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{"sheet":"説明","index":0,"n_rows":131,"n_cols":11,"rows_kept":131,"cut":false,"hidden":false,"merged":[]}
["「熱電対による表面温度測定の誤差解析」　熱抵抗網解析シートの説明"]
[]
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["１．概要"]
["・","図１のように，熱電対の測温接点を測定面に接着し，リード線の一部を等温面に這わせた場合の誤差解析を行います．"]
[null,"（解析方法の詳細は，日本機械学会論文集, Vol.84, No.867, DOI: 10.1299/transjsme.18-00216 をご参照ください）"]
["・","簡単のため，測定面は等温（温度 Tw）であり，熱電対の接触により温度が変化しないと仮定しています．"]
[null,"（一般に，測定面の熱容量が大きく熱伝導率が高い場合にはこの近似が成り立ちます）"]
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[null,null,null,null,null,"図１　熱電対による表面温度測定"]
[]
["・","測温接点（junctiuon, 直径 dj）と測定面（measuring surface, 温度 Tw）は，接着剤（adhesive, 熱伝導率 ka）で"]
[null,"接着されています．"]
["・","一対の金属素線（metal wires，直径 dm）が被覆から露出している領域を“素線露出部(exposed region，長さ lm)”，"]
[null,"一対の被覆線（insulated wires，直径 di）がシースから露出している領域を“内側被覆部(inner insulated region, 長さ li)”"]
[null,"と表記しています．また，それ以降のリード線は，2本の被覆線が1本のシース（等価直径 ds）に覆われており，"]
[null,"そのうち加熱面に這わせている領域を“シース加熱部(heated sheathed region, 長さ ls)”，全周が空気流にさらされている"]
[null,"領域を“フィン部(fin region, 長さ ls')”と表記しています．"]
[]
[]
["２．熱抵抗網モデル"]
["・","図１の伝熱経路を，図２のように熱抵抗網でモデル化しています．"]
["・","熱抵抗網は，27個の熱抵抗および19個の節点（熱抵抗の結合点）から構成されています．"]
[null,"図2の赤色の数値は節点番号をして示しています．"]
["・","節点番号1が測定面（温度 Tw），節点番号2が測温接点（温度 Tj），節点番号19が周囲空気（温度 Tf）を表しています．"]
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[]
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[null,null,null,null,null,"図２　図１の伝熱経路の熱抵抗網"]
[]
["・","各熱抵抗の記号，意味，および論文中の式番号は以下の通りです．"]
[null,"Rj","測温接点と測定面間の熱抵抗",null,null,null,null,null,null,null,"式(10)"]
[null,"Rm","金属素線（素線露出部）の熱抵抗，長さ lm/2 の熱抵抗 Rm/2 が2つ直列に接続",null,null,null,null,null,null,null,"式(1)"]
[null,"Rmi","金属素線（内側被覆部）の熱抵抗，長さ li/2 の熱抵抗 Rmi/2 が2つ直列に接続",null,null,null,null,null,null,null,"式(2)"]
[null,"Rms","金属素線（シース加熱部）の熱抵抗，長さ ls/2 の熱抵抗 Rms/2 が2つ直列に接続",null,null,null,null,null,null,null,"式(3)"]
[null,"Rms'","金属素線（フィン部）の熱抵抗，長さ lc の熱抵抗 Rms' が4つ直列に接続",null,null,null,null,null,null,null,"式(16)"]
[null,null,"lc は，フィン部の代表長さ",null,null,null,null,null,null,null,"式(15)"]
[null,"Ri","被覆（内側被覆部）の厚さ方向の熱抵抗",null,null,null,null,null,null,null,"式(4)"]
[null,"Rs","被覆+シース（シース加熱部）の厚さ方向の熱抵抗",null,null,null,null,null,null,null,"式(5)"]
[null,"Rs'","被覆+シース（フィン部）の厚さ方向の熱抵抗",null,null,null,null,null,null,null,"式(17)"]
[null,"Rit","絶縁テープの熱抵抗",null,null,null,null,null,null,null,"式(14)"]
[null,"Rgm","素線露出部と絶縁テープ間の熱抵抗",null,null,null,null,null,null,null,"式(11)"]
