ヅᢡ⇐᱿ᥖЗӠኔ
ޙᏕཪʳ ᓐᄭ
Օဎݾᖂೃ۞೯֏ՠ࿓ߓ
ၪ ⣬
ႚอऱ߁᛭ऄ៶طᗏᗈۦ౻ࢨᢐ౻ขسᑷΔᆖطلۯऱᑷࠨᖿۖআګݼఐ ऱய࣠Ζײ۔ऱࢸ᧾ਢܓش᧾ᕴףᑷၞ۩᠔᛭ΔႊലᑷᖄԵ᧾ᕴࢨࣦᕴփΔ٦
߰ຒऱᆝڇؼᓅՂΖ߁᛭ፖࢸ᧾ൄٽಾ᛭ٵழਜΔຍࠄ᛭ऄࠠڶऱ٥ຏ
ࢤΔ༉ਢሎشᑷΖྥۖΔ߁᛭ऄڇਜழᄎขسᄿΔທګڍ൛ृࡅܮᕴࡴ
ऱլᔞΙࢸ᧾᛭ऄঞᄎژڇᗈؼᓅհᇄΖءᓵ֮༼נԫጟܓشሽᑷጥףᑷऱ ᄅীሽ߁᧾Δࠠڶ߁᛭ፖࢸ᧾ऱᠨૹפயΖ᧾ᕴආشᚘ܌Ժޗᔆ፹ګΔ࣐࣍ף ՠױຘီؼᓅ᛭யणኪΔٍױݮګ२ۿᑷऱᢰයٙΖءᓵ֮אᑇଖ։࣫
ሽ߁᧾փऱᑷႚᎠΔݺଚലሽ߁᧾ီףᑷᄭڇՂֱऱയຨ़ၴΔەၦ᧢ᑇץ ਔሽᑷጥऱࡳᄵ৫ (To) ፖᄵ (T )ΖݺଚܓشၸჁ֗ۊၸᄵᒵቹΔ∞ ᎅࣔ᧾ᕴփऱᑷႚᎠणउΖૠጩ࣠᧩قΔڇઌٵऱ᜕ᖩֺ (H /D) ൣउՀΔ ڇ᧾ᕴփऱᄵ৫༓ຟਢऎထၗᒵֱٻ᧢֏Ιিऴؼᓅֱٻऱᑷႚᖄଖ (Qcond) ઌᅝ՛Δڼრ࠺ऱᑷႚᎠᖲዌᑷኙੌயᚨΖ
〦⼫⥱Ř߁᛭Δࢸ᧾ΔᑷႚᎠΔሽ߁᧾Ζ!
ANALYSIS OF HEAT TRANSFER IN ELECTROMOXIBUSTION CUP
Feng-Chyi Duh Yuen-Tai Tsai
Department of Automation Engineering Ta Hwa Institute of Technology
Hsinchu, Taiwan 307, R.O.C.
Key Words: moxibustion, cupping, heat transfer, electomoxibustion cup.
ABSTRACT
Moxibustion therapy is a traditional Chinese medical technique which applies heat produced from ignited moxa or mugwort herb over the skin to stimulate acupuncture points of the body for the prevention or treatment of disease. Cupping therapy is usually performed by introducing heat into a cup or similar object and placing it immediately on the skin. Moxibustion and cupping therapies are used along with acupuncture therapy. These techniques are characterized by their amazingly rapid attainment of the desired results by the heat. Because moxibustion often includes the burning of moxa or mugwort herb, patients who have respiratoy problems should avoid the use of smoking moxa or mugwort herb. Cupping therapy has a risk of burning the patient if not carefully executed. In this study, a new electromoxibustion cup is designed. We can place the cup on the skin and gently heat the air in the cup with an electroheater. An acrylic cup has been used for this purpose, because, one can see the skin within the cup and
produce insulated boundary conditions. A numerical analysis is used to study the heat transfer of the electromoxibustion cup. We focused on heat transfer in the electromoxibustion cup, an enclosure heated from the top.
