠍ↪޿㧘ߎࠇࠍ᳓ࡊ࡯
࡞ౝߢㅢ㔚ടᾲߒ㧘વᾲ㕙ࠃࠅ⊒↢ߔࠆ᳇ᵃߩ᜼േࠍⷰኤߒߚ㧚߹ߚ㧘વᾲ㕙ⵣ㕙ߦ⸳⟎ߒߚᶧ᥏ߩ⦡
ߩᄌൻ㧔104 ͠ߢ⿒⦡㨪123 ͠ߢ✛⦡㧕߆ࠄવᾲ㕙ㆊᾲᐲߩಽᏓ߿᳇ᵃߦࠃࠆㆊᾲᐲߩᄌൻࠍ⸘᷹ߒߚ㧚વᾲ㕙ߪࡒࠢࡠᶧ⤑ߩ⫳⊒ߦࠃߞߡ಄ළߐࠇࠆ㧚ߘߩવᾲ㕙ㆊᾲᐲߪ㧘ࠠࡖࡆ࠹ࠖ߆ࠄߩ᳇ᵃߩ↢ᚑߣ㔌⣕ߦࠃߞߡᄌേߒ㧘ࡒࠢࡠᶧ⤑ߩ⫳⊒ߦᓇ㗀ࠍ෸߷ߒߡ޿ࠆ㧚વᾲ㕙ࠍ಄ළߔࠆࡒࠢࡠᶧ⤑⫳⊒ߩᓇ㗀▸࿐ߪ㧘ࠠࡖࡆ࠹ࠖ߆ࠄᚑ㐳ߔࠆ᳇ᵃߩᦨᄢඨᓘ
એౝߢ޽ࠅ㧘ߘߩ▸࿐߆ࠄ㔌ࠇࠆ߶ߤ㧘વᾲ㕙ࠍ಄ළߔࠆലᨐߪዊߐߊߥࠆߣㅀߴߡ޿ࠆ㧚
Judd [2]ࠄߪࠟ࡜ࠬ᧼ߦ㉄ൻ㍯ࠍႣᏓߒ㧘ㅢ㔚ടᾲߒ㧘ᴣ㛛ታ㛎ࠍⴕߞߡ޿ࠆ㧚ᵴ⊒ߥᴣ㛛᜼േࠍ␜ߔ
ⶄᢙߩࠠࡖࡆ࠹ࠖߦ⌕⋡ߒ㧘ߘࠇࠄߩࠠࡖࡆ࠹ࠖ㑆㓒 S ࠍᐔဋ㔌⣕᳇ᵃᓘ Db ߢ㒰ߒߚήᰴరᢙ S/Db ࠍ↪޿ߡ㧘ࠠࡖࡆ࠹ࠖ㑆㓒ߩᴣ㛛᭽⋧߳ߩᓇ㗀ࠍᢛℂߒߡ޿ࠆ㧚S/Db < 1 ߩߣ߈㧘ㅪ⛯⊒ᵃߒߡ޿ࠆᵴᕈ
ߥࠠࡖࡆ࠹ࠖߪ๟࿐ߩਇᵴᕈߥࠠࡖࡆ࠹ࠖౝߦ᳇ᵃᩭࠍଏ⛎ߒ⊒ᵃࠍଦㅴߐߖࠆ㧚߹ߚ 1 < S/Db < 3 ߢߪ㧘᳇ᵃ⊒↢ߩᵴ⊒ߥࠠࡖࡆ࠹ࠖߪ๟࿐ߩࠠࡖࡆ࠹ࠖߦ
ኻߒ⊒ᵃࠍᛥᱛߔࠆ㧚S/Db > 3 ߢߪ㧘ࠠࡖࡆ࠹ࠖ㑆ߩᐓᷤߪή޿ߣ㧘3 㗔ၞߦ඙ಽߌߒߡ޿ࠆ㧚ᐣมࠄ[3-7] ߪ㧘DRIE ߥߤߩࡑࠗࠢࡠࡑࠪ࠾ࡦࠣ
ᛛⴚࠍ೑↪ߒߡ㧘න৻ࠠࡖࡆ࠹ࠖ߿ⶄᢙࠠࡖࡆ࠹ࠖ
ࠍࠪ࡝ࠦࡦ࠙ࠚࡂ਄ߦടᎿߒ㧘ੱὑ⊛ߦⷙᩰ⛔৻ߐࠇߚવᾲ㕙ࠍ૞⵾ߒ㧘ࡊ࡯࡞ᴣ㛛ታ㛎ࠍⴕߞߚ㧚㓞ធߔࠆࠠࡖࡆ࠹ࠖߣߩ㑆㓒߇᳇ᵃ㔌⣕๟ᦼ㧘㔌⣕᳇ᵃ߳ᜬߟᓇ㗀ߩ㕖✢ᒻᕈߦߟ޿ߡ⺰ߓߡ޿ࠆ㧚߹ߚ㧘ᴣ㛛⃻⽎ߦ߅ߌࠆ᳇ᵃᩭᐓᷤࠍᵹ૕⊛ᓇ㗀㧘વᾲ㕙᷷ᐲᄌേߩᓇ㗀㧘᳇ᵃว૕ߦࠃࠆᓇ㗀ߩ 3 ߟߦಽ㘃ߒߡ޿ࠆ㧚ᧄ⎇ⓥߢߪ㧘㏜㕙઀਄ߍߐࠇߚࠪ࡝ࠦࡦ࠙ࠚࡂߦ
MEMS㧔Micro Electro Mechanical Systems㧕ᛛⴚࠍ↪
޿ߡ㧘ᒻ⁁߿ࠨࠗ࠭㧘߹ߚ㑆㓒ࠍ⛔৻ߒߚࠠࡖࡆ࠹
ࠖࠍ૞⵾ߒ㧘ᴣ㛛߳ᓇ㗀ࠍ෸߷ߔᓇ㗀࿃ሶߦᏅ⇣߇಴ߥ޿⁁ᴫࠍ૞ࠅ಴ߒ㧘Ⴚ⇇᧦ઙࠍ᣿⏕ߦߔࠆ㧚ߎߩવᾲ㕙ߦኻߒ㧘ࠠࡖࡆ࠹ࠖ㑆㓒ࠍࡄ࡜ࡔ࡯࠲࡯ߦ
ߒߚᴣ㛛ታ㛎ࠍⴕ޿㧘ᐣมࠄߩ⎇ⓥࠍෳ⠨ߦߒߟߟ㧘ᴣ㛛⃻⽎߳ߩࠠࡖࡆ࠹ࠖ㑆㓒ߩᓇ㗀ࠍታ㛎⊛ߦ⸃᣿ߔࠆߎߣࠍ⋡⊛ߣߒߡ޿ࠆ㧚㧞 ታ 㛎 ੱᎿࠠࡖࡆ࠹ࠖ૞⵾ᣇᴺ વᾲ㕙ߦߪ㧘⴫㕙ࠍ㏜㕙઀਄ߍߒߚෘߐ 0.525 mm
ߩࠪ࡝ࠦࡦ࠙ࠚࡂࠍ↪޿ߚ㧚ᐣมࠄߪᩭᴣ㛛߇቟ቯߦ⛮⛯ߔࠆੱᎿࠠࡖࡆ࠹ࠖᒻ⁁ࠍ⺞ߴߡ޿ࠆ[3-4]㧚
ߘߩ⚿ᨐࠍෳ⠨ߦߒߡ㧘ߎߩࠪ࡝ࠦࡦ࠙ࠚࡂ⴫㕙਄ߦ㧘ᓘ 10 ȝm㧘ᷓߐ 40 ȝm ߩ౞╴⁁ᷓⓣࠍជࠅ㧘ߎࠇࠍࠠࡖࡆ࠹ࠖߣߒߚ㧚ੱᎿࠠࡖࡆ࠹ࠖ૞ᚑᚻ㗅ࠍ Fig. 2 ߦ␜ߔ㧚ࠟ࡜ࠬ᧼ߦࠢࡠࡓ⭯⤑ࠍᒻᚑߒߚࠢࡠࡓࡑࠬࠢߦ SEM㧔⿛ᩏ㔚ሶ㗼ᓸ㏜㧕ߣ㔚ሶ✢ឬ↹ⵝ⟎ࠍ↪޿ߡࠠࡖࡆ࠹
ࠖߩࡄ࠲࡯ࡦࠍォ౮ߒ㧘ᰴߦ࠙ࠚ࠶࠻ࠛ࠶࠴ࡦࠣߦ
ࠃࠅ㧘ࠠࡖࡆ࠹ࠖㇱಽߩࠢࡠࡓ⭯⤑ࠍṁ߆ߔ㧚⛯޿ߡࠪ࡝ࠦࡦ࠙ࠚࡂߦ࡟ࠫࠬ࠻ࠍႣᏓߒ㧘ߘߩ਄߆ࠄ
ࠠࡖࡆ࠹ࠖࡄ࠲࡯ࡦઃࠢࡠࡓࡑࠬࠢࠍ㊀ߨ㧘ࡑࠬࠢࠕ࡜ࠗ࠽࡯ⵝ⟎ߦࠃࠅ⚡ᄖ✢ࠍᾖ኿ߔࠆ㧚ᗵశߒߚ࡟ࠫࠬ࠻ㇱಽࠍ⃻௝ᶧߢṁ߆ߒੇ῎ߔࠆ㧚ߎࠇߦࠃ-2- - 102

