(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. The line below identifies what version of Mathematica created this file, but it can be opened using any other version as well."; FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2"; MacintoshStandardFontEncoding; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L2, e8, 24, "Times"; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, italic, L2, e6, 20, "Geneva"; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L2, e6, 18, "Times"; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, L2, a20, 14, "Times"; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, L2, a15, 12, "Times"; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, L2, a12, 10, "Geneva"; fontset = text, inactive, noKeepOnOnePage, preserveAspect, M7, L2, 12, "Chicago"; fontset = smalltext, inactive, noKeepOnOnePage, preserveAspect, M7, L2, 10, "Geneva"; fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, L2, 12, "Times"; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L2, 10, "Courier"; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L2, 9, "Courier"; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L2, 10, "Courier"; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L2, 10, "Courier"; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, L2, 12, "Courier"; fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, B65535, L2, 10, "Geneva"; fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7, L2, 10, "Chicago"; fontset = leftheader, inactive, L2, 10, "Chicago"; fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, L2, 12, "Chicago"; fontset = leftfooter, inactive, center, L2, 12, "Chicago"; fontset = help, inactive, noKeepOnOnePage, preserveAspect, M7, L2, 10, "Geneva"; fontset = clipboard, inactive, noKeepOnOnePage, preserveAspect, M7, L2, 12, "Chicago"; fontset = completions, inactive, noKeepOnOnePage, preserveAspect, M7, L2, 12, "Chicago"; fontset = special1, inactive, noKeepOnOnePage, preserveAspect, M7, L2, 12, "Chicago"; fontset = special2, inactive, noKeepOnOnePage, preserveAspect, center, M7, L2, 12, "Chicago"; fontset = special3, inactive, noKeepOnOnePage, preserveAspect, right, M7, L2, 12, "Chicago"; fontset = special4, inactive, noKeepOnOnePage, preserveAspect, M7, L2, 12, "Chicago"; fontset = special5, inactive, noKeepOnOnePage, preserveAspect, M7, L2, 12, "Chicago"; paletteColors = 128; currentKernel; ] :[font = input; initialization; preserveAspect] *) << Graphics`Graphics` (* :[font = input; PICT; formatAsPICT; output; inactive; Cclosed; dontPreserveAspect; pictureLeft = 47; pictureTop = 1; pictureWidth = 441; pictureHeight = 282; startGroup; pictureID = 16387] :[font = input; dontPreserveAspect] :[font = input; PICT; formatAsPICT; output; inactive; dontPreserveAspect; pictureLeft = 17; pictureWidth = 439; pictureHeight = 65; pictureID = 7729] :[font = text; inactive; dontPreserveAspect; center] Stand: April 1999 :[font = subtitle; inactive; dontPreserveAspect; startGroup] Notation :[font = smalltext; inactive; dontPreserveAspect; endGroup] afak ............ Sonnenbestrahlungssteigerung auf Glashausdach (22 Grad geneigt) gegenüber der Bestrahlung eines senkrechten Fensters: Index s: Sommerhalbjahr, Index w: Winterhalbjahr, nach RWE-Energie Bauhandbuch S. 17/19. alphai .......... Wärmedurchlaßkoeffizient einer horizontalen Luftschicht im Rauminneren, alphi ............ mittlerer Wärmedurchlaßkoeffizient einer horizontalen Luftschicht im Außenraum bei mittlerem Wind nach Kraft, Seite 589 und Ihle 176.5, bilanz[tf, ti, tout] .... grobe Wärmebilanz im Glashaus, basierend allein auf den Grenz-Luftschichten, Cst ............... Stefan-Boltzmann Konstante. e1, e2 .......... Emissivität der inneren, äußeren Glasscheibe (bei Zweischeibenglas). fb ............... Bodenfläche (31 m^2). fg ............... Fensterfläche (93 m^2). flag ..............flag = -1: W-Bilanzen nur für Apr ... Sept, flag = 0: W-Bilanzen für tf = 32 C, tin = 19 C, flag = 1: W-Bilanzen bei tf = 32 C, tin = 19 C außer Jan/Feb: tf = 2 C, tin = 2 C, März, Okt., Nov., Dez.: tf = 22 C, tin = 19 C. F(Wand) .... Wandfläche, die auch Sonnenwärme speichert (12 m^2). g .................... Gesamtenergiedurchlässigkeitsgrad. ii ................. Index für Monat (ii = 1 ist Januar, ii = 2 Februar etc.). k ................... Wärmedurchlaßkoeffizient für Aggregat von Schichten. kr ................. Wärmedurchlasskoefffizient des Rahmens, 1: RMG 1, 2: RMG 2.1 ({kr[1], kr[2]} = {1.7, 2.7}W/(m^2 K). kv .................. Wärmedurchlasskoeffizient der Glasscheibe (Bundesanzeiger), 1: Einfachglas, 2:Zweischeiben-Isolierglas, 3: Zweischeiben-Wärmeschutzglas {kv[1], kv[2], kv[3]} = {5.8, 3.0, 1.8}. kf[kv, kr] ...... = kv 0.7 + kr 0.3, Wärmedurchlasskoeffiz. eines Fensters mit 30% Rahmenanteil. kf ....... Wärmedurchlaßkoeffizient einer Isolierglasscheibe. lpwbilv[lambda, 0] ..... ...... Plot des Wärmebilanzvektors wbilv[lambda, 0]. maptemps[lambdaF, q] ..... rechnet den Jahresgang von tout, tf, tin für datao, so, sonnenqo, mtempo bei lambdaF. mtemp .......... Jahresgang der mittleren Außenluft-Temperatur, Index o wie bei sonnenq. mtin[tF] ....... rechnet den Jahresgang von tin (für tout aus mtemp) bei Fußbodentemp = tF, indem es solv verwendet. m^2 .............. die Wärmeströme werden auf 1 m^2 Bodenfläche bezogen. plottemps[lambdaF, qel] ..... zeichnet den Jahresgang von tout, tf, tin für datao, so, sonnenqo, mtempo bei lambdaF und Zusatzheizung qel (W/m^2). plottin[tF] ... zeichnet den Gang der Innenluft-Temp., wenn Fußboden auf tF gehalten wird. q .................... Leistung der Fußbodenheizung (W/m^2). qg .................. Transmissionswärmeverlust durch die Glasscheiben. Normiert auf die Fußbodenfläche fb. qst ................. von der Glasfläche abgestrahlte Leistung. Bei Zweischeibenglas abhängig von der Emissivität der äußeren (e2) und inneren Scheibe (e1), letztere ist durch Beschichtung reduziert. qst ist auf die Einheitsbodenfläche fb normiert. s ..................... Schichtdicke. Vektor sv = {s[1], s[2], s[3], s[4]}. SF ................... Solargewinnkoeffizient (W/(m^2 K)). solve[q, tout] löst Wärmebilanzgleichung wbodenup[tf, tin] + wbodendown[tf, ts] = q, wbodenup[tf, tin] = wglas[tin, tout] nach stationären Fußboden tf und Innenluft-Temperaturen tin. solv[tout] ..... löst die Wärmebilanz wbodenup[tfu, tin] = wglas[tin, tout] für tf = tfu und tout. sonnenq ........ Jahresgang der über 24 h gemittelte Sonnen-Einstrahlungsleistung : ohne Index (sonnenq): W pro unter 45 Grad geneigte nach Süden ausgerichtete Fläche (m^2) nach Ihle, Bader, Golla, Index f(sonnenqf): W/m^2, globale Sonneneinstrahlung auf Fassade nach Wasserausstellung in NB, Index g(sonnenqg): W/m^2, globale Sonneneinstrahlung auf Gebäude nach Wasserausstellung in NB, Index o (sonnenqo,sonnenqfo, sonnenqgo ): wie oben, nur ohne Einheiten. sv ................. {s[1], s[2], s[3], s[4]} = Vektor der Schichtdicken. tf ................. Temperatur des Fußbodens (Speicher). tin .............. Lufttemperatur im Glashaus. tout ............. Temperatur der Außenluft, gemittelt über einen Monat. Tagesmittelwert errechnet sich nach Kraft S. 112 zu tout(Tag) = 1/4 (t(7 Uhr) + t(14 Uhr) + 2 t(21 Uhr)). ts ................ Temperatur des Erdreichs unter Stahlbeton. wbil[{ii_,tout_}] ............ ..... Wärme, die im Glashaus pro m^2 Bodenfläche gewonnen wird, wenn durch eine Wärmeabfuhr (z.B. Wasserschlangen im Boden, Lüftung) eine Fußbodentemp. tf = 22 C und eine Innenlufttemp. tin = 19 C eingestellt wird. wbilv[lambda, 0] ..... ...... Wärmebilanzvektor für Fenster-k-Wert lambda und reine Sonneneinstrahlung. Vektor ist aus den monatlichen Werten von wbil aufgebaut. wbodenup .. Wärmeabgabe durch die Fliesenschicht in die Innenluft. wbodendown .. Wärmeabgabe durch Dämmschicht und Stahlbeton ins Erdreich. wglas ......... Wärmestrom durch die Fensterfläche. wglasb ........Wärmestrom aus Glashaus hinaus, durch Glas und Boden, ist eine Funktion von tf, tin, tout und ts. Schichtenfolge: ========== 1 .............. Stahlbeton auf Erdreich, 0.20 m dick, lambda[1] = 2.10 W/m K; 2 .............. Dämmschicht, 0.08 m dick, lambda[2] = 0.04 W/m K; 3 .............. Zementestrich als Sonnenwärmespeicher, 0.10 m dick, lambda[3] = 1.4 W/m K; hierin ist im Glashaus der Wärmeträger angeordnet; 4 .............. Fliesen, 0.01 m dick, lambda[4] = 1.0 W/m K. :[font = subtitle; inactive; Cclosed; dontPreserveAspect; startGroup] Quelle der Daten :[font = smalltext; inactive; dontPreserveAspect; endGroup; endGroup] Gerhard Gasser, Harry Timm, Beheizte Fußbodenkonstruktionen, Estriche, Industrieböden, Beläge, Bauverlag GmbH, Wiesbaden und Berlin, 1985. Claus Ihle, Rolf Bader, Manfred Golla, Tabellenbuch - Sanitär, Heizung, Lüftung, Schroedel Schulbuchverlag GmbH, Hannover, 1991. Kilmadaten der DDR - ein Handbuch für die Praxis, Reihe B, Band 3 "Strahlung und Bevölkung, Potsdam, 1981. Günther Kraft, Handbuch der Technischen Gebäudeausrüstung, 2. Auflage, VEB Verlag für Bauwesen, Berlin, 1983. Poroton-Merk- und Formelblatt: Planung und Ausführung von Ziegelmauerwerk, Deutsche Poroton GmbH, Cäsariusstr. 