[null,"Rgi","内側被覆部と測定面間の熱抵抗",null,null,null,null,null,null,null,"式(12)"]
[null,"Rgs","シース加熱部と測定面間の熱抵抗",null,null,null,null,null,null,null,"式(13)"]
[null,"Rhj","測温接点からの熱伝達による熱抵抗（対流+放射）",null,null,null,null,null,null,null,"式(6)"]
[null,"Rhm","素線露出部からの熱伝達による熱抵抗（対流+放射）",null,null,null,null,null,null,null,"式(7)"]
[null,"Rhi","内側被覆部からの熱伝達による熱抵抗（対流+放射）",null,null,null,null,null,null,null,"式(8)"]
[null,"Rhs","シース加熱部からの熱伝達による熱抵抗（対流+放射）",null,null,null,null,null,null,null,"式(9)"]
[null,"Rhs'","フィン部からの熱伝達による熱抵抗（対流+放射）",null,null,null,null,null,null,null,"式(18)"]
[]
[null,"注意：素線露出部（長さlm），内側被覆部（長さli），シース加熱部（長さls）をそれぞれ2つの熱抵抗で表しているため，"]
[null,"　　　lm，li，ls が長くなると素線の温度分布を正しく評価できなくなり，誤差率の予測精度が下がります．"]
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["３．熱抵抗網解析シートの使い方"]
["(1)","「熱抵抗網解析」シートの水色のセルに条件を入力ます．"]
[null,"熱電対の種類",null,"T or K",null,"T熱電対の場合は\"T\"を，K熱電対の場合は\"K\"を入力"]
[null,null,null,"素線径 dm",null,"金属素線の直径を入力"]
[null,"測温接点",null,"隙間の熱伝導率 ka",null,"測温接点と測定面間の接着剤の熱伝導率を入力"]
[null,null,null,null,null,"瞬間接着剤は0.1W/(m・K)程度，導電性接着剤は1~4W/(m・K)程度，はんだは50W/(m・K)程度"]
[null,"素線露出部",null,"長さ lm",null,"素線露出部の長さを入力"]
[null,"内側被覆部",null,"長さ li",null,"内側被覆部の長さを入力．内側被覆部がない場合は0に近い値（例えば 1e-6）を入力"]
[null,"シース加熱部",null,"長さ ls",null,"シース加熱部の長さを入力．シース加熱部がない場合は0に近い値（例えば 1e-6）を入力"]
[null,"熱伝達率",null,"周囲風速 u",null,"測定面の周囲風速（時間平均風速）を入力"]
[null,null,null,"測定面辺長 L",null,"測定面の流れ方向辺長（論文の式(32)の Lの値）を入力"]
[null,null,null,"※ 測定面の対流熱伝達率が推定できる場合は，hcv (I36)の値を直接入力（この場合，測定面辺長は入力不要）"]
[null,null,null,"※ フィン表面の対流熱伝達率が推定できる場合は，hcv' (I39)の値を直接入力"]
[null,"測定面温度",null,null,null,"測定面温度 Tw を入力"]
[null,"周囲空気温度",null,null,null,"周囲空気温度 Tf を入力"]
[]
["(1)'","必要に応じて，以下の値を入力します"]
[null,"測温接点",null,"直径 dj",null,"測温接点の直径を入力．デフォルト値として，素線径 dmの2倍の値が入力されています"]
[null,null,null,"測定面との隙間 gi",null,"最小隙間（実効値）を入力"]
[null,null,null,null,null,"デフォルト値として，論文で評価された値(0.01mm)が入力されています"]
[null,"素線露出部",null,"絶縁テープ厚さ δit",null,"絶縁テープの厚さを入力．絶縁テープがない場合は0に近い値（例えば 1e-10）を入力"]
[null,null,null,"絶縁テープ熱伝導率 kit",null,"絶縁テープの熱伝導率を入力．デフォルト値として，0.2W(m・K)が入力されています"]
[null,null,null,"絶縁テープとの隙間 gm",null,"最小隙間（実効値）を入力"]
[null,null,null,null,null,"デフォルト値として，論文で評価された値(0.065mm)が入力されています"]
[null,null,null,"隙間の熱伝導率 kgm",null,"隙間が接着剤等で充填されている場合は，充填剤の熱伝導率を入力"]
[null,null,null,null,null,"デフォルト値として，空気の熱伝導率が入力されています"]
[null,"内側被覆部",null,"内側被覆直径 di",null,"デフォルト値として，素線径の3倍の値が入力されています"]
[null,null,null,"内側被覆の熱伝導率 ki",null,"被覆材の熱伝導率を入力．デフォルト値として，0.2W(m・K)が入力されています"]