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)ࠅࠪ࡝ࠦࡦ࠙ࠚࡂ਄ߩ࡟ࠫࠬ࠻ߦࠠࡖࡆ࠹ࠖࡄ࠲࡯
ࡦ߇ォ౮ߐࠇࠆ㧚ߎߩࠪ࡝ࠦࡦ࠙ࠚࡂࠍ DRIE ⵝ⟎ߦ⸳⟎ߒ㧘࠼࡜ࠗࠛ࠶࠴ࡦࠣࠍⴕ߁㧚ߎߩߣ߈㧘෻ᔕᕈࠗࠝࡦߦࠃࠅࠠࡖࡆ࠹ࠖߣߥࠆ౞╴ᒻⓣ߇ᷓߊជࠄࠇߡ޿ߊ㧚ᦨᓟߦ࡟ࠫࠬ࠻ࠍ O2 ࡊ࡜࠭ࡑߢ㒰෰ߒ㧘࠙ࠚࡂࠍᵞᵺ࡮ੇ῎ߔࠆ㧚ߎߩࠪ࡝ࠦࡦ࠙ࠚࡂ
ࠍ࠳ࠗࠪࡦࠣⵝ⟎ࠍ↪޿ߡ 20 mm20 mm ߦⵙᢿߔࠆ㧚ᧄႎߢߪන৻ࠠࡖࡆ࠹ࠖߩ႐ว㧘෸߮㧘Fig. 3 ߦ␜ߔࠃ߁ߦ 3 ࠠࡖࡆ࠹ࠖࠍ⋥✢਄ߦ㈩⟎ߒ㧘ࠠࡖࡆ࠹ࠖ㑆㓒 S ࠍ 1 mm㨪4 mm ߩ▸࿐ߢᄌൻߐߖߚ႐ว
ߦߟ޿ߡᴣ㛛ታ㛎ࠍⴕߞߚ㧚 ታ㛎ⵝ⟎෸߮ታ㛎ᣇᴺ
Fig. 4 ߦታ㛎ⵝ⟎᭎ⷐࠍ␜ߔ㧚20 mm20 mm ߦⵙᢿߐࠇߚવᾲ㕙ߪ㧘ࡐ࡝ࠗࡒ࠼᮸⢽ࡊ࡟࡯࠻ߦធ⌕ߐࠇ㧘ߘߩ᮸⢽᧼ߪ⌀㎕⵾ࠕ࠳ࡊ࠲ߦ࿕ቯߐࠇࠆ㧚ߘߩࠕ࠳ࡊ࠲ߪ Fig. 4 ߦ␜ߔࠃ߁ߦኒ㐽ᴣ㛛࠹ࠬ࠻ኈེᐩㇱߦขࠅઃߌࠄࠇࠆ㧚વᾲ㕙਄ㇱߦߪ㧘ᶧ㕙േំࠍᛥ೙ߔࠆߎߣࠍ⋡⊛ߣߒߡࡐ࡝ࠞ࡯ࡏࡀ࡯࠻
⵾ࡈࠚࡦࠬ߇⸳⟎ߐࠇߡ޿ࠆ㧚ᴣ㛛࠹ࠬ࠻ኈེߪ㜞ߐ 230 mm㧘ᢿ㕙 200 mm200 mm ߩ⌀㎕⵾ኒ㐽ኈེߢ޽ࠆ㧚஥㕙ߦߪⷰኤ↪⓹߇޽ࠅ㧘ኈེߦߪ᳓ട
ᾲ↪ࡅ࡯࠲࡯㧘ኈེౝ࿶ജ⺞ᢛ↪ߩ᳓಄ළಝ❗ེ߇ขࠅઃߌࠄࠇߡ޿ࠆ㧚વᾲ㕙ടᾲߪવᾲ㕙ⵣ㕙ߦඨዉ૕࡟࡯ࠩ࡯ࠍᾖ኿ߔࠆߎߣߦࠃࠅⴕߞߚ㧚ߎߩⵣ







Convection

Buoyancy㕙ߪߟ߿ᶖߒ㤥⦡ࠬࡊ࡟࡯ߢ็߈ઃߌ⌕⦡ߐࠇ㧘᡼኿₸ࠍ 0.98 ߣߒߚ㧚♖⵾᳓ࠍᴣ㛛ኈེౝ߳ᵈ߉ㄟߺ㧘ࡅ࡯࠲࡯ߦࠃࠅ
ടᾲߔࠆ㧚᳓᷷ߪ K ဳᾲ㔚ኻߦࠃࠅ᷹ቯߐࠇ㧘ᴣ㛛ኈེౝ࿶ജߪ࿶ജ⸘ߦࠃࠅ᷹ቯߐࠇࠆ㧚વᾲ㕙ⵣ㕙᷷ᐲߪ㧘᷷ᐲಽ⸃⢻ 0.08 K㧘ᤨ㑆ಽ⸃⢻ 3 ms/line ߩ⿒ᄖ✢᡼኿᷷ᐲ⸘ߦࠃߞߡ᷹ቯߐࠇࠆ㧚᳓᷷ടᾲࡅ
࡯࠲࡯ߣಝ❗ེߦࠃࠅኈེౝࠍ 0.1 MPa ߩ㘻๺⁁ᘒߦ଻ߜߟߟવᾲ㕙ⵣ஥ࠍඨዉ૕࡟࡯ࠩ࡯ߦࠃࠅടᾲ
ߔࠆ㧚ᚲቯߩ୯߹ߢવᾲ㕙ടᾲ㊂ࠍᓢ‫ߦޘ‬Ⴧടߐߖࠆ㧚વᾲ㕙ⵣ㕙᷷ᐲߣᴣ㛛⁁ᘒ߇ቢోߦ቟ቯߒߚᓟ㧘ኈེౝߩ᷷ᐲߣ࿶ജࠍ⸥㍳㧘߹ߚ㧘㜞ㅦᐲࡆ࠺ࠝࠞ
ࡔ࡜ࠍ⿒ᄖ✢᡼኿᷷ᐲ⸘ߣหᦼߐߖ㧘વᾲ㕙ⵣ㕙᷷ᐲ᷹ቯߣੱᎿࠠࡖࡆ࠹ࠖࠃࠅ⊒↢ߔࠆ᳇ᵃ᜼േߩ᠟ᓇࠍⴕߞߚ㧚㧟 ታ㛎⚿ᨐ෸߮⠨ኤ ੱᎿવᾲ㕙ߩᴣ㛛․ᕈ
ታ㛎ߦࠃࠅᓧࠄࠇߚ᷹ቯ⚿ᨐࠍᴣ㛛ᦛ✢ߩᒻߢ
Fig. 5 ߦ␜ߔ㧚ዏ㧘࡟࡯ࠩ࡯ᾖ኿ㇱ߆ࠄᾲવዉߦࠃ
ࠅ៊ᄬߔࠆᾲ㊂ࠍᑼ(1)ߦࠃࠅ᳞߼ߚ㧚