The phenomena of natural convection in the enclosure are as varied as the heating temperature (T ) and room temperature (o T∞). The colorful temperature contours and isothermal lines are simultaneously presented to illustrate heat transfer within the cup. Subject to the same aspect ratio (H /D), the temperature within the cup is found to vary along the axial direction. The heat conduction normal to the skin (Qcond) is relatively small;
hence, the heat transfer mechanism is dominated by heat convection.
ɺȮԊ ⤵
ಾ᛭ (acupuncture) ፖ߁᛭ (moxibustion) ݁ਢ᥆࣍
խഏႚอ᠔ᖂऱ؆ए᛭ऄ[1-3]Δಾ᛭ਢආشٺڤಾࠠࠨԵ Գ᧯لۯΔਜ۩ࡳհሎಾऄԫழၴΔขسࠨᖿ܂شۖ
ᖿ࿇ᆖΔሒࠩए᛭ఐ࿀ፖ༚ൈհפயΖ߁᛭ঞਢආ ش፹ऱᢐ౻ΔڇԳ᧯لۯऱؼᓅ।૿ᗈࢨ៷ᑸΔขس
ڶ࠺ፖᄵᑷऱࠨᖿயᚨΔ៶אᓳᆏسᖲ౨Εᏺၞߪ
᧯ൈΔሒګᇞᑷ࿀ፖ塄سঅհؾऱΖಾ᛭ፖ߁᛭ڇ
᛭யࠠڶઌ᎖ઌګհפ౨ΔਚڇᜯݩՂൄٽࠓሎشࢨ٣৵
ٌཙࠌشΔਚຏൄٽጠಾ߁ (zhenjiuology)Δൕײᤄհᓵ ឰΚψಾࢬլΔ߁հࢬࡵωΔܛߩאᇭᤩಾ᛭ፖ߁᛭ࠠڶ യլױ։ऱᣂᜤࢤΖ
߁᛭ڇਜ߁ழլ܍ڶᄿ៷ࡉۦ౻࠺Δۦ౻ءਝࠠ
ڶ॑ଉ࠺ΔឈྥڶऱԳፊ৵ᤚငዃΔ܀լױᘨߢऱਢ ڶԳᄎ༞ࠡ࠺Δڂڼڇᝩ܍ଅܬ༉်൛ृऱणउՀΔ
်ࢬؘႊؚၲ࿗֪ᓳང़Ζ؆Δ߁᛭ڇၞ۩መ࿓ؘࡳ
ᄎขسᄿᣆΔທګ़ᖼലਢլױᝩ܍ऱࠃኔΖ٦ृΔ
վ৬ᗰढ݁ආ࠷യຨڤ़ၴૠΔԫխ᠔ೃࢨ်ࢬ݁
ࠠڶ़ᓳࢨܐໂΔܛࠌ֧ᗏհᢐ౻ଉ࠺ᐴᏗΕ៷ᄿᇚ ៥Δ܀ᣵደऱᄿᣆኙ࣍Գ᧯ۖߢΔؘࡳขسਬጟ࿓৫ऱլ ငࣚΔ۟ലᄎٲ୭ࠩԳ᧯ൈΖڼ؆Δਜ߁ழൄᏁๅ
۪ࣚΔࢬאՈࣹრփऱᄵ৫ࡉփ؆ሶᎽΔ֠ࠡڇמࡱ
ᣤ༃ࡉࡱᎩཔհᎾΔޓႊࣹრࠌ༉်൛ृငᔞΖאՂࢬ ຫ૪ऱጟጟլঁΔലਢທګ߁᛭ດዬڤპऱԫՕીࡎ႞Ζ
ڇ߁᛭ऱመ࿓խΔط࣍ᢐ౻ᗏᗈऱழၴྤऄፂᢀመ ՆΔڇᗏᗈཚၴլױ౨ፂࡐࡳऱᄵ৫ଖΔኙ࣍᛭யؘࡳ
ᄎڶઌᅝ࿓৫ऱ྇ჾΖೈڼհ؆Δ߁᛭່࣐ᆵ־Δ֧ದؼ ᓅ႞ࢨ۪ࣚᗈΔਚڇਜ߁ழؘႊݹშஎ᥈՛֨Δ ࠀᚨᙟழ༼؈־Ζڂ壆ڍऱլঁΔࢬאൄחԳ֨س
᥈ۖ፷ߩլছΙ֠ࠡشऴ൷߁ऄΔᄎ࿇سದచΕగΕ ᑭᥓ߁ᒈွΖאՂࢬඖ૪ऱ؈Δທګ߁᛭բᆖ૿ᜯ
ࠩ؈ႚऱ૰֊ٲᖲΖ
Գᣊሎشཬढ࣍ए᛭ఏఐऱᖵՆΔ၌။Գᣊऱ֮
ࣔΔਚբีᗨઌᅝ᠆༄ऱᆖ᧭ፖႚࢭ[4]ΖאխഏࠏΔ ཬढऱሎشᄩᄭ࣍۫ցছ 2600 ڣছΔڇ০׆壀ልࢬᒳᤊऱ
ཬढᢐࠢόء౻ύխΔփ୲ܛբᇡ٨ 250 ጟऱᢐ౻ᇷறΔ
ࠡխڶڍ۟վսᖵՆᚦഒΖ۟࣍ݦ܄ࠐΕॳࢮ܄֗ٱ৫Ξ
ײ۔اගΔܓشཬढဇ࠷॑ଉढᔆࠀᚨشڇ᠔एఏఐΔ ߩߠཬढڇ᠔᛭Ղފዝᜰߩ᎘ૹऱߡۥΖڇୗ֗ΔԳଚޓ ᨃཬढऱሎش࿇ཀැዟጐીΔൕཬढဇ࠷॑ଉढᔆᘜԵ سܛ່ࠋऱᇭᤩΖطڼױߠΔԳᣊऱႚอ᠔᛭ኙ࣍ཬ ढᢐ౻ऱଘૹΔ۟վսࠠڶᄕऱᏝଖΙઌኙ࣍߁᛭
ழආشᢐ౻ղא֧ᗏΔࠡኔፖֱ۫ࢬࠌشऱཬढ᛭ऄژڇ ฆڴٵՠհݎΖ
ڰཚऱԳᣊषᄎΔ᠔᛭ፖࡲඒژڇയլױ։ऱٽ ࢤΔਚڇࡨऱࡲඒ೯խΔൄߠរ־ದᄿऱᏚڤΔۖܓ شψᄿωएఐԯਢԫጟऱ᠔᛭ֱڤΖ۟վΔڍࡲඒ սڶঅఎ៷ଉ (ᗈଉ) ऱ៖ᏚΔ܀ഗ࣍ᛩቼঅᥨऱە ၦΔܓشψᄿωൕࠃ᠔᛭ऱֱऄբڤპΖᗏᗈᢐ౻ਢ߁᛭
ؘऱ᛭࿓Δഄ܌ࣚ៷ᄿऱܺឫΔૉޏආཬढဇ࠷ऱ壄 ईၞ۩॑ଉ᛭ऄΔຍലਢԫጟݙ٤ሂๅႚอ߁᛭ऱᑓڤΔ ࠀࠠڶኧࢍᣌႚอ߁᛭ऱ৸ፂΖ
ཬढ壄ईਢطڍጟڶᖲ։ิګΔࢬࠠᗑଉ࠺ᄭ۞
࣍։ၴऱؓᘝ܂شΔٺጟ壄ईࠠڶ૮ྥլٵऱ᛭யΖૉ
౨ຘመ॑ଉ᛭ऄऱᒷࡉਫࢤֱڤΔאঁငᒷڇಾ߁᛭࿓
խΔ߁ಾ༺Ե⟿لհጹ്ࣷΔኙ࣍ए᛭ؘࡳࠠڶף։ऱ פயΖڇᘜٽז塄سΕભ୲ΕᥨᓅΕᒇߪΕ྇ॅᄅس
ऱ৸ፂΔઌॾΔຘመזઝݾऱᘜٽΔലႚอಾ߁ፖ॑
ଉ᛭ऄ[5-7]ղאٽΔؘ౨আࠌಾ߁᠔᛭ๅ઼ངΔጳ
࣋٠Ζ
ࢸ᧾ײזጠψߡऄωΔຏൄԾጠࢸ־᧾Εܮ᛭ऄΕ ێ᛭ऄࢨࢸ᧾ऄΔԯ៶ᗏᗈΕᄵᑷࢨࢼֱڤࠌ᧾
փขسᚘۖऴ൷ܮထؼᓅ।૿Δທګךۨွۖሒࠩए
᛭ؾऱհԫጟֱऄ[8,9]Δຍጟ᛭ऄᆖൄፖಾ߁ٽࠌشΔ ޓਢاঋ᛭ऄൄߠऱ֫ऄΖڶࠄᖂृ༼נΔࢸ᧾ࢬขسऱ ݝຝܮԺΔױທګࢬܮࢸຝۯऱᐋิ៣࿇س೯ࢤך
ۨΔڶܗ࣍ޏᖲ᧯ิ៣ऱᛜ塄णउፖᓳᖞۨ༛ᛩΔၞ
ۖআၞᄅຫזΖٵழΔࢸ᧾ऱݝຝࠨᖿᝫױຏመࡌᢰ壀 ᆖߓอ֘୴ࠩՕᆰؼᐋΔࠌࠡᘋᕿࢤᏺൎΔൕۖڶܗ࣍ఐ
ऱൈ༚Ζ
ឈྥࢸ᧾ኙ࣍ਬࠄఏఐڶৰړऱ᛭யΔৰڍԳՈຟ۞
۩၇ࢸ᧾ᕴ܂ࡺ୮অհشΔྥۖࢸ᧾ࠀॺۍྤᆃ ݲΔڕխ৫֗ᣤૹհ֨ఐ൛ृΕ֖ۨఐΕ٤ߪ௬ᆭΕࠠ
ሽᑷጥ(ӽ4,L25)
z
D=20 o r
H=46
C=38
ຯᛩ(ӽ20,L4) R
ӽ36 ሽᄭ12VAC
ᚘ܌Ժ᧾ᕴ(t4)
4
ڶؼᓅఐࢨݝຝؼჾΕ᧯ᔆᒇஇ՛ΕଡִאՂհ؋ഡΕ քᄣאՀհࠝ࿙ΕԮԼᄣאՂհ۔ԳΔࢨ࣍ᑷΕࢼ