[null,null,null,"測定面との隙間 gi",null,"最小隙間（実効値）を入力"]
[null,null,null,null,null,"デフォルト値として，論文で評価された値(0.065mm)が入力されています"]
[null,null,null,"隙間の熱伝導率 kgi",null,"隙間が接着剤等で充填されている場合は，充填剤の熱伝導率を入力"]
[null,null,null,null,null,"デフォルト値として，空気の熱伝導率が入力されています"]
[null,"シース加熱部",null,"シース等価直径 ds",null,"シースの長辺と短辺の平均値を入力"]
[null,null,null,null,null,"デフォルト値として，素線径の8倍の値が入力されています"]
[null,null,null,"シースの熱伝導率 ks",null,"シース材の熱伝導率を入力．デフォルト値として，0.2W(m・K)が入力されています"]
[null,null,null,"測定面との隙間 gs",null,"最小隙間（実効値）を入力"]
[null,null,null,null,null,"デフォルト値として，論文で評価された値(0.065mm)が入力されています"]
[null,null,null,"隙間の熱伝導率 kgs",null,"隙間が接着剤等で充填されている場合は，充填剤の熱伝導率を入力"]
[null,null,null,null,null,"デフォルト値として，空気の熱伝導率が入力されています"]
[null,"フィン部",null,"長さ ls'",null,"デフォルト値として，100mm(十分長い値)が入力されています"]
[null,null,null,null,null,"（ある程度以上の長さになると誤差率が変化しなくなります）"]
[null,"熱伝達率",null,"金属素線の放射率",null,"金属素線2本の放射率の平均値を入力．デフォルト値として0.2が入力されています"]
[null,null,null,"シース表面の放射率",null,"シース材表面の放射率を入力．デフォルト値として0.9が入力されています"]
[]
["(2)","「計算実行」のボタンを押す"]
[null,"→　マクロ（SOLVE）が実行され，各節点の温度（O37~O53）および誤差率（W36）が計算されます．"]
[]
[null,"誤差率は ηerrは次式で定義されます.",null,null,null,"ηerr = (Tw - Tj)/(Tw - Tf) ×100 (%)"]
[]
[null,"※ 計算実行の際は，あらかじめマクロを利用できる設定にしておく必要があります．"]
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["４．ご利用に際して"]
["・","本解析シートはご自由にお使いください．ご利用しやすいように自由に加工していただいて構いません．"]
[null,"ただし，ご利用に際して，何らかのトラブルや損失・損害等が発生したとしても，製作者は一切責任を負いません．"]
[]
[null,"製作者：　防衛大学校 システム工学群 機械工学科　中村　元"]

{"sheet":"熱抵抗網解析","index":1,"n_rows":54,"n_cols":24,"rows_kept":54,"cut":false,"hidden":false,"merged":[]}
["熱電対による表面温度測定の誤差解析（熱抵抗網解析）"]
[null,"空気の熱伝導率（Tw）",null,null,{"$f":"-0.000000022933*$O$2^2+0.000072925*$O$2+0.024175","v":2.9862228799999998E-2},"W/(m・K)",null,null,null,"熱抵抗網解析",null,"測定面温度",null,"Tw =",80,"℃","節点番号",1,null,"節点数",19]
[null,"空気の熱伝導率（(Tw+Tf)/2）",null,null,{"$f":"-0.000000022933*(($O$2+$O$3)/2)^2+0.000072925*(($O$2+$O$3)/2)+0.024175","v":2.7940353418749998E-2},"W/(m・K)",null,null,null,null,null,"周囲空気温度",null,"Tf =",25,"℃","節点番号",19,null,"熱抵抗数",27]
[null,"空気の動粘性係数（(Tw+Tf)/2）",null,null,{"$f":"(8.2925*0.00001*(($O$2+$O$3)/2)^2+9.4005*0.01*(($O$2+$O$3)/2)+13.4885)*0.000001","v":1.8652324531249998E-5},"m2/s"]
["熱電対の種類",null,null,null,null,null,null,null,null,"熱抵抗",null,null,"論文の式",null,null,null,null,null,"節点1","節点2","熱コンダクタンス",null,"熱抵抗(K/W)","熱流量(W)"]
