{"text_format":"1","workbook":"xlsx","n_sheets":2,"sheets":["問題","解答"],"not_rendered":{"charts":2,"images":2,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"問題","index":0,"n_rows":3,"n_cols":2,"rows_kept":3,"cut":false,"hidden":false,"merged":[[1,1,1,8],[2,1,24,8]]}
[]
[null,"C5.1　球形固体触媒粒子内の拡散（偏微分方程式、VBA：陽解法）"]
[null,"半径Rの球形固体触媒粒子内を拡散する反応物質の濃度分布qの時間変化を計算する。濃度、長さ、時間をそれぞれ無次元化して求める。ただし、固体触媒粒子は均一体と仮定する。（化学工学会編「改訂化学工学プログラミング演習」培風館(2000)の問題から）\n　固体触媒粒子内微小部分の物質収支式から、球座標における拡散方程式は式(C5.1)で与えられる。この偏微分方程式を差分法により解く。\n\n　　　　 　　　　　　　　　　　　　　　　　　(C5.1)\n\nここで、qは吸着物質の粒子内濃度[kg m-3]、Dは粒子内有効拡散係数[m2 s-1]、rは半径方向の座標[m]、tは時間[s]である。\n初期条件（t=0で粒子内の濃度は0）と境界条件（粒子表面r=Rと粒子中心における条件r=0）は\n\n\n                                 　　　　　　 (C5.2)\n\n\nである。Qは粒子表面における吸着物質の濃度[kg m-3]で一定とする。\n\n"]

{"sheet":"解答","index":1,"n_rows":50,"n_cols":13,"rows_kept":50,"cut":false,"hidden":false,"merged":[]}
[]
[]
[]
[]
[]
[]
[null,null,1,0.9,0.8,0.7,0.6,0.5,0.4,0.3,0.2,0.1,0]
[null,"計算結果"]
[null,"T","Ys(surface)","Y1","Y2","Y3","Y4","Y5","Y6","Y7","Y8","Y9","YC(center)"]
[null,0,1,0,0,0,0,0,0,0,0,0,0]
[null,1.0000399999997741E-2,1,0.52342851553421821,0.18859496940642029,4.4663628958578352E-2,6.7760972733458772E-3,6.4796404393774776E-4,3.8507232715668448E-5,1.2312907218059329E-6,0,0,0]
[null,2.0000000000000694E-2,1,0.674404734301151,0.38097314591059755,0.17645920695793363,6.6148706005906055E-2,1.9884899854664347E-2,4.7619609938521672E-3,9.0402780214601309E-4,1.3542439967742485E-4,1.5829014813767621E-5,2.619304408435604E-6]
[null,3.0000000000028042E-2,1,0.74622997044555706,0.49666877216071276,0.2908876135951653,0.14865610928084294,6.5869143738198868E-2,2.5185204212196388E-2,8.2794914672633061E-3,2.3354235358688333E-3,5.7845906424757051E-4,2.2510541915475739E-4]
[null,4.0000399999979494E-2,1,0.78996668682281213,0.57392637579905093,0.37976594056411461,0.22746800603162803,0.12273991446898008,5.944220204951179E-2,2.5768031292525206E-2,1.0010645665150151E-2,3.6526337043645582E-3,2.0067730637791628E-3]
[null,5.0000399999920106E-2,1,0.82001583462603256,0.62971478759444643,0.44944931598178028,0.29672617952783964,0.18051320001194504,0.10089145846771583,5.1727837691082586E-2,2.4473909741270401E-2,1.1383700111406514E-2,7.5409938854275544E-3]
[null,6.0000399999860718E-2,1,0.84220887076544648,0.67222592322025276,0.50537241813656664,0.35646872962035431,0.2351719685385667,0.14478469638572181,8.3179470193302907E-2,4.508497141461415E-2,2.4747041397670134E-2,1.8342995641094987E-2]
[null,7.000039999980133E-2,1,0.85940982573864111,0.70589064577615246,0.55126799499238388,0.40800857304010441,0.28545766712962395,0.18850349135733246,0.11768649401516144,7.0529973408909902E-2,4.3586995343448558E-2,3.4736153140158779E-2]
[null,8.0000399999741942E-2,1,0.87321089417396858,0.73333007204811707,0.58967047181341692,0.45275186834345371,0.33125125910377951,0.230771009780845,0.15359966707241063,9.9474661668097361E-2,6.7114131189395174E-2,5.6191257772428414E-2]
[null,9.0000399999682554E-2,1,0.88457750606520502,0.75620487143984205,0.62233953572707268,0.4919199951482614,0.37286978046374408,0.27104445686675349,0.18987015976169075,0.13077372487667083,9.4312951488141214E-2,8.1780208065347956E-2]
[null,0.10000039999962317,1,0.89413440158862778,0.77562560421668569,0.65053161324770237,0.52651273035728929,0.41076567944858949,0.30915672110510578,0.22584282372844672,0.16350572579390357,0.12417574084003509,0.11048483061847356]