83a, D - 53639 Königswinter, Tel.: (02223) 91 10 30 RWE Energie Bau-Handbuch, 12. Ausgabe, RWE Energie AG, Bereich Anwendungstechnik, D-45117 Essen, Tel.:(0201) 12 - 01, Fax: (0201) 12 - 2 45 43, www.rweenergie.de :[font = subsubtitle; inactive; dontPreserveAspect; startGroup] Mit Einheiten dataU, sU, areaU, qsU, datasU, mtempnU, mtempkU ;[s] 2:0,0;14,1;62,-1; 2:1,20,14,Times,1,18,0,0,0;1,17,12,Times,0,14,0,0,0; :[font = section; inactive; dontPreserveAspect; startGroup] Wärmeleitfähigkeiten, Erdreich-Temp. :[font = input; dontPreserveAspect; endGroup] Clear[dataU]; dataU := ( Clear[alphai, alphaa, alphi, lambda,ts, kf]; alphai = 1/0.13 W/(m^2 K); alphaa = Infinity; alphi = 1/0.04 W/(m^2 K); (*Ihle 176.5, Kraft: 1/0.15, Seite 589, Tab. 7.1/8*) {lambda[1], lambda[2], lambda[3], lambda[4]} = {2.1, 0.035, 1.4, 1.0}W/(m K); ts = 5 K; (*eigentlich (5 + 293) K, 293 fällt raus, weil immer Temp.-Diff. verwendet*) lambdav := Array[lambda, 4]; kf[kv_] := 0.7 kv + 0.3 2.5 W/(m^2 K) ); dataU; ;[s] 3:0,0;172,1;195,0;439,-1; 2:2,14,9,Times,0,12,0,0,0;1,14,10,Geneva,0,10,0,0,0; :[font = section; inactive; Cclosed; dontPreserveAspect; startGroup] Dicken, Flächen (Achtung: Estrichdicke ist 100 mm, Betondicke ist 100 mm) :[font = input; dontPreserveAspect] sU := ( s[1] = 100/1000 m; s[2] = 90/1000 m; s[3] = 100/1000 m; s[4] = 10/1000 m) sU; Clear[sv]; sv := Array[ s, 4]; areaU := ( fn3 = 1/4 3.7 7 m^2; fn1to3 = 1/4 1.5 20 m^2; fd1to2 = 1/2 1.95 6.5 m^2; fd3 = 1/4 8 7.5 m^2; fd2 = 1/4 ( 5.5 8 + 1.7 5.5) m^2; fd1 = 1/4 4.5 7.5 m^2; fs1 = 1/4 4.7 7 m^2; fs2to3 = 1/4 13 2.5 m^2; fw = 1/4 (8.5 2.5 + (7.5 2.5)/2 + 4 2) m^2; fo = fw; fdach = fd1 + fd2 + fd3; fg = fn3 + fn1to3 + fd1to2 + fdach + fs1 + fs2to3 + fw + fo; fwand = fg - fdach; fb = 1/4 (9 20 - 6 7 - 1.7 7) m^2); areaU; :[font = input; preserveAspect; endGroup] :[font = smalltext; inactive; Cclosed; preserveAspect; startGroup] Einzelne Flächen :[font = input; preserveAspect; startGroup] fb/fg 200 W/m^2 :[font = output; output; inactive; preserveAspect; endGroup] (67.97843665768194*W)/m^2 ;[o] 67.9784 W --------- 2 m :[font = input; preserveAspect; startGroup] fg :[font = output; output; inactive; preserveAspect; endGroup] 92.75*m^2 ;[o] 2 92.75 m :[font = input; preserveAspect; startGroup] fd1to2 :[font = output; output; inactive; preserveAspect; endGroup] 6.3375*m^2 ;[o] 2 6.3375 m :[font = input; preserveAspect; startGroup] fwand :[font = output; output; inactive; preserveAspect; endGroup] 55.97500000000001*m^2 ;[o] 2 55.975 m :[font = input; preserveAspect; startGroup] fb :[font = output; output; inactive; preserveAspect; endGroup] 31.525*m^2 ;[o] 2 31.525 m :[font = input; preserveAspect; startGroup] fdach :[font = output; output; inactive; preserveAspect; endGroup; endGroup] 36.775*m^2 ;[o] 2 36.775 m :[font = input; preserveAspect; startGroup] (*Grundfläche = *) (3.55 3.639 + (6.557 - 3.639) (3.55 + 0.859) + 1.455 3.546) m^2 :[font = output; output; inactive; preserveAspect; endGroup] 30.943342*m^2 ;[o] 2 30.9433 m :[font = smalltext; inactive; Cclosed; preserveAspect; startGroup] Umbauter Raum :[font = input; preserveAspect; startGroup] Vol = 10^-6 m^3/cm^3 (330. 