[null,"T or K",null,null,"K",null,null,null,null,"測温接点と測定面間",null,null,"式(10)","1/Rj = 2πka((rj+gj)ln((rj+gj)/gj)-rj)",null,null,null,null,1,2,{"$f":"2*PI()*$E$11*((($E$9/1000)/2+($E$10/1000))*LN((($E$9/1000)/2+($E$10/1000))/($E$10/1000))-($E$9/1000)/2)","v":2.7605156546613846E-4},"W/K",{"$f":"1/U6","v":3622.5116068855036},{"$f":"(O36-O37)/W6","v":9.3523967142073751E-4}]
[null,"素線径",null,"dm =",0.2,"mm",null,null,null,"金属素線（素線露出部1）",null,null,"式(1)","2/Rm = (km・2πrm2) / (lm/2)",null,null,null,null,2,3,{"$f":"($E$14*2*PI()*(($E$7/1000)/2)^2)/(($E$13/1000)/2)","v":6.1575216010359944E-4},"W/K",1624.0300315499526,6.9418220094321118E-4]
["測温接点（形状を球と仮定した場合）",null,null,null,null,null,null,null,null,"金属素線（素線露出部2）",null,null,"式(1)","2/Rm = (km・2πrm2) / (lm/2)",null,null,null,null,3,4,{"$f":"($E$14*2*PI()*(($E$7/1000)/2)^2)/(($E$13/1000)/2)","v":6.1575216010359944E-4},"W/K",1624.0300315499526,7.6797549723004084E-4]
[null,"直径",null,"dj =",{"$f":"E7*2","v":0.4},"mm","（dm×2）",null,null,"金属素線（内側被覆部1）",null,null,"式(2)","2/Rmi = (km・2πrm2) / (li/2)",null,null,null,null,4,5,{"$f":"($E$14*2*PI()*(($E$7/1000)/2)^2)/(($E$22/1000)/2)","v":6.1575216010359944E-4},"W/K",1624.0300315499526,7.6797549723004084E-4]
[null,"測定面との隙間",null,"gj =",0.01,"mm",null,null,null,"金属素線（内側被覆部2）",null,null,"式(2)","2/Rmi = (km・2πrm2) / (li/2)",null,null,null,null,5,6,{"$f":"($E$14*2*PI()*(($E$7/1000)/2)^2)/(($E$22/1000)/2)","v":6.1575216010359944E-4},"W/K",1624.0300315499526,1.8833498018903572E-3]
[null,"隙間の熱伝導率",null,"ka =",0.1,"W/(m・K)",null,null,null,"金属素線（シース加熱部1）",null,null,"式(3)","2/Rms = (km・2πrm2) / (ls/2)",null,null,null,null,6,7,{"$f":"($E$14*2*PI()*(($E$7/1000)/2)^2)/(($E$28/1000)/2)","v":4.1050144006906633E-4},"W/K",2436.0450473249284,1.8833513678290785E-3]
["素線露出部",null,null,null,null,null,null,null,null,"金属素線（シース加熱部2）",null,null,"式(3)","2/Rms = (km・2πrm2) / (ls/2)",null,null,null,null,7,8,{"$f":"($E$14*2*PI()*(($E$7/1000)/2)^2)/(($E$28/1000)/2)","v":4.1050144006906633E-4},"W/K",2436.0450473249284,8.6005159786577186E-3]
[null,"長さ",null,"lm =",5,"mm",null,null,null,"金属素線（フィン部1，長さ lc）",null,null,"式(16)","1/Rms' = km(2πrm2) / lc",null,null,null,null,8,9,{"$f":"$E$14*(2*PI()*(($E$7/1000)/2)^2)/$U$33","v":6.2611341850025537E-4},"W/K",1597.1547174237603,8.6005101079341083E-3]
[null,"素線の平均熱伝導率",null,"km =",{"$f":"IF($E$6=\"T\",211,IF($E$6=\"K\",24.5))","v":24.5},"W/(m・K)","（T→211，K→24.5）",null,null,"金属素線（フィン部2，長さ lc）",null,null,"式(16)","1/Rms' = km(2πrm2) / lc",null,null,null,null,9,10,{"$f":"$E$14*(2*PI()*(($E$7/1000)/2)^2)/$U$33","v":6.2611341850025537E-4},"W/K",1597.1547174237603,1.5177370076226914E-3]