Qloss

Tin  Tout
2Srlaser G'xkߎߎߢ㧘 Tin ߪ࡟࡯ࠩ࡯ᾖ኿▸࿐ౝߩછᗧὐߦ߅ߌ
ࠆ᷹ቯᤨ㑆 1 ⑽㑆ߩᤨ㑆ᐔဋ᷷ᐲߢ޽ࠅ㧘 Tout ߪ࡟Phase-change࡯ࠩ࡯ᾖ኿▸࿐ᄖߩછᗧὐߦ߅ߌࠆหߓߊᤨ㑆ᐔဋ᷷ᐲߢ޽ࠆ㧚߹ߚ㧘ߘࠇࠄ 2 ὐ㑆ߩ〒㔌ࠍ'x ߣߒߡ޿ࠆ㧚

Coalescence

20mm

Heat conduction

Cavity parameters
Diameter: 10 ȝm,
Depth: 40 ȝm
S: cavity spacing

S

20mm

S

Fig. 1 Effect factors of boiling.









(1)

CavityUltraviolet rays

Cr-MaskFig. 3 Cavity pattern on silicon wafer.

SF6+C4F8
Reactive ions

GP

Digital

Silicon wafer(a) Expose 







 (b) Development

Condenser

Multi-meter

Resist film

Test container(c) Dry etching   (DRIE)

TC

TC
Funnel

Fence

Video
HSC

Artificial cavities

HeaterRadiation

Heat transfer surface
bonded to polyimide resin

thermometer(d) Resist removal

PC

Fig. 2 Process of artificial cavity fabrication.

Laser
Mirrors

Fig. 4 Experimental apparatus.
-3- - 103

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)

Fig. 5 ਛ㧘਄ะ᳓ᐔ᧼⥄ὼኻᵹᾲવ㆐ߩ㑐ଥߪᰴᑼߦࠃࠅ᳞߼ߚ㧚(2)

ߎߎߢ㧘Nu = hx/k ߪ࠿࠶࠮࡞࠻ᢙ㧘Gr =gȕ(Tw-Tп)x3/Ȟ2
ߪࠣ࡜ࠬࡎࡈᢙߢ޽ࠅ㧘Pr ߪࡊ࡜ࡦ࠻࡞ᢙߢ޽ࠆ㧚ዏ㧘ᧄታ㛎᧦ઙߪጀᵹߩ 104 < Gr ǜ Pr < 109 ߩ▸࿐ౝߦ޽ࠆ[8-9]㧚
Fig. 5 ਛ㧘ࡊ࡯࡞ᩭᴣ㛛ߩ㑐ଥߪ㧘ᑼ(3)ߢ⴫ߐࠇ
ࠆ Rohsenow ⋧㑐ᑼ[10]ߦࠃߞߚ㧚ߎߎߢ㧘ଥᢙ Csf =0.013 ߣߒߚ㧚
0.33

(3)

2

,

W/m

º
V
»
g U l  U g »¼

߹ߚ㧘Fig. 5 ਛߩᴣ㛛㐿ᆎ(ONB)᷷ᐲߪએਅߩᚻ㗅ߢ᳞߼ߡ޿ࠆ㧚ᶧਛߦ㧘ඨᓘ Re ߩ᳇ᵃ߇ᐔⴧ⊛ߦሽ࿷ߔࠆߚ߼ߦᔅⷐߣߐࠇࠆᶧㆊᾲᐲߪ㧘ᰴᑼߢ␜ߐ
ࠇࠆ[11]㧚

'Tsat

2V (v g  v l )Tsat
hlg R e.

(4)ߎߎߢ㧘ᲧኈⓍ Ȟ (=1/ȡ)ߢ޽ࠆ㧚ߎߩߣ߈ߩࠠࡖࡆ࠹
ࠖ㐿ญඨᓘ㧔ᧄታ㛎ߩ႐ว㧘ࠠࡖࡆ࠹ࠖ౞╴ⓣᓘ㧕
ࠍ Rc ߣߔࠆ㧚ࠠࡖࡆ࠹ࠖ਄ߦඨ⃿ߣߒߡሽ࿷ߔࠆ᳇
ᵃߩ㗂ㇱߩᶧ᷷߇ᑼ(4)ߢਈ߃ࠄࠇࠆ୯ࠃࠅ߽ᄢ߈
ߊߥߞߚߣ߈㧘᳇ᵃ߇ᚑ㐳ߒᆎ߼ࠆߣߔࠆ[12]ߣ᳇
ᵃᚑ 㐳㐿 ᆎ㧘 ߔߥ ࠊߜ ᴣ 㛛㐿 ᆎᤨ ߩო 㕙ㆊ ᾲᐲ( ǻTsat )ONB ߣ Rc ߩ㑐ଥߪᰴᑼߢਈ߃ࠄࠇࠆ[13]㧚

('Tsat ) ONBHeat fluxª q
C sf ««¬ P l hlg

C l 'Tsathlg Pr 1.7

 ࠠࡖࡆ࠹ࠖ㑆᷷ᐲ⋧੕ᐓᷤ࠻࡝ࡊ࡞ࠠࡖࡆ࠹ࠖߩવᾲ㕙᷷ᐲᄌേࠍ Fig. 6 ߦ␜ߔ㧚 એਅ㧘વᾲ㕙᷷ᐲߪ᷹ቯߐࠇߚવᾲ㕙ⵣ㕙᷷ᐲߢ޽ࠆ㧚ᾲવዉ⸘▚߆ࠄ㧘ⵣ㕙᷷ᐲߣ⴫㕙᷷ᐲߩᏅߪήⷞߢ߈ࠆ⒟ᐲߢ޽ࠆߎߣࠍ⏕⹺ߒߡ޿ࠆ㧚Fig.
6 ߪ㧘 S = 3 mm㧘q = 4.54 u 104 W/m2 ߩ⚿ᨐࠍ␜ߔ㧚
Fig. 6 (a)ߪ㧘Center ࠠࡖࡆ࠹ࠖ߆ࠄ Right ࠠࡖࡆ

105





Natural convection
Pool nucleate boiling
ONB
Mirror-finished surface
Single cavity