[null,0.11000039999956378,1,0.90230681381603273,0.79236752980861325,0.67516728366861178,0.55733226034103245,0.44540028876940468,0.34512204753783843,0.26110957136395363,0.19695262232264948,0.15580981316822642,0.14135786043046203]
[null,0.12000039999950439,1,0.90939589609011939,0.80699050533371564,0.69693578057238414,0.58501811995722763,0.47719427249255103,0.37903512103816783,0.29541706561132158,0.23056610258211263,0.18847240475437493,0.17358834666866424]
[null,0.13000039999961849,1,0.91562163921943929,0.81990966543309807,0.7163621363626157,0.61007970370575748,0.50651241681674453,0.41102048242094275,0.32861056784485571,0.26393443853951309,0.22156963683097858,0.20651565060265223]
[null,0.14000039999990604,1,0.92114864356192394,0.83143918886956136,0.7338518322051818,0.63292344406555356,0.53366335691987643,0.44120825383475826,0.36059971969302518,0.29675378009603304,0.25464016768537351,0.23961940238148322]
[null,0.15000000000019359,1,0.92610217627928959,0.84182025612425992,0.74972091094578008,0.65387388345857622,0.55890425568076707,0.46972217992111642,0.39133605748071404,0.32880326158998857,0.28733283465051385,0.27249896997145495]
[null,0.16000000000048115,1,0.93057964087857448,0.85124179261753374,0.76422023659264182,0.67319428385174251,0.58245218811105026,0.49667993936465243,0.42080424384917264,0.35993112170793906,0.31939107579492099,0.3048576693711027]
[null,0.1700000000007687,1,0.93465671956721785,0.85985135298677406,0.77754754283246585,0.69109524882535511,0.60448544800710913,0.52218530764587234,0.44900565999542097,0.3900319680770476,0.35062658911648081,0.3364752864659612]
[null,0.18000000000105626,1,0.9383933655370934,0.8677664287658029,0.7898617737573852,0.70774882513321613,0.6251542032084132,0.5463331994777163,0.47595720324847285,0.41904013314680333,0.38090902940930038,0.36719647671359901]
[null,0.19000000000134382,1,0.94183735724607787,0.87508108062836487,0.80129126309306475,0.72329599045609483,0.64458499030801675,0.56920946255985361,0.50168569675432317,0.44691914731411353,0.41015198183789048,0.39691545510515797]
[null,0.20000000000163137,1,0.94502708728082252,0.88187122762908832,0.81194046446725932,0.73785318999327054,0.66288526755360111,0.59089197879336008,0.52622477722504601,0.47365455821981289,0.438302779920413,0.4255646887076715]
[null,0.21000000000191893,1,0.94799366077618241,0.88819865499209905,0.82189511333762511,0.75151744511048146,0.68014709317245092,0.61145171610832849,0.54961262547840317,0.49924836121226335,0.46533444892820985,0.45310589666473033]
[null,0.22000000000220649,1,0.95076249196562201,0.89411407888722094,0.83122620878515963,0.76437034679074289,0.69645006760380668,0.63095366072767822,0.57189029464908858,0.52371469165767781,0.49123938511262588,0.47952296048155868]
[null,0.23000000000249404,1,0.95335452871955662,0.89965950572471109,0.83999309802249422,0.7764811790554903,0.71186367356856828,0.64945761336242191,0.59310047220088702,0.54707650234462157,0.51602442737057541,0.50481637963559634]
[null,0.2400000000027816,1,0.95578719728226624,0.9048700572697409,0.8482458736079409,0.78790936402396794,0.72644913186321092,0.66701885647021653,0.6132865623771635,0.56936300816178154,0.53970703318760482,0.52899895935452057]
[null,0.25000000000306916,1,0.95807513432795743,0.90977538777339728,0.85602724145166253,0.79870637819622847,0.74026087175637323,0.68368870860550701,0.63249200834496078,0.5906077273476833,0.56231232375694895,0.5520924717132385]