[null,"絶縁テープ厚さ",null,"δit =",0.05,"mm",null,null,null,"金属素線（フィン部3，長さ lc）",null,null,"式(16)","1/Rms' = km(2πrm2) / lc",null,null,null,null,10,11,{"$f":"$E$14*(2*PI()*(($E$7/1000)/2)^2)/$U$33","v":6.2611341850025537E-4},"W/K",1597.1547174237603,1.5177358134061186E-3]
[null,"絶縁テープ熱伝導率",null,"kit =",0.2,"W/(m・K)",null,null,null,"金属素線（フィン部4，長さ lc）",null,null,"式(16)","1/Rms' = km(2πrm2) / lc",null,null,null,null,11,19,{"$f":"$E$14*(2*PI()*(($E$7/1000)/2)^2)/$U$33","v":6.2611341850025537E-4},"W/K",1597.1547174237603,{"$f":"(O43-O54)/W16","v":1.2141898449414676E-2}]
[null,"絶縁テープとの隙間",null,"gm =",6.5000000000000002E-2,"mm","2rm+gm =",{"$f":"$E$7+$E$17","v":0.26500000000000001},"mm","内側被覆（測定面側）",null,null,"式(4)","1/Ri = π(2li)ki / ln(ri/rm)",null,null,null,null,13,5,{"$f":"PI()*2*($E$22/1000)*$E$21/LN($E$20/$E$7)","v":5.7192017347602554E-3},"W/K",{"$f":"1/U17","v":174.84957628302988},{"$f":"(O45-O40)/W17","v":-0.25598115150490774}]
[null,"隙間の熱伝導率",null,"kgm =",{"$f":"$E$2","v":2.9862228799999998E-2},"W/(m・K)","（空気→E2）",null,null,"内側被覆（空気流側）",null,null,"式(4)","1/Ri = π(2li)ki / ln(ri/rm)",null,null,null,null,5,15,{"$f":"PI()*2*($E$22/1000)*$E$21/LN($E$20/$E$7)","v":5.7192017347602554E-3},"W/K",174.84957628302988,{"$f":"(O40-O47)/W18","v":-3.7930160253834992E-2}]
["内側被覆部（金属素線＋内側被覆）",null,null,null,null,null,null,null,null,"内側被覆＋シース（測定面側）",null,null,"式(5)","1/Rs = 1/{ln(ri/rm)/(πls ki)+ln(rs/((√2)ri))/(πls ks)}",null,null,null,null,14,7,{"$f":"1/(LN($E$20/$E$7)/(PI()*($E$28/1000)*$E$21)+LN($E$26/(SQRT(2)*$E$20))/(PI()*($E$28/1000)*$E$27))","v":2.7194160850963164E-3},"W/K",367.72600025441932,{"$f":"(O46-O42)/W19","v":-0.10751404402666623}]
[null,"内側被覆直径",null,"di =",{"$f":"$E$7*3","v":0.60000000000000009},"mm","（dm×3）",null,null,"内側被覆＋シース（空気流側）",null,null,"式(5)","1/Rs = 1/{ln(ri/rm)/(πls ki)+ln(rs/((√2)ri))/(πls ks)}",null,null,null,null,7,16,{"$f":"1/(LN($E$20/$E$7)/(PI()*($E$28/1000)*$E$21)+LN($E$26/(SQRT(2)*$E$20))/(PI()*($E$28/1000)*$E$27))","v":2.7194160850963164E-3},"W/K",367.72600025441932,{"$f":"(O42-O48)/W20","v":-2.5202380275513553E-2}]
[null,"内側被覆の熱伝導率",null,"ki =",0.2,"W/(m・K)",null,null,null,"内側被覆＋シース（フィン部1，長さ 2lc）",null,null,"式(17)","1/Rs' = 1/{ln(ri/rm)/(2π(2lc)ki)+ln(rs/((√2)ri))/(2π(2lc)ks)}",null,null,null,null,9,17,{"$f":"1/(LN($E$20/$E$7)/(2*PI()*(2*$U$33)*$E$21)+LN($E$26/(SQRT(2)*$E$20))/(2*PI()*(2*$U$33)*$E$27))","v":3.5658849853529048E-3},"W/K",280.43529281161966,{"$f":"(O43-O54)/W21","v":6.9151390299471524E-2}]