⛂Ε࿂᧑ຍࠄൣउழΔઃլױࠌشࢸ᧾Ζࢸ᧾ਢԫጟڜ ٤Ծֱঁऱए᛭֗অֱڤΔ܀ࠌشழսڶᗍ႞հᇄΔਚ ࠌشழսႊࣹრڜ٤Ζ
ܓشሽ߁࠷זႚอۦ߁Δឈբګפऱሎشڇ߁᛭᛭࿓
[10]Δ܀ઌᣂऱᖂսבհᠥڕΖط࣍᠔᛭Ꮪᕴਢሎ شڇԳ᧯ֱ૿Δࢬאؘႊࠠໂᄕऱڜ٤ࢤΕױᔾࢤ֗
ڶயࢤΔאཚᒔঅࠌشृऱڜ٤ྤᇄΖڂڼΔءᓵ֮ല៶ ط ANSYS ຌ᧯ൕࠃᑇଖᇞ࣫Δאঁᛵᇞܓشሽᑷጥ
ףᑷᄭऱֱڤΔൕሽᑷጥऱᄵ৫ࡳයٙ൶ಘᑷႚᎠऱൣ
उΔ៶אᛵᇞሽ߁᧾ऱףᄵய࣠Ζሽ߁᧾ࠠڶ߁᛭ፖࢸ᧾
ᠨயԫ᧯հᘜٽפ౨Δᖑڶڜ٤ፖڶயऱףᑷᄭΔࠀࠠໂ
ࡳழፖਁᄵऱףᑷய࣠Δױڶயऱ༼֒ႚอխ᠔᛭ऄऱए
᛭פயΖ
ʷȮᶇἄᅞᘍ
1. ヅᢡ⇐⥑⤺
ءᓵ֮ڇ࣍ᇞ࣫ሽ߁᧾փऱᑷၦႚᎠΔឈྥᑇଖᇞऴ
൷ආش ANSYS ຌ᧯[11]ၞ۩Δ܀᧭ᢞᑇଖ࣠ऱإᒔ ࢤΔݺଚսႊኙഗءऱᑷႚᎠֱऄڶࢬᎁवΖڇءᓵ֮խΔ ݺଚࠀլආشᑇଖֱऄऴ൷ᇞอൗֱ࿓ڤΔኙ࣍ڕ۶៶ط
ANSYS ຌ᧯൶ಘሽᑷጥऱ່ࠋ֏ᇘᆜΔא֗ڕ۶ຘመ
ANSYSຌ᧯Δᇞ࣫ሽᑷጥڇሽ߁᧾փऱףᑷயᚨΔࠀױ
Եᛵᇞሽ߁᧾փੌ೯ፖᑷႚᎠऱွΖ
ႚอࢸ־᧾ऱڤᑌ݁Ց՛ߚՕऱੲᑿ᧾ΔՑհᢰ ᒴࡵٻ؆Δ؆ᨠܧᤪݮۖՑฃٻ؆Ζءᓵ֮ᚵૠڜ٤ ࢤለऱኔ᧭ীሽ߁᧾Δ༓۶֡՚փஉ 20 mmΕ৫ 50 mmΕᕻদ 4 mm հၲՑ᧾ᕴΔ؆ᨠܧଙࣦणΔڕቹ 1(a) ࢬقΙࠡխΔ᧾ᕴऱ᜕ᖩֺ (aspect ratioΔփຝ৫ H ፖ փஉ D ऱֺଖ) H/D=2.3Δሽᑷጥխ֨ၗ৫ C ፖփஉ DऱֺଖC/D=1.9Δ᧩ߠ᧾ᕴ᥆࣍ለา९ऱীڤΔ
ਢቃఎ़ၴאঁ୲ᆜ߁ಾΔڕቹ 1(b) ࢬقΖሽ߁᧾ऱޗᔆ ආشᚘ܌Ժ (acrylic) ፹܂ۖګΔᖑڶףՠ୲࣐ऱᚌរΔࠀ
ࠠڶለ܅ᑷႚᖄএᑇ (k≈0.2W/m⋅K) ऱᔆΔֺԳ᧯ؼ ᓅ (k≈0.37W/m⋅K) ޓ܅Δڇၞ۩ኔ᧭ழױለ२ۿ
ᑷऱයٙΖ
ቹ 1 ࠢীऱᖩᆜڤ(ሽᑷጥխ֨ၗፖሽ߁᧾խ֨ၗ
ܧऴߡ)ሽ߁᧾Δףᑷᄭפᐘীሽᑷጥ(ऴஉ 4 mmΕפ 15 WΕሽᚘ 12 VACΕ९৫ 25 mmΕرയ৫
6W/cm )Ζሽ߁᧾ऱףᑷᄭױܓش൳ࠫᕴࠉᙁԵਁᄵଖፖ2
ڃᄵ৫ଖհฆΔࠌሽᑷጥሒࠩࢬࡳऱਁᄵଖ[12]Ζ ڇኔᎾਜ۩ए᛭ழ٣ຏሽᨃሽᑷጥၲࡨףᑷΔᅝሒࠩཚඨ ऱᄵ৫৵Δܛױڇਜلۯၞ۩ᄵಾΕजᑸࢨࢸ᧾ए᛭Ζ ሽ߁᧾ױڇಾࠨԵلۯऱఎಾመ࿓խΔല᧾ᕴᆝڇנؼ
(a)
(b)
ߧ 1 (a)ヅᢡ⇐⦀ߧř(b)ヅᢡ⇐૪㋤
ᓅ૿ऱಾਲ਼ፖಾݠΔ៶ڼਜղףᑷۖሒࠩᄵಾհؾऱΖሽ ߁᧾ٍױᗑലᆝڇلۯऱؼᓅՂΔ٦ਜղףᑷ܂شۖݮ ګ߁ᑸऱࢸ᧾᛭யΔຍፖؾছՕຝ։խ᠔်ࢬࠌشऱట
़ࢸ᧾ऄΔឈྥࠌشऱֱऄ૮ྥઌฆΔ܀ທګךۨွۖ
ሒࠩए᛭ऱؾऱথਢઌٵΖྥۖΔሽ߁᧾থႚࢭܓش”ᑷ”
᠔᛭ֱڤऱႚอ壄᧮Ζ 2. ᥖЗӠኔ
ءᓵ֮ऱ։࣫ྡྷរΔ༉ਢൕሽᑷጥፖᄵऱࡳය
ٙΔ൶ಘڇ᧾ᕴփऱᑷႚᎠऱൣउΔ៶אᛵᇞሽ߁᧾ऱף ᄵய࣠Ιەᐞऱᄵ৫᧢ᑇץਔሽᑷጥऱࡳᄵ৫ፖᄵऱ
᧢֏Ζ༉ᑷႚᎠᖂۖߢΔᓵ։࣫᥆࣍ڇയຨ़ၴऱ۞ྥ
ኙੌ (natural convection in enclosure) ݮኪΖ۞ྥኙੌԾጠ
۞طኙੌΔط࣍ᄵ৫ڇᚘणउՀᏺףΔআࠌ़࠹ᑷ ऱ़ၲࡨᘉΔڕڼᄎ᧢ऱለ᎘ΕለงΔڂڼᄎขس Ղ֒ွΖڇڼٵழΔᠦၲףᑷᄭለऱ़Δط࣍ᄵ ৫ለ܅യ৫ለՕΔਚയ৫़ലᄎՀ૾Δڂڼڇሽ߁᧾
փऱᄵലױ౨ᄎݮګੌ೯ऱွΔຝ։ऱᑷၦٍല
೯ՀႚᎠΖ
0 300 600 900 1200 ழၴ(ઞ)
200к 150к 100к 50к 1
0.8
0.6
0.4
0.2
0
ઌኙᄵֺଖ
0 300 600 900 1200 ழၴ(ઞ)
200к 150к 100к 50к 1.0E-02
1.0E-03
1.0E-04
ઌኙᄵ᧢֏(1/ઞ)
ڇሽ߁᧾փऱੌ೯ፖᑷႚᎠΔਢطሽᑷጥףᑷᄵ ৫Ղ֒ۖขس۞ྥኙੌயᚨΔط࣍ሽ߁᧾ᆝڇؼᓅ।૿ۖ
ݮګԫଡയຨ़ၴΔࢬא۞ྥኙੌڇሽ߁᧾փࢬ֧ದऱੌ
೯᥆࣍փੌ (internal flow) ੌ೯Ζڇയຨ़ၴփऱ۞ྥኙ
ੌΔਢፖࡌࢬڶওૻऱᕻ૿ၞ۩ᑷٌངխΔڶૻ֡՚ੌ
᧯ߓอ (finite-size fluid system) ᓤᠧऱٌյ܂شݮګऱ
࣠Ζ
ڇയຨ़ၴऱ۞ྥኙੌွΔբᆖਢᑷႚᎠઌᅝګᑵ ऱᏆΔۖءᓵ֮ژڇᣊۿऱणउΔਚױ֧ش᧭ᢞઔ ߒᑇଖૠጩऱٽࢤፖإᒔࢤΖૉආشءᓵ֮հሽ߁᧾
ၞ۩ᄵಾ߁᛭Δڂല߁ಾ֬Եؼᓅ৵Δ٦ᆝՂሽ߁᧾
ףᄵၞ۩ए᛭Ιࢨਢലሽ߁᧾ऴ൷ᆝڇلሐՂၞ۩ࢸ᧾ए
᛭Δሽᑷጥऱૠᚨᇠਢᝩ܍൷२ؼᓅΖڂڼΔݺଚല ආشᖩᆜڤऱሽᑷጥૠᇘᆜΔױאᒔࡳऱਢףᑷᄭؘႊ
ڇയຨ़ၴऱՂֱΔຍጟणउڇᑷႚᎠᖂխਢ᥆࣍ൕՂֱ
ףᑷऱയຨ़ၴ (enclosure heated from above)Ζ
ຏൄᄵ৫ሒࠩ 42 °C ᛮาઽലᄎ۞ྥऱᄰΔڼ؆ڇ Գ᧯᧯փऱઔߒֱ૿ΔԳ᧯ऱิ៣าઽڇ 58 ±C ፂ