4
Triple cavities S=1mm
10
Triple cavities S=2mm
Triple cavities S=3mm

Triple cavities S=4mm

110Wall superheat Tw-Tsat K
Fig. 5 Boiling curve of artificial cavities.
Distance from center to right0 mm (center)
0.41 mm
1.1 mm
1.5 mmTemperature °C

0.54(Gr  Pr )1 / 4 ,2V ( U l  U g )Tsat § sin T ·¨¨¸¸U l U g hlg© Rc ¹u

1ª h § Rc ·º¸(1  cosT )»«1  ¨¬ k l © sin T ¹
¼

(5)

108

107
0

0.02

0.04
Time

0.06

0.08

0.1

s

(a) Center to rightߎߎߢ㧘ᶧߩធ⸅ⷺ ș ߢ޽ࠆ㧚ᧄታ㛎ߢ੍஻⊛ߦⴕߥߞߚࠠࡖࡆ࠹ࠖήߒ㧘▚ⴚᐔဋᐔ㕙☻ߐ߇ 0.01 ȝm
એਅߩ㏜㕙઀਄ߍࠪ࡝ࠦࡦ࠙ࠚࡂࠍવᾲ㕙ߣߒߚታ㛎ߢߪ㧘᳇ᵃߩ⊒↢ߪ⏕⹺ߐࠇߡ޿ߥ޿㧚ߎߩ႐วߩ᷹ቯ⚿ᨐ߇㧘Fig. 5 ߦ߅޿ߡ㤥ਣࡊࡠ࠶࠻ઃ߈ߩ
ታ✢ߢ␜ߐࠇߡ߅ࠅ㧘⥄ὼኻᵹᾲવ㆐ߩ㑐ଥߣห৻௑ะࠍ␜ߒߡ޿ࠆ㧚ࠠࡖࡆ࠹ࠖࠍᣉߒߚੱᎿવᾲ㕙ࠍ↪޿ߚታ㛎ߢߪ㧘ోߡടᾲᾲᵹ᧤਄᣹ߦ઻޿ࠠࡖࡆ࠹ࠖࠃࠅ᳇ᵃߩ⊒↢߇⷗ࠄࠇߚ㧚Fig. 5 ਛ㧘ੱᎿࠠࡖࡆ࠹ࠖࠍ᦭
ߔࠆ᷹ቯὐߪోߡ᳇ᵃߩ⊒↢ߩ⷗ࠄࠇߚ⚿ᨐߢ޽ࠆ㧚ߎߩ႐วߩታ㛎ߢߩᴣ㛛㐿ᆎ᷷ᐲߪᑼ(5)ߩ੍᷹୯
ߦㄭ޿㧚ᴣ㛛㐿ᆎᓟߩᾲᵹ᧤ߣㆊᾲᐲߩ㑐ଥߪ⎕✢Temperature °C

Nuߢ␜ߐࠇߚᑼ (3) ߦࠃࠆᩭᴣ㛛⋧㑐ᑼߩ㑐ଥߣห᭽ߩ௑ะࠍ␜ߒߡ޿ࠆ㧚ߎࠇࠄߩ⚿ᨐࠃࠅ㧘ᩭᴣ㛛ਅߦ߅޿ߡ㧘ੱᎿࠠࡖࡆ࠹ࠖઃ߈ੱᎿવᾲ㕙ߪㅢᏱવᾲ㕙ߣห᭽ߩ᜼േࠍ␜ߔߎߣ߇⏕⹺ߢ߈ࠆ㧚

108

Distance from right to center
0 mm (right)
0.41 mm
1.1 mm
1.5 mm

107
106
0

0.02

0.04
0.06
Time s0.08

0.1(b) Right to center
Fig. 6 Surface temperature fluctuation (Triple S = 3 mm).

-4- - 104

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)࠹ࠖߩਛ㑆ߢ޽ࠆ 1.5 mm ૏⟎߹ߢߩ 4 ૏⟎ߦ߅ߌࠆવᾲ㕙ᄌേߢ޽ࠆ㧚߹ߚห᭽ߦ Fig. 6 (b)ߪ Rightࠠࡖࡆ࠹ࠖ߆ࠄ Center ࠠࡖࡆ࠹ࠖ߳ߩਛ㑆૏⟎ 1.5
mm ߹ߢߩ 4 ૏⟎ߦ߅ߌࠆવᾲ㕙᷷ᐲᄌേߢ޽ࠆ㧚
Fig. 6 (a), (b) ࠃࠅવᾲ㕙᷷ᐲᄌേߩᝄ᏷ߪࠠࡖࡆ
࠹ࠖ⋥ਅὐߦ߅޿ߡᦨ߽ᄢ߈ߊ㧘ࠠࡖࡆ࠹ࠖ߆ࠄ㔌ࠇࠆߦߟࠇ㧘᷷ᐲᄌേߪዊߐߊߥߞߡ޿ࠆߎߣ߇ࠊ
߆ࠆ㧚વᾲ㕙᷷ᐲᄌേߪ᳇ᵃߩ↢ᚑ࡮㔌⣕ߦࠃࠅ߽ߚࠄߐࠇߡ޿ࠆ߽ߩߣ⠨߃ࠄࠇࠆ㧚᳇ᵃߩ⊒↢࡮㔌⣕࡮ว૕ߩᓇ㗀ߦࠃߞߡ↢ߕࠆવᾲ㕙᷷ᐲᄌേࠍ⴫ߔᜰᮡߣߒߡ㧘ࠠࡖࡆ࠹ࠖ⋥ਅߣߘߩ๟࿐૏⟎ߩ㑆ߩવᾲ㕙᷷ᐲᄌേ⋧㑐ଥᢙࠍᑼ(6)ߦࠃࠅ᳞߼ߚ[5]㧚

C cj

Rcj

(6)

rc r jߎߎߢ㧘 C cj ߪ᷷ᐲᄌേߩ⋧㑐㑐ᢙ
n

i
c

i
j

¦ T T T T
c

j

(7)

i 1

Ccj

n

n

(8)