[null,"長さ",null,"li =",5,"mm",null,null,null,"内側被覆＋シース（フィン部2，長さ 2lc）",null,null,"式(17)","1/Rs' = 1/{ln(ri/rm)/(2π(2lc)ki)+ln(rs/((√2)ri))/(2π(2lc)ks)}",null,null,null,null,11,18,{"$f":"1/(LN($E$20/$E$7)/(2*PI()*(2*$U$33)*$E$21)+LN($E$26/(SQRT(2)*$E$20))/(2*PI()*(2*$U$33)*$E$27))","v":3.5658849853529048E-3},"W/K",280.43529281161966,{"$f":"(O44-O50)/W22","v":-0.14587375006101458}]
[null,"測定面との隙間",null,"gi =",6.5000000000000002E-2,"mm","2ri+gi =",{"$f":"$E$20+$E$23","v":0.66500000000000004},"mm","絶縁テープ",null,null,"式(14)","1/Rit = kit(2dmlm) / δit",null,null,null,null,1,12,{"$f":"$E$16*2*($E$7/1000)*($E$13/1000)/($E$15/1000)","v":8.0000000000000002E-3},"W/K",125,{"$f":"(O44-O38)/W23","v":-0.35862852478027346}]
[null,"隙間の熱伝導率",null,"kgi =",{"$f":"$E$2","v":2.9862228799999998E-2},"W/(m・K)","（空気→E2）",null,null,"素線露出部と測定面間",null,null,"式(11)","1/Rgm = -πkgm(2lm) + 4kgm(2lm)(rm+gm)/(2rm+gm)√((2rm+gm)/gm)×atan(√((2rm+gm)/gm))",null,null,null,null,12,3,{"$f":"-PI()*$E$18*2*($E$13/1000)+4*$E$18*2*($E$13/1000)*($E$7/2+$E$17)/$H$17*SQRT($H$17/$E$17)*ATAN(SQRT($H$17/$E$17))","v":7.3017310836557495E-4},"W/K",1369.5382485920463,{"$f":"(O36-O44)/W24","v":3.6029555914121235E-2}]
["シース加熱部（金属素線＋内側被覆＋シース）",null,null,null,null,null,null,null,null,"内側被覆部と測定面間",null,null,"式(12)","1/Rgi = -πkgi(2li) + 4kgi(2li)(ri+gi)/(2ri+gi)√((2ri+gi)/gi)×atan(√((2ri+gi)/gi))",null,null,null,null,1,13,{"$f":"-PI()*$E$24*2*($E$22/1000)+4*$E$24*2*($E$22/1000)*($E$20/2+$E$23)/$H$23*SQRT($H$23/$E$23)*ATAN(SQRT($H$23/$E$23))","v":1.7204474550715063E-3},"W/K",581.24413916403944,{"$f":"(O36-O45)/W25","v":8.9063978864650548E-2}]
[null,"シース等価直径",null,"ds =",{"$f":"$E$7*8","v":1.6},"mm","（dm×8）",null,null,"シース加熱部と測定面間",null,null,"式(13)","1/Rgs = -πkgsls + 4kgsls(rs+gs)/(2rs+gs)√((2rs+gs)/gs)×atan(√((2rs+gs)/gs))",null,null,null,null,1,14,{"$f":"-PI()*$E$30*($E$28/1000)+4*$E$30*($E$28/1000)*($E$26/2+$E$29)/$H$29*SQRT($H$29/$E$29)*ATAN(SQRT($H$29/$E$29))","v":2.5370047185976673E-3},"W/K",394.16560508123587,{"$f":"(O36-O46)/W26","v":0.13748529537153259}]
[null,"シースの熱伝導率",null,"ks =",0.2,"W/(m・K)",null,null,null,"測温接点と空気流間（半周）",null,null,"式(6)","1/Rhj = h・2πrj2",null,null,null,null,2,19,{"$f":"$E$38*2*PI()*(($E$9/1000)/2)^2","v":4.6705912210182976E-6},"W/K",214105.65658151876,{"$f":"(O37-O54)/W27","v":2.4105894379024856E-4}]