[null,0.26000000000335671,1,0.96023075613368236,0.91440078758920718,0.86337397982720165,0.80891725657436742,0.75334769666855994,0.69951498383957245,0.65075979515805338,0.61084698592225639,0.58387080972814687,0.57412508078160107]
[null,0.27000000000364427,1,0.96226470234069572,0.9187680448232145,0.87031808145409717,0.81858177547029898,0.76575370987619851,0.71454237314263946,0.66813208983791805,0.63011878127103249,0.60441664801054107,0.59512936495459778]
[null,0.28000000000393183,1,0.96418618278976209,0.92289611965848473,0.87688764951177522,0.82773538474538388,0.77751905165040336,0.7288127624119225,0.68464998570892976,0.64846192386314316,0.62398631180936381,0.61514080457851184]
[null,0.29000000000421938,1,0.96600324924174852,0.92680167332748409,0.88310760231243723,0.83640994455987894,0.78868048838381133,0.74236549939724616,0.7003533260460626,0.66591539406892419,0.64261758151844295,0.63419663123887082]
[null,0.30000000000450694,1,0.96772300876895878,0.93049948410646022,0.88900022900262232,0.8446343095083293,0.79927188555883777,0.75523761950914436,0.71528058798752248,0.68251786507390877,0.66034878427411381,0.65233495759289417]
[null,0.3100000000047945,1,0.96935179178037878,0.93400277537280374,0.89458562915105544,0.85243479351860985,0.80932458950996577,0.76746403853416978,0.72946881210730985,0.69830735381885267,0.67721822587127267,0.66959412442290744]
[null,0.32000000000508205,1,0.97089528471662023,0.93732347513263303,0.89988206173449992,0.85983554150046948,0.81886773749500708,0.77907771865349207,0.74295356642243415,0.71332097040702291,0.69326377120856209,0.68601221557084113]
[null,0.33000000000536961,1,0.9723586351974407,0.94047242208081605,0.90490622334747606,0.86685882797803626,0.82792851132373391,0.79010981283878989,0.7557689361969907,0.72759474304237948,0.70852253917657337,0.70162670236295088]
[null,0.34000000000565717,1,0.97374653566503677,0.94345952989541981,0.90967347105380536,0.87352529846608051,0.83653234645391183,0.80058979164138289,0.76794753289512507,0.74116350071252579,0.72303068550854122,0.71647418768565996]
[null,0.35000000000594472,1,0.97506329021982152,0.94629391886523617,0.91419800187711076,0.87985416586869836,0.84470310585738528,0.81054555555121699,0.77952051716933513,0.75406079983421481,0.73682325303952489,0.73059022654174022]
[null,0.36000000000623228,1,0.97631286830156105,0.9489840219294291,0.91849299827053288,0.88586337147075733,0.85246322592467882,0.82000353544011662,0.79051763195609381,0.76631888419091787,0.74993407343373786,0.74400920510948165]
[null,0.37000000000651984,1,0.97749894805870452,0.95153767064024319,0.92257074684135565,0.89156971798532203,0.85983384009072261,0.82898878308302826,0.80096724266757691,0.77796866990969338,0.76239570802871504,0.75676426436906141]
[null,0.38000000000680739,1,0.97862495161954288,0.95396216534140454,0.92644273600123583,0.89698898048071796,0.86683488462839353,0.8375250533423102,0.81089638217770943,0.78903974910249419,0.77423941823555764,0.76888725750341569]
[null,0.39000000000709495,1,0.97969407398994313,0.9562643329078041,0.93011973696453132,0.90213599973497993,0.87348519009349546,0.84563487927964309,0.82033079884965476,0.79956040725522681,0.78549515810309556,0.7804087327241509]
[null,0.40000000000738251,1,0.98070930692225811,0.95845057465569827,0.93361187154643399,0.90702476157239331,0.8798025611543282,0.85333964120881023,0.82929500627646979,0.80955765057976992,0.79619158333846851,0.79135793507132812]