170 990 + 85 85 990 + 1/2 (85 290 990 + 205 50 990 + 300 105 990)) cm^3 :[font = output; output; inactive; preserveAspect; endGroup] 95.55975*m^3 ;[o] 3 95.5597 m :[font = input; preserveAspect; startGroup] 10^-6 m^3 / cm^3 (142 397 655.7 + 111 261 354.6 + 90 228 646.2 + 0.5 145 367 655.7 + 28 94 (655.7 + 354.6)) cm^3 :[font = output; output; inactive; preserveAspect; endGroup] 80.60321975*m^3 ;[o] 3 80.6032 m :[font = input; preserveAspect; endGroup] :[font = section; inactive; dontPreserveAspect; startGroup] Jahresgang der Sonneneinstrahlung und Temperatur :[font = smalltext; inactive; Cclosed; preserveAspect; startGroup] RWE Energie Bau-Handbuch, 12. Ausgabe, RWE Energie AG, Bereich Anwendungstechnik, D-45117 Essen, Tel.:(0201) 12 - 01, Fax: (0201) 12 - 2 45 43, www.rweenergie.de Seite 17/5 :[font = smalltext; inactive; preserveAspect] (*max. Strahlungsleistung auf senkrecht bestrahlte Fläche*) qs[1] = 1000 W/m^2; (*Strahlungsleistung bei sehr dichter Bevölkung*) qs[2] = 20 W/m^2; (*min. diff. Strahlungsleistung bei vollständig verdeckter Sonne*) qs[3] = 20 W/m^2; (*max. diff. Strahlungsleistung bei vollständig verdeckter Sonne*) qs[4] = 250 W/m^2; :[font = input; preserveAspect] qsU := ( (*jährl. Einstrahlung auf horiz. Meckl.Ebene, dividiert durch 24h/d 365d*) qs[5] = 10.^6 W h /(m^2 24 h/d 365 d); (*durchschn. Globalstrahlung, Meckl., April-Sept.*) qs[6] = 8. 10^5 W h/(m^2 24 h/d 365/2 d); (*max. tägl. Einstrahlg., sehr klares Sommerwetter*) qs[7] = 8. 10^3 W h/(m^2 24 h); (*mittl. tägl. Einstrahlg. an den besten 100 Sonnentagen des Jahres*) qs[8] = 5500 W h/(m^2 24 h); (*mittl. tägl. Einstrahlg. an den 100 ungünstigsten Tagen des Jahres*) qs[9] = 10^3 W h/(m^2 24. h); (*min. tägl. Einstrahlg., sehr trübes Winterwetter*) qs[10] = 100. W h/(m^2 24 h); (*Sonnenscheindauer pro Jahr, min*) Tamin = 1300 h/(365 d 24. h/d); (*Sonnenscheindauer pro Jahr, max*) Tamax = 1900 h/(365 d 24. h/d); (*Sonnenscheindauer April-Sept., min*) Tamin = 1000 h/(365/2 d 24. h/d); (*Sonnenscheindauer April-Sept., max*) Tamax = 1400 h/(365/2 d 24. h/d); (*Sonnenscheindauer Okt.-März, min*) Tamin = 300 h/(365/2 d 24. h/d); (*Sonnenscheindauer Okt.-März, max*) Tamax = 500 h/(365/2 d 24. h/d) ); qsU; :[font = input; preserveAspect; startGroup] Table[qs[ii], {ii, 5, 10}] :[font = output; output; inactive; preserveAspect; endGroup] {(114.1552511415525*W)/m^2, (182.648401826484*W)/m^2, (333.3333333333333*W)/m^2, (1375*W)/(6*m^2), (41.66666666666666*W)/m^2, (4.166666666666667*W)/m^2} ;[o] 114.155 W 182.648 W 333.333 W 1375 W 41.6667 W 4.16667 W {---------, ---------, ---------, ------, ---------, ---------} 2 2 2 2 2 2 m m m 6 m m m :[font = input; preserveAspect; startGroup] 24 h/d 1 kW/(1000 W) Table[qs[ii], {ii, 5, 10}] :[font = output; output; inactive; preserveAspect; endGroup] {(2.73972602739726*h*kW)/(d*m^2), (4.383561643835617*h*kW)/(d*m^2), (8.*h*kW)/(d*m^2), (11*h*kW)/(2*d*m^2), (1.*h*kW)/(d*m^2), (0.1*h*kW)/(d*m^2)} ;[o] 2.73973 h kW 4.38356 h kW 8. h kW 11 h kW 1. h kW 0.1 h kW {------------, ------------, -------, -------, -------, --------} 2 2 2 2 2 2 d m d m d m 2 d m d m d m :[font = input; preserveAspect; startGroup] 1/5 24 h/d 1 kW/(1000 W) Sum[qs[ii], {ii, 5, 9}] :[font = output; output; inactive; preserveAspect; endGroup] (4.324657534246576*h*kW)/(d*m^2) ;[o] 4.32466 h kW ------------ 2 d m :[font = input; preserveAspect; startGroup] 1/5 Sum[qs[ii], {ii, 5, 9}] :[font = output; output; inactive; preserveAspect; endGroup] (180.1940639269406*W)/m^2 ;[o] 180.194 W --------- 2 m :[font = input; preserveAspect; startGroup] BarChart[Table[ 24/1000 m^2/W qs[i], {i, 5, 10}], Frame->True, GridLines->{None, Automatic}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.0645161 0.16129 0.0147151 0.0735755 [ [(1)] .09677 0 0 2 Msboxa [(2)] .25806 0 0 2 Msboxa [(3)] .41935 0 0 2 Msboxa [(4)] .58065 0 0 2 Msboxa [(5)] .74194 0 0 2 Msboxa [(6)] .90323 0 0 2 Msboxa [(0)] -0.0125 .01472 1 0 Msboxa [(2)] -0.0125 .16187 1 0 Msboxa [(4)] -0.0125 .30902 1 0 Msboxa [(6)] -0.0125 .45617 1 0 Msboxa [(8)] -0.0125 .60332 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p 0 0 .5 r .001 w 0 .16187 m 1 .16187 L s P p 0 0 .5 r .001 w 0 .30902 m 1 .30902 L s P p 0 0 .5 r .001 w 0 .45617 m 1 .45617 L s P p .002 w .09677 0 m .09677 .00625 L s P [(1)] .09677 0 0 2 Mshowa p .002 w .25806 0 m .25806 .00625 L s P [(2)] .25806 0 0 2 Mshowa p .002 w .41935 0 m .41935 .00625 L s P [(3)] .41935 0 0 2 Mshowa p .002 w .58065 0 m .58065 .00625 L s P [(4)] .58065 0 0 2 Mshowa p .002 w .74194 0 m .74194 .00625 L s P [(5)] .74194 0 0 2 Mshowa p .002 w .90323 0 m .90323 .00625 L s P [(6)] .90323 0 0 2 Mshowa p .002 w 0 0 m 1 0 L s P p .002 w 0 .01472 m .00625 .01472 L s P [(0)] -0.0125 .01472 1 0 Mshowa p .002 w 0 .16187 m .00625 .16187 L s P [(2)] -0.0125 .16187 1 0 Mshowa p .002 w 0 .30902 m .00625 .30902 L s P [(4)] -0.0125 .30902 1 0 Mshowa p .002 w 0 .45617 m .00625 .45617 L s P [(6)] -0.0125 .45617 1 0 Mshowa p .002 w 0 .60332 m .00625 .60332 L s P [(8)] -0.0125 .60332 1 0 Mshowa p .001 w 0 .04415 m .00375 .04415 L s P p .001 w 0 .07358 m .00375 .07358 L s P p .001 w 0 .10301 m .00375 .10301 L s P p .001 w 0 .13244 m .00375 .13244 L s P p .001 w 0 .1913 m .00375 .1913 L s P p .001 w 0 .22073 m .00375 .22073 L s P p .001 w 0 .25016 m .00375 .25016 L s P p .001 w 0 .27959 m .00375 .27959 L s P p .001 w 0 .33845 m .00375 .33845 L s P p .001 w 0 .36788 m .00375 .36788 L s P p .001 w 0 .39731 m .00375 .39731 L s P p .001 w 0 .42674 m .00375 .42674 L s P p .001 w 0 .4856 m .00375 .4856 L s P p .001 w 0 .51503 m .00375 .51503 L s P p .001 w 0 .54446 m .00375 .54446 L s P p .001 w 0 .57389 m .00375 .57389 L s P p .002 w 0 0 m 0 .61803 L s P P p p .002 w .09677 .61178 m .09677 .61803 L s P p .002 w .25806 .61178 m .25806 .61803 L s P p .002 w .41935 .61178 m .41935 .61803 L s P p .002 w .58065 .61178 m .58065 .61803 L s P p .002 w .74194 .61178 m .74194 .61803 L s P p .002 w .90323 .61178 m .90323 .61803 L s P p .002 w 0 .61803 m 1 .61803 L s P p .002 w .99375 .01472 m 1 .01472 L s P p .002 w .99375 .16187 m 1 .16187 L s P p .002 w .99375 .30902 m 1 .30902 L s P p .002 w .99375 .45617 m 1 .45617 L s P p .002 w .99375 .60332 m 1 .60332 L s P p .001 w .99625 .04415 m 1 .04415 L s P p .001 w .99625 .07358 m 1 .07358 L s P p .001 w .99625 .10301 m 1 .10301 L s P p .001 w .99625 .13244 m 1 .13244 L s P p .001 w .99625 .1913 m 1 .1913 L s P p .001 w .99625 .22073 m 1 .22073 L s P p .001 w .99625 .25016 m 1 .25016 L s P p .001 w .99625 .27959 m 1 .27959 L s P p .001 w .99625 .33845 m 1 .33845 L s P p .001 w .99625 .36788 m 