[null,"長さ",null,"ls =",7.5,"mm",null,null,null,"素線露出部と空気流間（半周）",null,null,"式(7)","1/Rhm = h・πrm(2lm)",null,null,null,null,3,19,{"$f":"$E$38*PI()*($E$7/1000)/2*($E$13/1000)*2","v":5.838239026272872E-5},"W/K",17128.452526521502,{"$f":"(O38-O54)/W28","v":2.9474180820006609E-3}]
[null,"測定面との隙間",null,"gs =",{"$f":"0.065","v":6.5000000000000002E-2},"mm","2rs+gs =",{"$f":"$E$26+$E$29","v":1.665},"mm","内側被覆部と空気流間（半周）",null,null,"式(8)","1/Rhi = h・πri(2li)",null,null,null,null,15,19,{"$f":"$E$38*PI()*($E$20/1000)/2*($E$22/1000)*2","v":1.7514717078818617E-4},"W/K",5709.4841755071666,{"$f":"(O47-O54)/W29","v":9.5669505197018296E-3}]
[null,"隙間の熱伝導率",null,"kgs =",{"$f":"$E$2","v":2.9862228799999998E-2},"W/(m・K)","（空気→E2）",null,null,"シース加熱部と空気流間（半周）",null,null,"式(9)","1/Rhs = h・πrsls",null,null,null,null,16,19,{"$f":"$E$38*PI()*($E$26/1000)/2*($E$28/1000)","v":3.5029434157637229E-4},"W/K",2854.7420877535837,{"$f":"(O48-O54)/W30","v":1.7378559502675032E-2}]
["フィン部（金属素線＋内側被覆＋シース）",null,null,null,null,null,null,null,null,"フィン部と空気流間2（長さ 2lc）",null,null,"式(18)","1/Rhs' = h'・2πrs・2lc",null,null,null,null,17,19,{"$f":"$E$41*2*PI()*(($E$26/1000)/2)*(2*$U$33)","v":1.9299726191165773E-3},"W/K",518.14206590026049,{"$f":"(O54-O50)/W31","v":-8.9867810340413884E-2}]
[null,"長さ",null,"ls' =",100,"mm",null,null,null,"フィン部と空気流間2（長さ 2lc）",null,null,"式(18)","1/Rhs' = h'・2πrs・2lc",null,null,null,null,18,19,{"$f":"$E$41*2*PI()*(($E$26/1000)/2)*(2*$U$33)","v":1.9299726191165773E-3},"W/K",518.14206590026049,{"$f":"(O50-O51)/W32","v":2.0890629867360087E-2}]
["熱伝達率（対流＋放射）",null,null,null,null,null,null,null,null,null,null,null,"式(15)","lc = √[km(2πrm2){1/(h'(2πrs))+ln(rs/((√2)ri))/(2πks)+ln(ri/rm)/(2πki)}]",null,null,null,null,null,null,{"$f":"SQRT($E$14*2*PI()*(($E$7/1000)/2)^2*(1/($E$41*2*PI()*(($E$26/1000)/2))+LN($E$26/(SQRT(2)*$E$20))/(2*PI()*$E$27)+LN($E$20/$E$7)/(2*PI()*$E$21)))","v":2.4586286681833359E-3},"m"]
[null,"周囲風速",null,"u =",0.7,"m/s"]
[null,"測定面の流れ方向辺長",null,"L =",0.03,"m",null,null,null,null,null,null,"節点番号",null,"温度",null,null,null,null,"熱電対の誤差率"]
[null,null,null,"ReL* =",{"$f":"($E$34/1^2)*$E$35/$E$4","v":1125.8650343991558},"NuL =",{"$f":"0.61*0.71^(1/3)*$E$36^0.5","v":18.259650069104953},"hcv =",{"$f":"$G$36*$E$3/$E$35","v":17.006035874449839},null,null,null,1,"Tw =",80,"℃","測定面",null,null,"ηerr = (Tw - Tj)/(Tw - Tf) =",null,null,{"$f":"(O36-O37)/(O36-O54)*100","v":6.1598482998934658},"%"]