n

Fig. 7 ߦ㧘න৻ࠠࡖࡆ࠹ࠖߣ㧘3 ࠠࡖࡆ࠹ࠖ㧔ࠠࡖࡆ࠹ࠖ㑆㓒 S = 1 mm㧘2 mm㧘3 mm㧘4 mm㧕ߩ႐วߩᑼ (6) ߦࠃࠅ᳞߼ߚ᷷ᐲ⋧㑐ଥᢙࠍ␜ߔ㧚ᮮゲߪ㧘Center ࠠࡖࡆ࠹ࠖߩ૏⟎ࠍ 0 mm ߣߒߚ㧚
Fig. 7 (a) ߢ㧘න৻ࠠࡖࡆ࠹ࠖߩ႐ว㧘ࠠࡖࡆ࠹ࠖ
ਛᔃ߆ࠄ 2 mm એ਄㔌ࠇࠆߣ㧘વᾲ㕙᷷ᐲߪࠠࡖࡆ
࠹ࠖ߆ࠄ⊒↢ߔࠆ᳇ᵃߦࠃߞߡᓇ㗀ࠍฃߌߥ޿ߎߣ
߇ࠊ߆ࠆ㧚 3 ࠠࡖࡆ࠹ࠖߩ Fig. 7 (b), (c), (d) (ࠠࡖࡆ࠹ࠖ㑆㓒 S = 1, 2, 3 mm)ߩ႐ว㧘㓞ធߔࠆࠠࡖࡆ࠹ࠖ
ߩ᷷ᐲ⋧㑐ଥᢙห჻߇㊀ߥࠅว߁㗔ၞ߇޽ࠅ㧘㓞ធߔࠆ᳇ᵃᩭߦࠃߞߡવᾲ㕙᷷ᐲ߇ᓇ㗀ࠍฃߌ޽ߞߡ
޿ࠆ⁁ᴫ߇⷗ߡߣࠇࠆ㧚ࠠࡖࡆ࠹ࠖ㑆㓒߇ 4 mm ߣᐢ޿ Fig. 7 (e)ߢߪ㧘᷷ᐲ⋧㑐ଥᢙߩ㊀ߥࠅว߁㗔ၞ߇㧘․ߦ Center ࠠࡖࡆ࠹ࠖߣ Right ࠠࡖࡆ࠹ࠖ㑆ߢ᣿⏕ߢ޽ࠆ߇㧘ታ⾰⊛ߦήߊߥߞߡ߅ࠅ㧘㓞ធߔࠆࠠࡖࡆ࠹ࠖ㑆ߢ᳇ᵃᩭᐓᷤ߇ᶖṌߒߡ޿ࠆ㧚߹ߚ㧘ᑼ(6)ߦࠃࠅ᳞߼ߚ᷷ᐲ⋧㑐ଥᢙࠍ↪޿㧘3ࠠࡖࡆ࠹ࠖߩ႐วߩ㓞ធߔࠆࠠࡖࡆ࠹ࠖ㑆ߢ↢ߓࠆ᷷ᐲ⋧੕ᐓᷤߩᒝᐲࠍએਅߩᑼࠃࠅ᳞߼ߚ[6]㧚
x2

x3¦R  ¦R

ࠠࡖࡆ࠹ࠖ๟࿐ߩછᗧὐߢ޽ࠆ㧚߹ߚ㧘 r ߪᑼ(8)ߦ
ࠃࠅ᳞߼ࠄࠇࠆ᷷ᐲᄌേߩᮡḰ஍Ꮕߢ޽ࠆ㧚cji x (1)

\t

cj

(9)

j x2

X 3  X (1)

  

1.2

1.2

1
0.8
0.6
0.4
0.2
0
-6 -5 -4 -3 -2 -1 0

1

2

3

Distance from center cavity

4

5

1.2
Temperature correlation coefficient

Temperature correlation coefficient

1
0.8
0.6
0.4
0.2
0
-6 -5 -4 -3 -2 -1 0

6

mm

1

2

Distance from center cavity

1.2
Temperature correlation coefficient

3

4

5

1
0.8
0.6
0.4
0.2
0
-6 -5 -4 -3 -2 -1 0

6mm(b) Triple cavities S = 1 mm(a) Single cavity

12Distance from center cavity



3

4

5

1
0.8
0.6
0.4
0.2
0
-6 -5 -4 -3 -2 -1 0

1

2

Distance from center cavity

3

4

5

(c) Triple cavities S = 2 mm

1
0.8
0.6
0.4
0.2
0
-6 -5 -4 -3 -2 -1 0

6

mm

1

2

Distance from center cavity

3

4

5

6

mm

(e) Triple cavities S = 4 mm(d) Triple cavities S = 3 mm

Fig. 7 Correlation coefficient of temperature fluctuation.

-5- - 105

6

mm

1.2
Temperature correlation coefficient

Temperature correlation coefficient

2

i 1

r

ߢ޽ࠅ㧘ᷝ߃ሼ c ߪࠠࡖࡆ࠹ࠖ⋥ਅὐ㧘ᷝ߃ሼ j ߪ㧘 i

¦ T T

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)ᑼߩ࡜ࡊ࡜ࠬ㐳ߐ㧘Magnitude of thermal interaction for triple cavities [ x10 3]

Results in this study: 2.47 ~ 3.16 x 104 W/m2
Left + Center
Center + Right

Lc

Shoji et als'. result : 3.38 ~ 5.56 x 104 W/m2
Left + Center
Center + Right
7

5
4
3
2
1
0
0.4

0.8

1.2

1.6

2

Dimensionless distance S/L c

Fig. 8 Intensity of thermal interaction.

0 sec

3 msec6 msec

12 msec

15 msec

18 msec

9 msec21 msec

Ratio of bubble coalescence pattern %Fig. 9 Bubble behavior from triple cavities.
Experimental range 3.02~3.72x10 4 W/m2
Normal Lift
Vertical Coalescence
Horizontal Coalescence
Declining Coalescence
100'H'+'T'+'C''H'+'T'

80
60
Single

40
20
0

0

0.4

0.8

1.2

1.6

(10)

ߢ㒰ߒߚήᰴర㑆㓒ࠍᮮゲߦߣߞߚ㧚Center ߣ Rightࠠࡖࡆ࠹ࠖ㑆㧘Center ߣ Left ࠠࡖࡆ࠹ࠖ㑆㧘౒ߦ᷷ᐲ⋧੕ᐓᷤߩᓇ㗀ߪ㧘ࠠࡖࡆ࠹ࠖ㑆㓒 S = 2 mm ߢᕆỗߦᒙߊߥࠅ㧘ߘࠇ߆ࠄࠠࡖࡆ࠹ࠖ㑆㓒߇ᐢߊߥࠆ
߶ߤ㧘ᓢ‫ߦޘ‬᷷ᐲ⋧੕ᐓᷤߩᓇ㗀ജ߇ዊߐߊߥߞߡ
޿ߊߎߣ߇ࠊ߆ࠆ㧚Fig. 8 ਛߦߪ㧘ห᭽ߦߒߡ᳞߼
ࠄࠇߡ޿ࠆᐣมࠄ [6] ߩታ㛎⚿ᨐ߽Ყセߩߚ߼␜ߐࠇߡ޿ࠆ㧚ᧄታ㛎ߩ႐วߣห᭽ߩ௑ะ߇ᓧࠄࠇߡ
޿ࠆ㧚ዏ㧘ᐣมࠄߩታ㛎ߢߪ㧘ᧄታ㛎ࠃࠅᾲᵹ᧤߇
㜞ߊ㧘ᓥߞߡ㧘᷷ᐲᐓᷤߩᒝᐲߪᧄታ㛎ߩ႐วࠃࠅ
ᄢ߈ߥ୯ߣߥߞߡ޿ࠆߣ⠨߃ࠄࠇࠆ㧚