Կ։ᤪΔܛᄎທګาઽᓂհᔆᠨᐋऱధᡏΔาઽփػ ᔆऱ᧢ࢤΔڂۖᖄીาઽᕩࡐࢤᡏڽ[12]Ζױߠ༳൳ሽ߁
᧾փᄵ৫ऱૹࢤΔڕ۶ஞࡵ٤ᖇ᠔ஃᖕఐ൛ऱᏁ ޣղאࡳΔڇءᓵ֮ലࡳၞԵؼᓅᄵ৫ᚨտ࣍ 42±C
۟ 58 ±C ऱڜ٤ᒤփΖڇኔᎾऱሽ߁᧾፹܂[13]Δႊ
ڇ᧾ᕴၲՑᒴףᇘᄵ৫ტྒྷᇘᆜΔࠀຘመਁᄵ࠹൳ߓอሒ
ࠩࢬࡳऱਁᄵଖΔലױࠌؼᓅ।૿ፂཚඨऱᄵ৫Ζ 3. ᄲϊᅞᘍ
ᑇଖ։࣫ଈऱઔߒᓰᠲΔ༉ਢ൶ಘሽᑷጥᇘᆜֱ
ڤኙ࣍ሽ߁᧾փᄵ৫༼֒णኪऱᐙΔݺଚאᖩᆜڤ (ሽ ᑷጥխ֨ၗፖሽ߁᧾խ֨ၗܧऴߡ) ։࣫ऱኔࠏΖڇ ᑇଖૠጩխΔૠጩ࣠ऱᄷᒔࢤፖױ൷࠹ࢤΔݙ٤ጤီᑇ ଖᇞ࣫խऱᑇۖࡳΖءᓵ֮ऱەၦයٙڶΚૠጩऱ ցై։໊ (meshing) ᑇፖᑉኪመ࿓խऱழၴၴ၏ (∆t)Ζ ലցై։໊ყาΔലᄎᏺףૠጩ࣠ऱᄷᒔࢤΔ܀
ࠌشመาऱցైᄎᏺף᜔ցైᑇΔڂڼᏁޓڍऱૠጩழ
ၴፖᚏژ़ၴΔ༉ᖞ᧯ய墿ࠀլਢ່ࠋ֏ऱणኪΙழၴၴ
၏ऱา։ٍ૿ᜯٵᑌऱൣउΖᆖطᑇଖྒྷᇢሒࠩሽᑷጥ 99
%ࡳᄵ৫ (To) ऱழၴֺለΔ᜔່֟ցైᑇΰ833 ଡα ፖ່ڍ᜔ցైհၴΰ9339 ଡαऱઌኙᎄႛ 0.248 %Ι۟
࣍ழၴၴ၏ঞլᐙᑇଖૠጩ࣠ΖᖕڼΔءᓵ֮ऱٺᑇ ଖૠጩࠏઃආش᜔ցైᑇ 833 ଡΔழၴၴ၏ঞ࠷ 30 ઞΖ
ɿȮᶇἄኞ
ڶᣂᑇଖ։࣫ࢬႊࡳऱᢰයٙ (ߠቹ 1)Δױല ሽ߁᧾ऱᢰයٙאႽਪஆᑑ (r,θ,z) ༴૪Ζط࣍ሽᑷ
ߧ 2 ヅᢡ⇐ҙ᱿ଃᝐಙʀ֗ᨊ๗
ߧ 3 ヅᢡ⇐ҙ᱿ଃᝐద⩐ջ᪓
ጥᑇۯᄵ৫൳ࠫΔਚᢰයٙ (r=d/2) ࡳᄵ ৫ (To)Δᇠᄵ৫ଖࡐࡳଖΙڇಾ᧾ࡌ (r=D/2֗
H
z= ) ऱᢰයٙᑷणኪΔڂڼᕻ૿உٻऱᑷႚ
ᎠؘႊሿΔრܛႚᖄᑷຏၦ qr′′=D/2=−k(∂T/∂r)r=D/2=0Ι ٵ Δ ື ૿ հ ၗ ٻ ऱ ᑷ ႚ Ꭰ ሿ Δ რ ܛ ႚ ᖄ ᑷ ຏ ၦ
(∂ /∂ ) =0
−
′′=H = z=H
z k T z
q Ζ
ኙ࣍ࠢীऱᖩᆜڤሽᑷጥᇘᆜΔቹ 2 ༴ᢄנሽ߁᧾փ
᧾Ցխ֨រऱᄵ৫Ղ֒णኪΖڇૠጩᒤࠏխΔሽᑷጥࡳ
ᄵ৫ (To) ᙇᖗ 50Ε100Ε150 ֗ 200 ±C ጟΙᄵ(T∞)
20 ±CΔૠጩ࣠ലאᄵֺଖ(Ts−T∞)/(To−T∞) ऱྤڂڻ֏ΔࠡխTs।قڇሽ߁᧾᧾ᕴՑ(ؼᓅ।૿) ऱխ֨រᄵ৫Ζຘመઌኙᄵֺଖ।قऄΔࠌٺጟࡳ
ᄵ৫ऱ࣠ٽۖԫΔٽࠓܧנԫයᄵ৫Ղ֒ڴᒵΖൕ
ࡳࢤऱڴᒵႨ堚ᄑױߠΔଶၲࡨᄵ৫Ղ֒ᄕ߰ຒΔᅝ Ղ֒ᄵ৫ሒࠩਬԫၸ৵թዬؓᒷΖݺଚױ࿇Δழၴ
Օપᖵᆖ 692 ઞΔઌኙᄵֺଖբሒࠩ 80 %Ιழၴᆖመ 949ઞΔঞઌኙᄵֺଖޓբሒ 90 %Μ
ၞԫޡᛵᇞࠀ༳༽ᄵ৫Ղ֒ݶኬऱणኪΔݺଚຘመ ઌኙᄵ᧢֏ (Ts,t+∆t−Ts,t)/∆t(To−T∞) ऱࡳᆠΔאঁ
ొऱᛀီڴᒵ᧢֏ (ڕቹ 3 ࢬق)ΔࠡխϦʳ t ז।ழၴၴ
၏ (time interval)ΔTs,tፖ Ts,t+∆t ։ܑ।قڇழၴၴ၏∆t ছ৵Δڇ᧾ᕴՑխ֨រऱᄵ৫Δڕڼࡳᆠࢬݮګऱۯ
0 50 100 150 200 To(к)
1000
100
10
t (sec)
ߧ 4 Თ⍋⠧ㄇᝐಙⳭቅቃϊ(42 ±C)トᆹ⿵
1/secΖٵᑌऱΔᄵᆖመྤڂڻ֏৵Δٺጟሽᑷጥ
ࡳᄵ৫ࢬܧऱ᧢֏ലᄎٽࠓګԫයڴᒵΔڼழ᧢֏
լ٦ፖࡳᄵ৫T ֗ᄵo T ڶᣂΙቹխऱ᜕ஆᑑএאኙ∞ ᑇֱڤܧΔ៶طתኙᑇቹ (semi-logarithmic chart) ലֺ
ለ୲࣐֘ਠנઌኙᄵࠠڶऱ᧢֏ൣݮΖൕቹ 3 ࢬᢄق ऱתኙᑇቹڴᒵणኪױ堚ᄑऱנΔڇၲࡨףᑷၸᄵ৫ Ղ֒ᄕ߰ຒΔᅝழၴᖵᆖપ 180 ઞؐ׳Δڴᒵലᄎሒࠩ
ଖ (peak value) ऱणኪΖጹ൷ထΔᄵ৫᧢֏ܧᎠ྇
ऱႨΔۖᎠ྇ऱൣउڇתኙᑇቹՂএܧᒵࢤणኪΔڼ რ࠺ᄵ৫ᏺףऱൣउၲࡨ࣍ࡳऱ྇இΖ
ቹ 4 ᜕ஆᑑאኙᑇֱڤܧऱתኙᑇቹΔشא֘ਠ
᧾ᕴխ֨រፖؼᓅ൷ᤛ૿Δᄵ৫ሒࠩཚඨଖTa (ءᓵ֮
Ta=42 ±C) ࢬᏁऱழၴΖൕᑇଖ։࣫ऱ࣠वΔሽᑷ ጥऱࡳᄵ৫ (To) ყΔঞሽ߁᧾၀ጹ࣍ؼᓅऱᄵ৫Δ Ո༉ყݶऱሒࠩཚඨᄵ৫ଖΖ٦ൕቹխऱڴᒵ᧢֏ױ
נΔࡳᄵ৫Օપሒࠩ 120 ±C אՂழΔڴᒵ༓ګᒵ ࢤᎠ྇ႨΖຍإߩא᧩قΔૉؼᓅ।૿ຘመሽ߁᧾ሒ
ࠩཚඨଖΔࡳᄵ৫ᚨᇠ࣍ 120 ±C אՂࡵΙૉאઌ ኙᄵ৫To/T ।قΔঞࡳᄵ৫ᚨᇠਢڇ∞ To/T∞>6ऱᒤ
Ζ
༉ኔᎾႚอऱխ᠔᛭ऄۖߢΔૉొਢၞ۩߁ᑸࢨ ࢸ᧾ழΔሽᑷጥᇘᆜᅝྥਢݙ٤אᑷႚᎠऱய࣠ഄԫऱ ەၦڂైΖ܀ૉၞ۩ᄵಾऄழΔؘႊ٣ല߁ಾ֬Եلۯ৵Δ ٦ലሽ߁᧾ᆝڇנؼᓅऱಾਲ਼ፖಾݠΔڼழආشലሽᑷ ጥᇘᆜڇሽ߁᧾ऱՂֱΔലᄎࠠڶለՕ୲ᆜ़ၴΔਚڜ ٤ەၦऱለࠋᙇᖗΖ
ૉאᑷႚᎠய࣠ࠐေ۷ሽᑷጥڜᇘֱڤऱߜⲀΔଈ
ऱەၦڂైᑷႚᎠயΖطᑷႚᎠऱഗءױवΔף ᑷᄭૉۯڇሽ߁᧾ऱՀֱΔڼრ࠺ሽ߁᧾փືຝᄵ৫ല՛
࣍ࢍຝᄵ৫ (∂T/∂z<0)Δڂڼڇሽ߁᧾փऱ़യ৫ڇ ૹԺֱٻ (gG zkG
−
= ) ܧᎠ྇ऱႨ (∂ρ/∂z>0)Ζط࣍ڇ