[null,"金属素線の放射率",null,"ε =",0.2,null,null,"hrd = εσ(Tw4-Tf4)/(Tw-Tf) =",{"$f":"$E$37*0.0000000567*(($O$36+273.15)^4-($O$54+273.15)^4)/(($O$36+273.15)-($O$54+273.15))","v":1.5776561252169901},null,null,null,2,"Tj =",76.612083435058594,"℃","測温接点"]
[null,"測定面熱伝達率(対流＋放射)",null,"h =",{"$f":"$I$36+$I$37","v":18.583691999666829},"W/(m2・K)","← hcv + hrd",null,null,null,null,null,3,"Tm =",75.484710693359375,"℃","金属素線（素線露出部）"]
[null,null,null,"ReD =",{"$f":"$E$34*($E$26/1000)/$E$4","v":60.046135167954979},"NuD =",{"$f":"IF($E$39<4,0.891*$E$39^0.33,IF($E$39<40,0.821*$E$39^0.385,0.615*$E$39^0.466))","v":4.1461895577522396},"hcv' =",{"$f":"$G$39*$E$3/($E$26/1000)","v":72.403750990455194},null,null,null,4,null,74.237495422363281,"℃"]
[null,"シース表面の放射率",null,"ε' =",0.9,null,null,"hrd' = ε'σ(Ts'4-Tf4)(Ts'-Tf) =",{"$f":"$E$40*0.0000000567*((($O$43+$O$54)/2+273.15)^4-($O$54+273.15)^4)/((($O$43+$O$54)/2+273.15)-($O$54+273.15))","v":5.6795842289338312},null,null,null,5,"Tmi =",72.990280151367188,"℃","金属素線（内側被覆部）"]
[null,"フィン部熱伝達率(対流＋放射)",null,"h' =",{"$f":"$I$39+$I$40","v":78.083335219389028},"W/(m2・K)","← hcv' + hrd'",null,null,null,null,null,6,null,69.931663513183594,"℃"]
[null,null,null,null,null,null,null,null,null,null,null,null,7,"Tms =",65.343734741210938,"℃","金属素線（シース加熱部）"]
[null,null,null,null,null,null,null,null,null,null,null,null,8,"T0' =",44.392490386962891,"℃","金属素線（フィン部始端）"]
[null,null,null,null,null,null,null,null,null,null,null,null,9,null,30.656145095825195,"℃"]
[null,null,null,null,null,null,null,null,null,null,null,null,10,null,28.232084274291992,"℃"]
[null,null,null,null,null,null,null,null,null,null,null,null,11,null,25.808025360107422,"℃"]
[null,null,null,null,null,null,null,null,null,null,null,null,12,null,79.622352600097656,"℃"]
[null,null,null,null,null,null,null,null,null,null,null,null,13,null,74.611305236816406,"℃"]
[null,null,null,null,null,null,null,null,null,null,null,null,14,null,72.417556762695313,"℃"]
[null,null,null,null,null,null,null,null,null,null,null,null,15,null,71.564292907714844,"℃"]
[null,null,null,null,null,null,null,null,null,null,null,null,16,null,60.739978790283203,"℃"]
[null,null,null,null,null,null,null,null,null,null,null,null,17,null,28.669883728027344,"℃"]
[null,null,null,null,null,null,null,null,null,null,null,null,18,null,25.524272918701172,"℃"]
[null,null,null,null,null,null,null,null,null,null,null,null,19,"Tf =",25,"℃","周囲空気"]