60

V g (U l  U g )2

Dimensionless distance S/L c

Fig. 10 Bubble coalescence.
㩷
Right ࠠࡖࡆ࠹ࠖߣ Center ࠠࡖࡆ࠹ࠖ㑆ߩ᷷ᐲ⋧੕ᐓᷤࠍ᳞߼ࠆ႐ว㧘 X 1 ߪ Right ࠠࡖࡆ࠹ࠖ㧘 X 3 ߪ
Center ࠠࡖࡆ࠹ࠖ㧘 X 2 ߪߘߩਛ㑆ὐߣߒߚ㧚Centerࠠࡖࡆ࠹ࠖߣ Left ࠠࡖࡆ࠹ࠖ㑆ߩ᷷ᐲ⋧੕ᐓᷤࠍ᳞
߼ࠆ㓙ߦ߽㧘 X 2 ࠍਛ㑆ὐߣߒߡ᳞߼ߚ㧚ࠠࡖࡆ࠹ࠖ㑆㓒ߩᄌൻߦ઻߁㧘᷷ᐲᐓᷤߩᒝᐲߩ
ᄌൻࠍ Fig. 8 ߦ␜ߔ㧚ห࿑ߢࠠࡖࡆ࠹ࠖ㑆㓒 S ࠍᰴ ᳇ᵃว૕
Fig. 9 ߦ 3 ࠠࡖࡆ࠹ࠖߩ႐วߩ᳇ᵃ᜼േ↹௝଀ࠍ␜ߔ㧚ߎࠇࠄߩ↹௝߆ࠄ㧘᳇ᵃว૕ߦߪ㧘ᐣมࠄ [7]߇ㅀߴߡ޿ࠆࠃ߁ߦ㧘એਅߩ㧠ߟߩ᭽ᑼ߇޽ࠆߎߣ
߇ࠊ߆ߞߚ㧚
࡮Normal Lift㧦ห৻ࠠࡖࡆ࠹ࠖ਄ߢవⴕ᳇ᵃߣᓟ⛯᳇ᵃ߇ว૕ߖߕ㔌⣕ߔࠆ㧚࡮Vertical coalescence㧦ห৻ࠠࡖࡆ࠹ࠖ਄ߢవⴕ᳇ᵃߣᓟ⛯᳇ᵃ߇ว૕ߔࠆ㧚࡮Declining coalescence㧦޽ࠆࠠࡖࡆ࠹ࠖࠃࠅ㔌⣕ߒߚ᳇ᵃߣ㧘㓞ធߔࠆࠠࡖࡆ࠹ࠖ਄ߢᚑ㐳ߔࠆ᳇ᵃ߇㧘ᢳ߼ߦว૕ߔࠆ㧚࡮Horizontal coalescence㧦㓞ធߔࠆࠠࡖࡆ࠹ࠖࠃࠅ↢ᚑਛߩ᳇ᵃห჻߇ว૕ߔࠆ㧚න৻ࠠࡖࡆ࠹ࠖߣ 3 ࠠࡖࡆ࠹ࠖߩ႐วߦ߅޿ߡ߶
߷ห৻ߩᾲᵹ᧤㧔⚂ 3.0104 W/m2㧕᧦ઙߢ㧘᳇ᵃߩว૕᭽ᑼ೎ߦߘߩ⊒↢㗫ᐲࠍᲧセ㧘ᢛℂߒߚ⚿ᨐࠍ
Fig. 10 ߦ␜ߔ㧚න৻ࠠࡖࡆ࠹ࠖߢߪ㧘ว૕ߖߕߦ᳇ᵃ㔌⣕߇↢ߓࠆ normal lift ߇߶ߣࠎߤߢ޽ࠆߩߦኻߒ㧘 3 ࠠࡖࡆ࠹ࠖߢߪᵴ⊒ߥ᳇ᵃว૕߇↢ߓߡ޿ࠆ㧚ࠠࡖࡆ࠹ࠖ
㑆㓒߇⁜޿႐ว㧘ᮮว૕ߩഀว߇ᄢ߈ߊ㧘⋥਄ว૕㧘ᢳ߼ว૕߇ߘࠇߦ⛯߈㧘ว૕ߩ↢ߓߥ޿ normal liftߪή޿㧘ࠠࡖࡆ࠹ࠖ㑆㓒߇ᐢ߇ࠆߦߟࠇ㧘ᮮว૕߇ήߊߥࠅ㧘ᢳ߼㧘⋥਄ว૕ߩഀว߇Ⴧ߃㧘ߟ޿ߢᢳ߼ว૕߽ߥߊߥࠆ㧚ࠠࡖࡆ࠹ࠖ㑆㓒߇ 4 mm ߩ႐ว
㧔S/Lc = 1.6㧕ߢ߽㧘න৻ࠠࡖࡆ࠹ࠖߩ႐วߢߪ߶ߣ
ࠎߤ↢ߓߡ޿ߥ޿⋥਄ว૕߇ 50%⒟ߩഀวߢ↢ߓߡ޿ࠆ㧚
Fig. 10 ߦ㧘ᐣมࠄ [5] ߦࠃࠅㅀߴࠄࠇߚએਅߦ␜
ߔ᳇ᵃᩭᐓᷤߩ 3 ߟߩਥⷐᓇ㗀࿃ሶ µH¶㧘µT¶㧘µC¶㧘ߩ⊒↢㗔ၞ߇૬⸥ߐࠇߡ޿ࠆ㧚µH¶㧦᳇ᵃ㑆ߩᵹ૕⊛⋧੕ᐓᷤµT¶㧦᳇ᵃᩭ㑆ߩ᷷ᐲ⋧੕ᐓᷤµC¶㧦Horizontal ߣ Declining ߩ᳇ᵃว૕ߦࠃࠆ⋧੕ᐓᷤ

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Thermal Science & Engineering Vol.15 No.3 (2007)

Qbubble Vb U g hlg f(11)

Bubble diametermm

Left cavity
Center cavity
Right cavity(12)Fig. 5 ߦ␜ߒߚࠠࡖࡆ࠹ࠖήߒવᾲ㕙ߩᾲᵹ᧤ 2.63
104 W/m2 ᤨߩ⥄ὼኻᵹᾲવ㆐₸ ho ߢᑼ(12)ߩ୯ࠍ
㒰ߒ㧘S/Lc ߦኻߒߡ Fig. 14 ߦ␜ߔ㧚
 Fig. 14 ߢ㧘h/ho ߪ S/Lc < 1.2 ߢߪ 1 ࠃࠅᄢ߈ߊ㧘᳇ᵃߩᡬᜈലᨐ߇ᄢ߈޿ߎߣ߇ࠊ߆ࠆ㧚৻ᣇ㧘S/Lc > 1.2
ߢߪ h/ho 㧨1 ߢ޽ࠅ㧘᳇ᵃߩᡬᜈലᨐߪήⷞߢ߈ࠆ⒟ᐲߢ޽ࠆߎߣ߇ࠊ߆ࠆ㧚ዏ㧘h/ho ߇ 1 એਅߣߥࠆ
-7- - 107

1
0
0

0.1

0.2

0.3

s

Fig. 11 Bubble diameter variation with time.

Triple cavities
42
S = 1 mm : 2.47 x 10 W/m
42
S = 2 mm : 3.16 x 10 W/m
42
S = 3 mm : 2.68 x 10 W/m
4
2
S = 4 mm : 2.54 x 10 W/m
250
200
150
100
50
0
0

0.5

1

1.5

2

Dimensionles distance S/L c

Fig. 12 Bubble departure frequency.