ືຝለയऱ़ૹԺՕ࣍ࢍຝለงऱ़ૹԺΔ૰ࠌືຝ ለૹऱ़Հ૾Ιࢍຝለ᎘ऱ़Ղ֒Δݮګኙੌऱฝ೯
ွΔਚڇሽ߁᧾փऱ़ലᄎܧլࡳणኪ (unstable
state)Δ່৵ດዬ࿇୶ګլࡳᛩੌ (unstable circulation)Ζ ڇڼጟሽᑷጥڜᇘֱڤխΔऱᑷႚᎠᖲዌᑷኙੌ
(thermal convection)Ζ
ࠌףᑷᄭۯڇሽ߁᧾ऱՂֱΔڼრොထሽ߁᧾փື
ຝᄵ৫ലՕ࣍ࢍຝᄵ৫ (∂T/∂z>0)Δڂڼڇሽ߁᧾փऱ
़യ৫ڇૹԺֱٻܧᎠᏺऱႨ (∂ρ/∂z<0)Ζڇڼण उՀΔط࣍ືຝለงऱ़ૹԺ՛࣍ࢍຝለയऱ़ૹ ԺΔਚሽ߁᧾փऱ़ᄎܧࡳणኪΔլᄎ٦ڶאՂࢬ
༴૪ऱ୲ᗨੌ᧯ฝ೯ (bulk fluid motion) ွΖڇڼؘႊ
ܑൎᓳΔڼጟሽᑷጥڜᇘֱڤխΔऱᑷႚᎠᖲዌ
ᑷႚᖄ (thermal conduction)Ζ
ڇءᓵ֮ࢬ൶ಘऱሽᑷጥᇘᆜֱڤխΔ᧾ᕴփऱ᜕ᖩ
ֺH/D=2.3Δሽᑷጥխ֨ၗ৫ C ፖփஉ D ֺଖঞ
9 . 1 /
C D= Δףᑷᄭڇ᧾ᕴփࣔ᧩ऱೣՂ (ߠቹ 1)Ζኙ
࣍ᐙሽ߁᧾ףᑷऱԫଡૹ᧢ᑇΔ༉ਢሽ߁᧾փऱᄵ (ࢨጠ؆ᄵ৫T )Ιط࣍؆ᄵ৫֘ਠڇ۞ྥኙੌ᧢֏∞
ွᄕඕტΔኙ࣍ᑇଖૠጩऱᐙޓਢլ୲࢙ီΖࠏڕΔ ڇᑇଖૠጩխࢬᏁऱᑷढࢤᔆΔຏൄאܛؓ݁ᄵ৫ Tm=(To+T ) ૠጩഗᄷΔ܀ڇլٵऱ؆ᄵ৫∞ T णउ∞ ՀΔࢬڶऱᑷढࢤᔆലᄎڶઌᅝՕऱฆΖ؆Δڶᣂ ᄵDT=Ts−T∞ऱࡳᆠֆڤຑٍ࠹ࠩᄕՕऱᐙΔڕ ᅗ ߺ ᑇ (Raleigh number) RaH ፖ ᆼ ᢅ ֛ ᑇ (Grashof number)Gr Բଡྤڂڻᑇ[14,15]Δܛലᄎ࠹ࠩᄕՕऱH ᐙΖطڼױߠΔ؆ᄵ৫T∞᧢֏࿑ՕΔ࣠ലᄎข سઌᅝՕऱᐙΖ
ኙ࣍ॣࡨᄵऱᐙࢤ։࣫Δݺଚലאऱࠢী
ଢەၦΔא່ഗءऱ༓ጟᄵ৫ (։ܑ 15Ε20Ε25 ֗ 30 ±C ଡᄵ৫ଖ) ᧢ᑇΔءᓵ֮ऱᑇଖ։࣫ࠏ
Ζቹ 5 ሽᑷጥࡳᄵ৫ (To =100±C) ৵Δڇሽ߁᧾
փॣࡨᄵT∞࠷ 15Ε20Ε25 ֗ 30 ±C ጟᑇଖ։࣫
ࠏΖ᧾ᕴՑխ֨រᄵ৫ऱૠጩ࣠Δຘመྤڂڻ֏ऱઌ ኙᄵֺଖ(Ts−T∞)/(To−T∞)ղאࡳᆠΔࠌٺጟᄵૠ ጩऱ࣠Δٽࠓګԫයᄵ৫Ղ֒ڴᒵΖൕڴᒵऱႨױ वΔଶၲࡨᄵ৫Ղ֒ᄕ߰ຒΔᅝՂ֒ᄵ৫ሒࠩਬԫၸ
৵թዬؓᒷΖݺଚױ࿇ΔழၴՕપᖵᆖ 693 ઞΔઌኙ ᄵֺଖբሒࠩ 80 %Ιழၴᆖመ 951 ઞΔঞઌኙᄵֺଖ ޓբሒ 90 %Μ
൷ထΔݺଚല൶ಘڇࡐࡳऱࡳᄵ৫ (To=100±C)ൣ
उՀΔլٵᄵ (15Ε20Ε25 ֗ 30 ̓C) ኙ࣍ሽ߁᧾փף ᑷய࣠ऱᐙΖڇءૠጩᒤࠏխΔݺଚܓشઌኙᄵ᧢֏
༴૪լٵᄵࢬທګऱ࣠Δຘመઌኙᄵ᧢֏
) ( / )
(Ts,t+∆t−Ts,t ∆tTo−T∞ ऱࡳᆠᛀီڴᒵ᧢֏ (ڕቹ 6ࢬق)ΔࠡխTs t, ΕTs,t+∆t։ܑ᧾ᕴՑխ֨រڇழၴtΕ
t
t+∆ ழऱᄵ৫ଖΖطቹݮࢬܧऱ࣠᧩قΔᄵᆖመ
ྤڂڻ֏৵Δٺጟᄵࢬܧऱ᧢֏ലᄎٽࠓګԫ යڴᒵΔڼழ᧢֏ፖࡳᄵ৫To֗ᄵT∞ྤᣂΖቹխ ऱ᜕ஆᑑএאኙᑇֱڤܧΔܓشתኙᑇቹലৰ୲࣐ऱ֘
ਠઌኙᄵ᧢֏ऱൣݮΖൕቹ 6 ױ堚ᄑऱנΔڇၲࡨ
0 300 600 900 1200 ழၴ(ઞ)
30к 25к 20к 15к 1
0.8
0.6
0.4
0.2
0
ઌኙᄵֺଖ
0 300 600 900 1200 ழၴ(ઞ)
30к 25к 20к 15к 1.0E-02
1.0E-03
1.0E-04
ઌኙᄵ᧢֏(1/ઞ)
0.1 0.2 0.3 0.4
/ o T∞ T
1000
100
10
t (sec)
ߧ 5 ヅᢡ⇐ҙ᱿ଃᝐಙʀ֗ᨊ๗
ߧ 6 ヅᢡ⇐ҙ᱿ଃᝐద⩐ջ᪓
ףᑷၸᄵ৫Ղ֒ᄕ߰ຒΔᅝழၴᖵᆖપ 180 ઞΔڴᒵ ലᄎሒࠩଖΙጹ൷ထΔᄵ᧢֏ܧᒵࢤᎠ྇ऱႨΔ ຍՈإრ࠺ထףᑷய࣠إࡳऱᒷխΖ
ᅝݺଚڇ։࣫ቹ 6 ऱ࣠ழΔࢨբࣹრࠩڼቹۿམ ઌᢝΖૉڃᙰ٦ᛀီቹ 3 ױ࿇Δࠟଡቹݮऱஆᑑၗࠥ৫ ፖۯݙ٤ԫીΔઌኙᄵ᧢֏ऱڴᒵ։ؒ༓ݙ٤ܭ ٽΖઌٵऱൣउٍٵழ࿇سڇቹ 2 ፖቹ 5Δطڼױߠࠌش ᄵֺଖ (Ts−T∞)/(To−T∞) ऱྤڂڻ֏ΔױലԲଡ ᄵ৫᧢ᑇ(ሽᑷጥࡳᄵ৫ToፖᄵT∞)ٽࠓګԫଡྤڂ ڻᑇΔڕڼױࠌംᠲՕ១֏Ζ
ጹ൷ထΔݺଚܓشቹݮܧᄵT∞ᐙףᑷழၴऱૹ
ࢤ (ቹ 7)Δࠡխ᜕ஆᑑএאኙᑇֱڤܧΔ៶א֘ਠழ
ၴࠠڶለՕऱ᧢೯ൣݮΙᖩஆᑑආشઌኙᄵT /∞ ToΔش א।ሒԲृհၴऱઌኙֺଖΖطቹق࣠᧩قΔڇתኙᑇ ቹՂऱ᧢֏༓२࣍ᒵࢤᎠ྇ऱႨΔط᜕࣍ஆᑑፖᖩஆᑑ ऱၦ֏ଖࠠڶԿၸ (1000 ) ऱฆΔطڼ᧩ߠᄵኙ࣍
ሽ߁᧾փףᑷᐙᄕሰΖԱឩՕᛀီᄵऱᐙࢤΔݺ ଚႉထ٣ૠጩ࣠ࢬܧऱऴᒵٻ؆ۼΔ៶אං۷ ڇޓՕऱઌኙᄵᒤΔؼᓅ।૿ᄵ৫ሒཚඨଖ (Ta =42
̓C) ࢬᏁऱழၴΖ៶طቹխऱං۷ऴᒵΔ৬ᤜױආشႚอ
壄ᗉቃᑷሽ߁᧾փऱ़Δ٦ඔ೯ሽᑷጥሽᄭ߰ຒ
ߧ 7 Თ⍋⠧ㄇᝐಙⳭቅቃϊ (42±C) ト᱿ᆹ⿵
!