Bubble departure diameter mm

Qlaser  Qbubble  Qloss(Tw  Tl ) A

2

Time

㩷
ߎߩ Qbubble ߣ㧘࡟࡯ࠩ࡯ߦࠃࠆᾖ኿ᾲ㊂ Qlaser ߣ㧘વᾲ㕙ᄖ๟࿐ᣇะ߳ߩᾲવዉ᡼ᾲ㊂ Qloss ߆ࠄੱᎿࠠࡖ
ࡆ࠹ࠖઃ߈વᾲ㕙ߩኻᵹᾲવ㆐₸ߪ㧘એਅߩᑼߦࠃ
ࠅ᳞߹ࠅ㧘

h

3

Hz

㩷 ኻᵹᾲવ㆐
 Fig. 9 ߦ␜ߔ㜞ㅦᐲࠞࡔ࡜ߦࠃࠅ᠟ᓇߒߚ᳇ᵃ᜼േ↹௝߆ࠄ㧘᳇ᵃߩ㔌⣕ᓘߣ㔌⣕๟ᦼࠍ᳞߼ߚ㧚ߎߎߢ㧘㔌⣕⋥೨ߩࠠࡖࡆ࠹ࠖ਄ߩ᳇ᵃߩ᳓ᐔᣇะ᏷
ࠍ᳇ᵃᓘߣߒߚ㧚Fig. 11 ߦࠠࡖࡆ࠹ࠖ㑆㓒 S = 4 mm㧘ᾲᵹ᧤ q = 1.86 × 104 W/m2 ᤨߩ᳇ᵃᓘߩᤨ㑆ᄌൻࠍ␜ߔ㧚ዏ㧘᳇ᵃ㔌⣕⋥ᓟ᳇ᵃᓘࠍ࠯ࡠߣߒߚ㧚
Fig. 11 ߆ࠄ㧘ฦࠠࡖࡆ࠹ࠖ਄ߩ᳇ᵃߩᚑ㐳ߣ㔌⣕ߪ㧘ฦࠠࡖࡆ࠹ࠖ㑆ߢᤨ㑆Ꮕࠍᜬߞߡⴕࠊࠇߡ޿ࠆ
ߎߣ߇ࠊ߆ࠆ㧚ࠠࡖࡆ࠹ࠖ㑆㓒ߩᄌൻߦ઻߁ᐔဋ᳇
ᵃ㔌⣕๟ᵄᢙࠍ Fig. 12 ߦ␜ߔ㧚߹ߚ㧘ࠠࡖࡆ࠹ࠖ
㑆㓒ߩᄌൻߦ઻߁ᐔဋ㔌⣕᳇ᵃᓘߩᄌൻࠍ Fig. 13
ߦ␜ߔ㧚Fig. 12 ߢߪ㧘ฦࠠࡖࡆ࠹ࠖᲤߦหᤨೞߩ 0.3⑽㑆ౝߢ᳇ᵃ㔌⣕๟ᵄᢙࠍ᳞߼㧘3 ߟߩࠠࡖࡆ࠹ࠖ
ߩᐔဋࠍᐔဋ㔌⣕๟ᵄᢙߣߒߚ㧚 Fig. 13 ߦ߅޿ߡߪ㧘
0.3 ⑽㑆ߦߔߴߡߩࠠࡖࡆ࠹ࠖ߆ࠄ㔌⣕ߔࠆ᳇ᵃߩ㔌⣕᳇ᵃᓘࠍ᷹ቯߒ㧘ߘߩᓘߩᐔဋ୯ࠍᐔဋ㔌⣕᳇ᵃᓘߣߒߚ㧚Fig. 12㧘13 ࠃࠅࠠࡖࡆ࠹ࠖ㑆㓒߇ዊߐ޿߶ߤ㧘᳇ᵃ߇චಽᚑ㐳ߔࠆ೨ߦ㔌⣕ߒߡ޿ࠆߎ
ߣ߇ࠊ߆ࠆ㧚Fig. 10 ߦ␜ߐࠇߡ޿ࠆࠃ߁ߦ㧘ࠠࡖࡆ࠹ࠖ㑆㓒߇⁜޿߶ߤ㧘ࠠࡖࡆ࠹ࠖ㑆ߢ᳇ᵃߩᮮ㧘ᢳ߼ว૕߇ᵴ⊒ߦ↢ߓ㧘ࠠࡖࡆ࠹ࠖ㑆ߢᓇ㗀ߒ޽ߞߡ᳇ᵃ㔌⣕߇ଦㅴߐࠇߡ޿ࠆߣ⠨߃ࠄࠇࠆ㧚 Fig. 13 ߩᐔဋ㔌⣕᳇ᵃᓘࠍ↪޿ߡ㧘᳇ᵃࠍ⌀⃿ߣߒߡ᳇ᵃ૕Ⓧࠍ▚಴ߒ㧘߹ߚ Fig. 12 ߩᐔဋ㔌⣕๟ᵄᢙࠍ↪޿ߡ㧘⋧ᄌൻߦࠃࠆવᾲ㕙߆ࠄߩᾲャㅍ㊂ࠍ
ᑼ(11)ࠃࠅ᳞߼ߚ㧚ߎߣߪ㧘ho ࠍ᳇ᵃߩሽ࿷ߔࠆ႐ᚲࠍ฽߼ߚടᾲ㕙ో૕ߦኻߒቯ⟵ߒߡ޿ࠆߎߣߦࠃࠆ㧚࡟࡯ࠩ࡯ߦࠃࠆᾖ኿ᾲ㊂ Qlaser ߆ࠄᾲવዉ᡼ᾲ㊂
Qloss ࠍᏅߒᒁ޿ߚోવᾲ㊂ࠍ Q ߣߒ㧘ኻᵹߦࠃࠆવ
ᾲ㊂ࠍ Qconve = Q - Qbubble ࠍ᳞߼㧘Qbubble/Q, Qconve/Q ߣ
S/Lc ߩ㑐ଥࠍ Fig. 15 ߦ␜ߔ㧚S/Lc < 1.2 ߢߪኻᵹᚑಽ
Qconve/Q ߇ᾲવ㆐ߩਥⷐㇱࠍභ߼ߡ޿ࠆߩߦኻߒ㧘
S/Lc > 1.2 ߢߪ⋧ᄌൻᚑಽ Qbubble/Q ߇ਥⷐㇱࠍභ߼ߡ޿ࠆߎߣ߇ࠊ߆ࠆ㧚એ਄ߩ⚿ᨐߪ㧘વᾲ㕙ᾲᵹ᧤ߩᄢ߈ߐߦࠃࠆᓇ㗀߽⠨ᘦߔࠆᔅⷐ߇޽ࠆ㧚੹ᓟߩᬌ⸛⺖㗴ߢ޽ࠆ㧚㠽㘺ߩᜰ៰ߦࠃࠇ߫[14]㧘ૐᾲᵹ᧤ၞߢߪ᳇ᵃᠣੂ㧘㗼ᾲャㅍߩലᨐ߇ᄢ߈ߊ㧘ᾲᵹ᧤ߩჇᄢߣߣ߽ߦẜᾲャㅍߩലᨐ߇ᄢ߈ߊߥࠆ㧚

Bubble deperture frequency

S/Lc = 1.6 ߢ¶C¶߇ᶖṌߒߡ޿ࠆߎߣߪ㧘ᐣมࠄߩ⚿ᨐߣหߓߢ޽ࠆ㧚Fig. 7 (e) ߦ␜ߔࠃ߁ߦ㧘S/Lc =1.6 ߢߪ㧘ᧄታ㛎ߢߪ¶T¶ߪᶖṌߔࠆߣ⷗ߥߖࠆ߇㧘ߎࠇߪ㧘ᐣมࠄߩ႐วߦᲧߴᾲᵹ᧤߇ૐ޿ߎߣߦࠃ
ࠆߣ⠨߃ࠄࠇࠆ㧚

Triple cavities
S = 1 mm : 2.47 x 104 W/m2
S = 2 mm : 3.16 x 1044 W/m22
S = 3 mm : 2.68 x 104 W/m2
S = 4 mm : 2.54 x 10 W/m
3
2
1
0
0

0.5

1

Dimensionless distance

1.5

2

S/L c

Fig. 13 Bubble departure diameter.