!
(a) t =30ấ
!
৵ᥛᑷᄭΔڕڼലױ࿇ཀمܛᥛऱᄵᑷய࣠Ζ ءᓵ֮ऴ൷ආش ANSYS ᇘຌ᧯৬مᑇᖂᑓীΔ່
৵ٍא contour ऱၸჁֱڤΔܧڇሽ߁᧾խऱᄵ৫
᧢ ޓ ण ኪ Ζ ሽ ߁ ᧾ փ ऱ Ⴡ ֱ ڤ ኙ ࣍ ം ᠲ ऱ ױ ီ ֏ (visulization) ઌᅝڶᚥܗΔءᓵ֮ലຘመ ANSYS ࿓ڤ༼
ࠎऱຌ᧯Δףൎױီ֏࣠ऱܧΔࠌٺழၴၴ၏ऱᄵ৫
᧢֏णउ堚ᄑܧנࠐΔჁຝ։ࡳ݁ൕ 15 ̓C ۟ 100
̓CΔط࣍ݺଚࢬᣂ֨ऱᄵ৫ਢڇ 42 ±C ࠩ 58 ̓C հၴΔڂ ڼჁൕ 15 ̓C ၲࡨޢ 5 ̓C ᧢ངԫጟᠱۥΔ50 ̓C אՂঞ ݙ٤ࠌشદۥΔᄵ৫։ؒჁڇሽ߁᧾ՀֱܛױܒܑΔط ڼױ堚ᄑᨠኘࠩ᧾ᕴփऱᑉኪᄵ৫᧢֏ൣݮΖ
ቹ 8 ሽ߁᧾փሽᑷጥऱףᑷൣउΔሽᑷጥऱࡳᄵ ৫To=100̓CΕᄵT∞=20̓CΕழၴၴ၏∆t=30ઞΔ ޢԫଡቹ।قڇሽ߁᧾փᑉኪऱᄵ৫᧢֏णउΖڇሽᑷጥ ଶၲࡨףᑷ৵Δط࣍ᑷੌऱയ৫܅Δਚᄎᖄીᔣ२ሽᑷ ጥऱᑷ़Ղ֒Ζط࣍ڇሽ߁᧾փऱሽᑷጥءਝૠ
ೣՂ (ߠቹ 1ΙC/D=1.9)Δᅝሽᑷጥၲࡨ܂ش৵ऱ 30 ઞփΔሽ߁᧾փຝՂֱऱ़ਝբ߰ຒऱ֒ᄵ۟ 50 ̓C א Ղ (દۥ)Δൕቹ 8 (a) ױ堚ᄑऱנڇሽ߁᧾փऱᄵ ৫᧢֏Ζط࣍ᑷ़ሒࠩሽ߁᧾ືຝ৵Δലᄎ᠏طᕻ૿٦ ៥ᆖሽᑷጥՀੌ೯Δط࣍ੌএאሽ߁᧾խ֨ၗܧؐ׳
ኙጠऱွΔڂڼڇቹ 8 (a) խऱદۥᄵܧןٻՀ (concave down) ऱൣݮΖ
(b) t =60ấ
(c) t =120ấ
(d) t =180ấ
(e) t =240ấ
(f) t =270ấ ߧ 8 ヅᢡ⇐ҙ᱿ᝐಙ⩐ջ ņ⥑હᝐಙ = 100 ±Dřાᝐ = 20 ±DŇ
ط࣍ᑷ़ലᄎ֧ી௬ԺயᚨΔᖄીᄵ़ٻՂੌ
೯Δڂڼሽ߁᧾ືດዬีᗨᑷ़Δط࣍ᑷၦৰݶऱႚᙁ
ࠩᔣ२։ΔڂڼןٻՀऱွ߰ຒऱ؈Δൕቹ 8(b) բ
᧩قנદۥᄵբܧؓᒷٻՀឩ്Δႛڶڇሽ߁᧾ᕻ૿
ࠄ၌ছٻՀΖڇڼཚၴΔሽ߁᧾㡕ຝᄵ৫ऱ᧢֏Δএ៶ طٺጟᑷႚᎠᖲዌ܂شࢬݮګऱ࣠Δ۟࣍۶ጟᑷႚᎠᖲ ዌऱயᚨለࣔ᧩Δݺଚലຘመࡳၦ։࣫ղא൶ಘΖ
ڇഗءऱᑷႚᎠᖂՕຟڶࡳᆠྤڂڻֺଖЁᅗߺᑇ (Raleigh number)RaHΔشאܒܑ۞ྥኙੌհᢰ
ᐋੌ೯ݮኪऱࠉᖕΔڕڤ(1)ࢬ٨
( )
m m
s T H
T T g TH Ra g
ν α αν
β 3 3
H
) / 1
( ∞ − ∞
∆ =
=
(1)
ૉ֧شءૠጩࠏऱࢬڶઌᣂᑇᖕΔࠡխ β ࡳᚘण उՀऱ᧯ᗨᑷᘉএᑇΔኙ࣍უ᧯Δβ = T1/ ∞Ιૠጩ ࢬᏁऱᑷढࢤᔆ (ᑷឩཋএᑇ αΕሎ೯យ৫ ν) এאؓ݁
ᄵ৫Tmഗᄷ(ڇءૠጩࠏTm=60̓C =333K)ΔਚՀᑑ
݁ףု ”m”ΖലࢬڶբवᑇᖕזԵՂڤΔױ
( ) ( )
×
⋅
×
×
⋅
−
⋅
⋅
=
−
−
−
s m s
m
m K K
s m
Ra 2
6 2
6
3 3 2
H
10 8 . 18 10
8 . 26
10 46 293 1 373
293 81 1
. 9
105
175 .
5 ×
= RaH
طૠጩᑇᖕױ堚ᄑऱנΔءૠጩࠏऱᅗߺᑇRaH
ሒ5.175×105Δڼᑇଖ᥆࣍ᅗߺᑇऱᢰᐋੌ೯ݮኪ (RaH <109)ΖഗءՂΔڼၸڇሽ߁᧾փऱᑷႚᎠᖲዌΔ
ਢᑷኙੌ୬ऱݮڤΖ
൷ထΔݺଚ٦ൕᆼᢅ֛ᑇ (Grashof number)GrH൶ ಘሽ߁᧾փऱᑷႚᎠᑓڤΖࠡխΔᅗߺᑇፖᆼᢅ֛ᑇژ ڇऱᣂএRaH =GrH⋅PrΔਝྥᅗߺᑇբૠጩנΔۖኙ ᚨ࣍ؓ݁ᄵ৫Tmऱཏிᑇ (Prandtl number) Pr ط।
ױ(Pr≈0.702)Δڂڼ
H
RaH
Gr = Pr (2)
5 5
H 7.372 10
702 . 0
10 175 .
5 × = ×
= Gr
ᆖૠጩऱ࣠वΔءૠጩࠏऱᆼᢅ֛ᑇGrHս
ྥઌᅝՕΖطڼߩߠΔڼၸڇሽ߁᧾փऱᑷႚᎠᑓڤΔ
ਢ௬ԺՕ࣍យࢤԺऱݮኪΔრܛ۞ྥኙੌயᚨࠉྥ
ઌᅝ᧩ထΖ
٦ᤉᥛൕቹ 8(c) ۟ቹ 8(f) ױנΔᄵᒷኬऱ
൷२ሽ߁᧾ࢍຝΔᄵՕીܧऴᒵणٻՀฝ೯Ζᅝף ᑷழၴᥛࠩ t = 270 ઞַΔᖞଡሽ߁᧾փऱᄵ৫݁ሒࠩ
NODAL SOLUTION STEP=1 SUB =2 TIME=60 TEMP (AVG) RSYS=0 SMX =100
APR 30 2000 15:59:17
0 25 35 45 100 20 30 40 50
NODAL SOLUTION STEP=1 SUB =4 TIME=120 TEMP (AVG) RSYS=0 SMX =100
APR 30 2008 15:59:55
0 25 35 45 100 20 30 40 50
NODAL SOLUTION STEP=1 SUB =6 TIME=180 TEMP (AVG) RSYS=0 SMX =100
APR 30 2008 16:00:33
0 25 35 45 100 20 30 40 50
NODAL SOLUTION STEP=1 SUB =8 TIME=240 TEMP (AVG) RSYS=0 SMX =100
APR 30 2008 16:01:11
0 25 35 45 100 20 30 40 50
50 ̓C אՂΔڕቹ 8(f) ࢬقΖ٣ছݺଚᆖط։࣫ (ߠቹ 3) բवΔሽᑷጥڇၲࡨףᑷၸऱᄵ৫Ղ֒ᄕ߰ຒΔ ᅝழၴᖵᆖપ 180 ઞؐ׳Δڇڴᒵሒࠩଖ৵Δᄵ৫᧢֏
༉ᄎܧᒵࢤᎠ྇ऱႨΙൕቹ 8(d) ױנڇףᑷ 180 ઞ৵Δؼᓅ।૿ऱ़ᄵ৫բ൷२᧯ᄵΔઌኙᄵ৫հᄵ (T Ts/ ∞=2.5)ছᒴ (৫ z) ٍբሒ၏ᠦؼᓅપz D/ =0.84 ऱ৫Ζ
طאՂංᓵױवΔڇᖩᆜڤሽᑷጥᇘᆜऱሽ߁᧾փΔ ط࣍᧾ᕴփऱॣࡨ़ᙩַणኪΔۖሽ߁᧾ऱޗᔆᚘ
܌ԺΔਚᕻ૿ऱᢰයٙࡳᑷणउ (∂T/∂rr=D/2=0
∂T/∂zz=H =0)Ζط࣍ሽᑷጥऱᇘᆜڇ᧾ᕴೣՂऱۯᆜΔ ڂڼሽᑷጥၲࡨຏሽףᑷ৵Δڇሽ߁᧾փऱᑷႚᎠᖲ ዌࡨึᑷኙੌݮڤΖᅝழၴሒࠩ 240 ઞհ৵Δቹ 8(e)Δ ط࣍ڇሽ߁᧾փऱᄵ৫Օ༏ऱᏺף (T∞ᏺף)Δਚ᧯ᗨᑷᘉ
এᑇӪലᄎᙟհ྇՛Δᄵٍല྇՛ (ϦT<5̓C)Ιᑷ ढࢤᔆ (αΕν) ᙟထؓ݁ᄵ৫ᏺףۖຟᄎᏺףΔڂڼᅗ ߺᑇRaH ലᄎՕ༏྇՛ΔຍՈრ࠺ᑷႚᎠᖲዌലڇດዬ
ၞ۩ᔆ᧢Δൕᑷኙੌ (thermal convection) ᖄऱݮڤ᠏᧢
ګᑷႚᖄ (thermal conduction) ୬ऱݮڤΔਚᑷၦऴ൷ऎ ሽ߁᧾ၗٻ (axial direction) ٻՀႚᎠ۟ؼᓅ।૿Ζ
ၞԫޡ൶ಘ᧾ᕴփऱᑷႚᎠᖲዌΔءᓵ֮ലᑇଖૠ ጩ࣠א contour ऱۊၸֱڤܧΔڕڼലױ堚ᄑ
נ᧾ᕴփऱᄵᒵ (ڕቹ 9 ࢬق)Ζቹ 9 ऱሽᑷጥࡳᄵ৫
To=100̓CΕᄵT∞=20̓CΔޢԫଡቹ।قڇሽ߁᧾
փᑉኪऱᄵ৫᧢֏णउΙൕ 20~50 ±C հၴΔޢሶ 5±C ࠠ ڶԫଡۊၸ᧢֏ (ޢሶ 5±C ԫයᄵᒵ)Ζൕቹ 9(a) ᧩ق ڇၲࡨףᑷ৵ழၴ t = 60 ઞழΔᄵᒵ༓բܧֽؓ
णΔհ৵ޢሶ 60 ઞऱᄵᒵ᧢֏Δ։ܑڕቹ 9(b) ~ (d) ࢬ قΔ᧩ྥڇሽ߁᧾փऱᄵ৫ऎထၗٻ (᧾ᕴխ֨ၗֱٻ)
༓ܧᒵࢤ᧢֏Ζ
່৵Δݺଚױܓشቹ 9 ۷ጩᑷႚᖄଖڕ৵
⋅
∆
− ∆
=
=
4 4
2 2
" D
z k T q D
Qcond cond π π
(3)
ࠡխሽ߁᧾ऱփஉ D = 20 mm = 0.02 mΔኙᚨ࣍ؓ݁ᄵ ৫ऱᑷႚᖄএᑇױطە֮[14]।ۖΙࠡהᑇᖕڕ ᄵϦT ፖၗٻ৫ϦzΔױطૠጩऱ࣠࠷Ζ
ലאՂᑇᖕזڃױሽ߁᧾փऱᑷႚᖄଖڕቹ 10 ࢬ قΖൕᑷႚᖄଖઌኙ࣍ழၴ᧢֏ऱڴᒵ։ؒ᧩قΔᑷႚᖄ ଖऱ᧢֏ઌᅝპ՛Δڇױૠጩᒤփऱᑇଖપႛտ࣍ 0.006
~ 0.009 WհၴΖᑇଖ࣠᧩قΔᑷႚᖄଖڇ t = 90 ઞழല ᄎሒ່ࠩՕଖ (Qcond,max=8.933×10−3W)Δڇ t = 120 ઞհ
৵ ܧ ᒵ ࢤ Ꭰ ྇ Ζ ױ ߠ ڇ ء ૠ ጩ ᒤ ࠏ խ Δ ᥆ ࣍ า ९ ী (H/D=2.3) ऱሽ߁᧾୲ᕴΔᑷኙੌऱயᚨթਢటإ୬ ᑷႚᎠऱᖲዌΖ
(a) t = 60ấ
(b) t = 120ấ
(c) t = 180ấ
(d) t = 240ấ ߧ 9 ヅᢡ⇐ҙ᱿ᾀᝐℬߧ ņ⥑હᝐಙ = 100 ±Dřાᝐ = 20±DŇ
0 60 120 180 200 t (sec)
20
15
10
5
0
ߧ 10 ヅᢡ⇐ҙ᱿ᥖЗϊ ߈Ȯ ⧄
Գᣊৰڰאছ༉ᎁᢝࠩ”ᑷ”ኙఏఐऱए᛭܂شΔ९Ն אࠐΔല”ᑷ”ሎشࠩ᠔ऱ֫ऄՈઌᅝऱ壄ྈΖڕվΔਈ
זઝݾၞޡࢬᔅΔԳଚኙ࣍”ᑷ”ऱ༳༽ፖሎشΔڇݾ
ՂբઌᅝऱګᑵΔ܀ሎشࠩႚอ᠔থਢࡹਐױᑇΖڇႚ
อऱ߁᛭խΔլጥࠌشऴ൷߁ࢨၴ൷߁Ιྤᓵආش۶ጟᢐ