C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)

⻢ㄉ

Dimensionless Heat Transfer coefficient h/h0

Mirror-finished surface : 2.63 x 10 4 W/m2ᧄ⎇ⓥࠍㅴ߼ࠆߦᒰߚࠅ␹ᄹᎹᄢቇᢎ᝼ ᐣมᱜᒄ᳁㧘᧲੩ᄢቇ ᷰㄝ⺈᳁㧘᧲੩ᄢቇᄢቇ㒮 ਤਅቇ᳁㧘ࠞ࡞ࡈࠜ࡞࠾ࠕᄢቇࠨࡦ࠺ࠖࠛࠧᩞ
Surapong Chatpun᳁ߦᓮᜰዉࠍ㗂߈߹ߒߚ㧚߹ߚ㧘ታ㛎ࠍⴕ߁ߦ޽ߚࠅరᎿቇ㒮ᄢቇᎿቇㇱᯏ᪾Ꮏቇ⑼ቇ↢ ዊේ๺਽᳁㧘₹⟎ᥰᐘ᳁㧘ᵄᾖ㑆⺬᳁ߦߏදജࠍ㗂߈߹ߒߚ㧚ߎߎߦ⻢ᗧࠍ⴫ߒ߹ߔ㧚

Triple cavities
S = 1 mm : 2.47 x 104 W/m2
S = 2 mm : 3.16 x 104 W/m2
S = 3 mm : 2.68 x 104 W/m2
S = 4 mm : 2.54 x 104 W/m2

2
1.5
1
0.5

ෳ⠨ᢥ₂

0

0

0.5

1

1.5

2

S/Lc

Fig. 14 Bubble agitation effect.

Experimental range: 2.47 ~ 3.16 x 10

4

W/m 2

Qbubble / Q and Qconve / Q

Qbubble / Q
Qconvec/ Q

1
0.8
0.6
0.4
0.2
0
0

0.5
1
1.5
Dimensionless distance S/L c

2Fig. 15 Relation between phase change and convective
heat transfer.

㧠 ⚿⺰MEMS ᛛⴚࠍ↪޿ߡࠠࡖࡆ࠹ࠖ㐿ญᓘ 10 ȝm㧘ᷓ
ߐ 40 ȝm ߩ౞╴ᒻࠠࡖࡆ࠹ࠖࠍᐔṖߥࠪ࡝ࠦࡦ࠙ࠚ
ࡂ਄ߦ૞⵾ߒ㧘߹ߚࠠࡖࡆ࠹ࠖ㑆㓒ࠍ 1 mm ~ 4 mm߹ߢᄌൻߐߖ㧘ߘࠇࠍવᾲ㕙ߣߒߡ↪޿㧘ᾲᵹ᧤~
4.54104 W/m2 ߩ▸࿐ߢࡊ࡯࡞ᴣ㛛ᾲવ㆐ታ㛎ࠍⴕ޿એਅߩ⚿⺰ࠍᓧߚ㧚(1) ࠠࡖࡆ࠹ࠖ⋥ਅ࡮๟࿐ߩ᷷ᐲᄌേߩ㑐ଥ߆ࠄ㧘ࠠࡖࡆ࠹ࠖ㑆㓒߇ᐢߊߥࠆ߶ߤᾲ⊛㓞ធ᳇ᵃᩭ㑆ᐓᷤߩᐲว޿߇ዊߐߊߥࠆߎߣࠍ⏕⹺ߒߚ㧚ᧄታ㛎▸࿐ߢߪ S/Lc = 1.6 ߢߪ߶߷ᾲ⊛ᐓᷤߪᶖṌߒߡ޿ߚ.
(2) ᳇ᵃߩว૕ߦߪ 4 ࡄ࠲࡯ࡦ޽ࠆߎߣࠍ⏕⹺ߒ㧘
S/Lc  1.6 ࠃࠅ Horizontal coalescence ߣ Declining
coalescence ߩ᳇ᵃว૕߇ήߊߥࠆߎߣ߇ࠊ߆ߞߚ㧚(3) ૐᾲᵹ᧤ၞߦ߅޿ߡ㧘S/Lc > 1.2 ࠃࠅ㓞ធ᳇ᵃ㑆ߩᵹ૕⊛ߥᐓᷤ߇ዊߐߊߥࠆߎߣ߇ࠊ߆ߞߚ㧚[1] Kenning, D. B. R. and Yan, Y., ³Pool boiling heattransfer on a thin plate: features revealed by liquid
crystal themography´, Int. J. Heat and Mass
Transfer, Vol. 39, No. 15 (1996), 3117-3137.
[2] Judd, R. L. and Chopra, A., ³Interaction of the
Nucleation Processes Occurring at Adjacent
Nucleation Sites,´ Trs. of the ASME, Journal of
Heat Transfer, Vol. 115 (1993), 955-962.
[3] ቟੗ᐽੑ㧘ᐣมᱜᒄ㧘̌න৻ࠠࡖࡆ࠹ࠖ߆ࠄߩ
⊒ᵃ․ᕈ´㧘╙ 39 ࿁ᣣᧄવᾲࠪࡦࡐࠫ࠙ࡓ⻠Ṷ⺰ᢥ㓸㧘(2002)㧘721-722.
[4] Shoji, M. and Takagi, Y., ´Bubbling features from asingle artificial cavity,´ Int. J. Heat and Mass
Transfer, Vol.44 (2001), 2763-2776.
[5] Zhang, L. and Shoji, M., ³Nucleation site
interaction in pool boiling on the artificial surface,´Int. J. Heat and Mass Transfer, Vol. 46 (2003),
513-522.
[6] Chatpun, S., Watanabe, M. and Shoji, M.,³Nucleation site interaction in pool nucleate boilingon a heated surface with triple artificial cavities,´
Int. J. Heat and Mass Transfer, Vol. 47 (2004),
3583-3587.
[7] Chatpun, S., Watanabe, M. and Shoji, M.,³Experimetal study on characteristics of nucleatepool boilng by the effects of cavity arrangement,´Experimental Thermal and Fluid Science, Vol. 29(2004), 33-40.
[8] Fujii, T., Imura, H., ´Natural Convection Heat
Transfer from a Plate with Arbitrary Inclination,´Int. J. Heat and Mass Transfer, Vol. 15 (1972), 755.
[9] Lloyd, J. P., Morran, W. R., ´Natural Convection
Adjacent to Horizontal Surface of Various
Planforms,´ ASME Pap.74-WA/HT-32.
[10] Rohsenow, W. M., ³A Method of Correlating Heat
Transfer Data for Surface Boiling Liquids,´ Trans.
ASME, Vol. 74 (1951), 969.
[11] ᫜Ỉ৻㇢, ⷏የ⨃ᢥ, ೨Ꮉㅘ, વᾲᎿቇ (1989),
83, ᦺୖᦠᐫ.
[12] Bergles, A. E. and Rohsenow, W. M., ³The
determination of forced-convection surface-boilingheat transfer, ³ASME Ser.C, 86 (1964), 372.
[13] ᄢ┻ᶈ㕏㧘੗਄ᚑታ㧘ዊᴰ቟㇢㧘̌⿥㖸ᵄࠍ↪
޿ߚᩭᴣ㛛㐿ᆎ᷷ᐲߩૐᷫൻߦ㑐ߔࠆ⎇ⓥ̍㧘

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C 2007 The Heat Transfer Society of Japan○

Thermal Science & Engineering Vol.15 No.3 (2007)ᣣᧄᯏ᪾ቇળ⺰ᢥ㓸㧔B ✬㧕㧘63-614 (1997),
3353-3361.

[14] ᣣᧄᯏ᪾ቇળ✬, ᴣ㛛ᾲવ㆐ߣ಄ළ (1989),
46-49, ᣣᧄᎿᬺ಴ .

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C 2007 The Heat Transfer Society of Japan○