౻ਜ߁ޗறΔਢຘመᑷႚᎠऱ܂شΔലᗏᗈᢐ౻ ࢬขسऱᑷၦΔᆖط߁ಾᖄԵلۯΔ៶طᑷࠨᖿ܂شۖ྇
᎘ఐ࿀ࠀᖿ࿇ݼఐ౨ԺΖڇࠌشᗏᗈᢐ౻ऱ߁᛭ֱڤΔڂ
ژڇڍլঁፖ؈Ζڇႚอऱࢸ᧾᛭ऄխΔए᛭ֱڤ ऱጟᣊڍΔࠌش᧾ᕴऱጟᣊՈৰڍΔ܀ਢ៶ط ᑷၦࠌ᧾ᕴขسᚘΔ٦ࠌ᧾ᕴܮॵڇؼᓅࢨلۯՂΔທ ګᄵᑷࠨᖿۖขسᣊۿᑷᑆऱய࣠Ζႚอऱࢸ᧾ਢല᧾ᕴ փຝऀՂ壄រᗏΔ߰ຒऱ።Ղ൛ຝΔ־ྣڇ᧾ᕴ።Ղ൛ ຝ৵ᄎ್ՂዽᄰΔࢬאᄵ৫᧢֏լ࣐༳൳Ζ
ءᓵ֮ਢܓش ANSYS ຌ᧯ၞ۩ᑇଖᇞ࣫Δൕ᧾ᕴऱ ᄵ৫ࡳයٙ൶ಘᑷႚᎠऱൣउΔ៶אᛵᇞሽ߁᧾ऱףᄵ ய࣠Ζڇᓵ֮խආش᜕ᖩֺH/D=2.3Δሽᑷጥխ֨ၗ
৫ C ፖփஉ D հֺଖC/D=1.9Ζઔߒऱૹរፋྡྷڇ ሽᑷጥࡳᄵ৫(T )ፖᄵ( To ∞)Բଡ᧢ᑇኙ࣍ሽ߁᧾ᑷ᛭
ய࣠ऱᐙΔֱऄऱઔߒֱऄΔ༉ਢຘመ᧾ᕴփऱᄵ ৫։܉ၞ۩ᑷႚᎠऱ։࣫Ζᆖطᑇଖ࣠वΔڇၲࡨף ᑷၸᄵ৫Ղ֒ᄕ߰ຒΔᅝழၴᖵᆖપ 180 ઞؐ׳Δڴ ᒵലᄎሒࠩଖऱणኪΔ൷ထᄵ৫᧢֏༉ᄎܧᒵࢤᎠ
྇ऱႨΖڇࡳᄵ৫ፖᄵԲ᧢ᑇऱઌኙֺଖ։࣫
वΔઌኙᄵ৫(T To/ ∞)ڇTo/T∞>6ऱൣउՀΔሽ߁᧾ലᄎ
ࠠڶለࠋऱףᑷய࣠Ζط࣍ሽ߁᧾᥆࣍า९ীऱૠΔᆖ طᑇଖ։࣫ࢬᛧીऱᓵױូנΔڇࡳᄵ৫տ࣍
50~200 ̓C ऱᒤΔᄵڇ 15~30 ̓C ऱၴΔ۞ྥኙੌ
ऱᑷႚᎠᖲዌΖ
ڇխഏऱႚอ᛭ऄխΔ߁᛭ፖࢸ᧾ຟਢຘመ”ᑷ”ऱ܂
شΔ៶طᑷࠨᖿۖ࿇ཀए᛭ऱפயΙሽ߁᧾ೈᖑڶਁᄵፖ
ࡳழऱףᑷפயΔٵழࠠໂڜ٤ፖڶயऱףᄵයٙΔਢଖ
ሎشڇႚอऱխ᠔᛭ऄΖઌॾءᓵ֮ऱઔߒګ࣠Δױ
ᘜٽזઝݾፖႚอ᠔ऱᇢ८فΔشאޏႚอ߁᛭
ፖࢸ᧾ڇਜխऱጟጟᅀፖٲᙠΔࠀױ༼ࠎڇሎشՂऱ
ঁ൸ࢤፖڜ٤ࢤΖ
א≙ᄽ᪇
1. ᅡ⩀Ȯؖʑ⎟Ŋȵ⸒ᢡ⎈ಉ᱗ᄓ⤽ȶŊᯍ˩ⷪણŊ Ὦ 34 ֱŊὮ 4 ቅŊὮ 313-317 ㅪ (2007)ȯ
2. ϼഗ⪽ȮኚᆭŊȵ͐ᮢ⸒ӿᗶ᱗⎞ᠰᄓᲩ〦ʠ૪
⨢ⷪણᄽ᪇⥫⩊ȶŊʑⓧ⸒ᢡⷪણሳグ⦒Ŋ95 ౺ಙŊ Ὦ 1-11 ㅪ (2006)ȯ
3. ㋧શጅȮ⢄ᇓᆨŊȵʑߡמ˩⸒ᢡ⚠ᅞ᧚⏨⎞ʑⓧᄽջ
ଃⴆἂʠഛㅨȶŊʑⓧ⸒ᢡⷪણሳグ⦒Ŋ95 ౺ಙŊὮ 23-31ㅪ (2006)ȯ
4. ̑୪Ŋȵቦᆹ᫂⎞ȳ⑽ℏᲿȴȶŊռᄽ᪇ŊὮ 165
ֱŊὮ 29-36 ㅪ (2007)ȯ
5. ሯ;ᆙȮኚ⻯␥Ŋȵ␖㈭᱗ᘍȮᖛ᱗⎞וૼ᱗ᘍଃ
ː㋤ΎϨר⠗ඖʠᶇἄȶŊ⇾ૌẤ༬ણӤŊὮ 5 ֱ 1Ŋ Ὦ 1 ቅŊὮ 25-50 ㅪ (2008)ȯ
6. 㓳ȮᘘҊȮⶎⴹᾍȮ᪗ズ⪬ȮؖȮ৵ُ
づඑᪿŊȵ␖㈭᱗ᘍ⎈ಉ⳥ᮢᄽ᪇ߊㆰ (1997-2005)ȶŊ ೩҆ણࢊŊὮ 50 ቅŊὮ 81-92 ㅪ (2007)ȯ
7. ⋟⬢∌Ȯ㓳ኼ⺐Ŋȵנㆩⷪણ߱⎊ᤋ᱗ᘍʠۓⲥ—ʑⷪ
Ҥ‣ଃ␖㈭᱗ᘍʠ⤐൳⎞ۓᱹȶŊʑⓧཱྀ⎞˩ನ
ുẤણグ⦒ŊὮ 3 ֱŊὮ 1 ቅŊὮ 1-16 ㅪ (2006)ȯ 8. Cui, J. and Zhang., G., “A Survey of Thirty Years’ Clinical
Application of Cupping,” Journal of Traditional Chinese Medicine, Vol. 9, No. 3, pp.151-154 (1989)ȯ
9. Subhuti D.,”Cupping,” Institute for Traditional Medicine, Portland, OR USA (1999).
10. ♫ᄎᎱȮቦબસȮづ५ᬎȮಽቄ⪮ُ⬰⎐Ŋȵͯ
Ҙೣ⠧ㄇヅ⸒ᢡᘍřṘřञなřҙ〦řᛖಙᴍ᳡ȶŊ ʑⓧᖁߡⷪᒑሳࢊŊὮ 19 ֱŊὮ 3 ቅŊὮ 28-30 ㅪ (2004)ȯ
11. Saeed, M., The Finite Element Analysis-Theory and Application with ANSYS, Prentice Hall, NJ, USA(1999).
12. 㓳ڏդŊȵᛞ⦹㋧ⳕᘘヅᥖᢣ⠛ (Radiofrequency Thermal Ablation, RTA) ߱⌭᱅ᗶ᱗ʀ᱿ະᮢȶŊ㋧゛
ⷪోሳ⦒ŊὮ 35 ቅŊὮ 27-28 ㅪ (2002)ȯ
13. ተ㏥ፖȮづኇબȮ⨀ᡝヌȮᎫᆙ≉Ȯづר⸿ُ⎟Ŋ ȵ⩕⸒ᢡⷪ᱗ㆺⓧҪ᱿⏦ᅞŋヅᥖᝐᢡяȶŊ2007
౺Қߡ༬૾ዮずણᮝ૪Ֆ૾㆛⢌̳Ὂ⫶ᇷໞኞଭ̳ٴ ゝŊ㋧゛ŊὮ 744-749 ㅪ (2007)ȯ
14. Incropera, F. P., DeWitt, D. P., Fundamentals of Heat Transfer, John Wiley and Sons, pp.1-504 NY. USA (1996).
15. Bejan,A., Convection Heat Transfer, John Wiley and Sons, NY. USA, pp.159-168 (1984).
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