1 .36788 L s P p .001 w .99625 .39731 m 1 .39731 L s P p .001 w .99625 .42674 m 1 .42674 L s P p .001 w .99625 .4856 m 1 .4856 L s P p .001 w .99625 .51503 m 1 .51503 L s P p .001 w .99625 .54446 m 1 .54446 L s P p .001 w .99625 .57389 m 1 .57389 L s P p .002 w 1 0 m 1 .61803 L s P P p p .002 w 0 .01472 m 1 .01472 L s P p .002 w 0 0 m 0 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p p 1 0 0 r .03226 .01472 m .03226 .21629 L .16129 .21629 L .16129 .01472 L F P p .004 w .03226 .01472 m .03226 .21629 L .16129 .21629 L .16129 .01472 L .03226 .01472 L s P P p p 1 0 0 r .19355 .01472 m .19355 .33724 L .32258 .33724 L .32258 .01472 L F P p .004 w .19355 .01472 m .19355 .33724 L .32258 .33724 L .32258 .01472 L .19355 .01472 L s P P p p 1 0 0 r .35484 .01472 m .35484 .60332 L .48387 .60332 L .48387 .01472 L F P p .004 w .35484 .01472 m .35484 .60332 L .48387 .60332 L .48387 .01472 L .35484 .01472 L s P P p p 1 0 0 r .51613 .01472 m .51613 .41938 L .64516 .41938 L .64516 .01472 L F P p .004 w .51613 .01472 m .51613 .41938 L .64516 .41938 L .64516 .01472 L .51613 .01472 L s P P p p 1 0 0 r .67742 .01472 m .67742 .08829 L .80645 .08829 L .80645 .01472 L F P p .004 w .67742 .01472 m .67742 .08829 L .80645 .08829 L .80645 .01472 L .67742 .01472 L s P P p p 1 0 0 r .83871 .01472 m .83871 .02207 L .96774 .02207 L .96774 .01472 L F P p .004 w .83871 .01472 m .83871 .02207 L .96774 .02207 L .96774 .01472 L .83871 .01472 L s P P P % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect; endGroup; endGroup] Graphics["<<>>"] ;[o] -Graphics- :[font = smalltext; inactive; dontPreserveAspect; startGroup] Die tägliche Sonneneinstrahlung in eine 45 Grad geneigte nach Süden ausgerichtete Fläche ist nach Ihle, Bader, Golla, 221.5 :[font = input; dontPreserveAspect; startGroup] sonnenqI = 1000{0.8, 1.55, 2.7, 4.25, 4.8, 4.3, 3.8, 3.75, 3.5, 1.9, 1.1, 0.4}(W h/(m^2 24 h)); (*Komponente 1 = Januar, 2 = Februar, etc.*) :[font = smalltext; inactive; preserveAspect; startGroup] Veränderung dieser Sonneneinstrahlung: Einstrahlung auf eine horizontale Fläche nach RWE-Energie, Seite 17/19 :[font = input; preserveAspect; endGroup] Clear[sonnenqU]; datasU := ( sonnenqU = {55/95 sonnenqI[[1]], 55/95 sonnenqI[[2]], 55/95 sonnenqI[[3]], sonnenqI[[4]], sonnenqI[[5]], sonnenqI[[6]], sonnenqI[[7]], sonnenqI[[8]], sonnenqI[[9]], 55/95 sonnenqI[[10]], 55/95 sonnenqI[[11]], 55/95 sonnenqI[[12]]} ); datasU; :[font = input; preserveAspect; startGroup] sonnenqU :[font = output; output; inactive; preserveAspect; endGroup] {(19.29824561403509*W)/m^2, (37.39035087719299*W)/m^2, (65.13157894736843*W)/m^2, (177.0833333333333*W)/m^2, (200.*W)/m^2, (179.1666666666666*W)/m^2, (158.3333333333333*W)/m^2, (156.25*W)/m^2, (145.8333333333333*W)/m^2, (45.83333333333333*W)/m^2, (26.53508771929824*W)/m^2, (9.64912280701754*W)/m^2} ;[o] 19.2982 W 37.3904 W 65.1316 W 177.083 W 200. W 179.167 W 158.333 W 156.25 W 145.833 W 45.8333 W {---------, ---------, ---------, ---------, ------, ---------, ---------, --------, ---------, ---------, 2 2 2 2 2 2 2 2 2 2 m m m m m m m m m m 26.5351 W 9.64912 W ---------, ---------} 2 2 m m :[font = smalltext; active; dontPreserveAspect; fontSize = 12; fontName = "Times"; startGroup] BarChart[24/1000 sonnenqI/(W/m^2), Frame->True, GridLines->{None, Automatic}] (*kWh/(d m^2)*) :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.0327869 0.0819672 0.0147151 0.122626 [ [(1)] .04918 0 0 2 Msboxa [(2)] .13115 0 0 2 Msboxa [(3)] .21311 0 0 2 Msboxa [(4)] .29508 0 0 2 Msboxa [(5)] .37705 0 0 2 Msboxa [(6)] .45902 0 0 2 Msboxa [(7)] .54098 0 0 2 Msboxa [(8)] .62295 0 0 2 Msboxa [(9)] .70492 0 0 2 Msboxa 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.01472 L s P P p p 1 0 0 r .83607 .01472 m .83607 .1496 L .90164 .1496 L .90164 .01472 L F P p .004 w .83607 .01472 m .83607 .1496 L .90164 .1496 L .90164 .01472 L .83607 .01472 L s P P p p 1 0 0 r .91803 .01472 m .91803 .06377 L .98361 .06377 L .98361 .01472 L F P p .004 w .91803 .01472 m .91803 .06377 L .98361 .06377 L .98361 .01472 L .91803 .01472 L s P P P % End of Graphics MathPictureEnd :[font = output; output; inactive; dontPreserveAspect; endGroup; endGroup; endGroup] Graphics["<<>>"] ;[o] -Graphics- :[font = input; dontPreserveAspect; startGroup] (*Jahresgang der mittleren Außenluft-Temperatur, kalte/normale Winter*) mtempkU = {-8, -10, -3, 0, 8, 15, 20, 20, 15, 8, 5, 0.2} C; mtempnU = {1.7, 2.7, 5.4, 5.5, 12, 16, 18, 17, 14, 7.7, 4, 1.6} C; mtemppU = {-2, 2, 6.5, 11.5, 17, 19.5, 21, 20.5, 17, 12.5, 6.5, 0.5} C; :[font = input; inactive; preserveAspect; startGroup] BarChart[mtempkU/(C), PlotRange->{{0, 13}, {-10, 20}}, AxesOrigin->{0, 0}, Frame->True, GridLines->{None, 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.24721 L .18462 .24721 L .18462 .20601 L .12308 .20601 L s P P p p 1 0 0 r .2 .20601 m .2 .33992 L .26154 .33992 L .26154 .20601 L F P p .004 w .2 .20601 m .2 .33992 L .26154 .33992 L .26154 .20601 L .2 .20601 L s P P p p 1 0 0 r .27692 .20601 m .27692 .44292 L .33846 .44292 L .33846 .20601 L F P p .004 w .27692 .20601 m .27692 .44292 L .33846 .44292 L .33846 .20601 L .27692 .20601 L s P P p p 1 0 0 r .35385 .20601 m .35385 .55623 L .41538 .55623 L .41538 .20601 L F P p .004 w .35385 .20601 m .35385 .55623 L .41538 .55623 L .41538 .20601 L .35385 .20601 L s P P p p 1 0 0 r .43077 .20601 m .43077 .60773 L .49231 .60773 L .49231 .20601 L F P p .004 w .43077 .20601 m .43077 .60773 L .49231 .60773 L .49231 .20601 L .43077 .20601 L s P P p p 1 0 0 r .50769 .20601 m .50769 .63864 L .56923 .63864 L .56923 .20601 L F P p .004 w .50769 .20601 m 0 0 rlineto .50769 .61803 m .50769 .20601 L s s .56923 .61803 m .56923 .20601 L s .56923 .20601 m .50769 .20601 L s P P p p 1 0 0 r .58462 .20601 m 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for this cell was not generated. Use options in the Actions Preferences dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = input; preserveAspect; startGroup] mtempbeitzke = {3.3, 4.6, 6.5, 8.8, 15.8, 17, 20, 20, 13, 8, 5, 5} :[font = output; output; inactive; preserveAspect; endGroup] {3.3, 4.6, 6.5, 8.8, 15.8, 17, 20, 20, 13, 8, 5, 5} ;[o] {3.3, 4.6, 6.5, 8.8, 15.8, 17, 20, 20, 13, 8, 5, 5} :[font = input; preserveAspect; startGroup] Length[mtempbeitzke] :[font = output; output; inactive; preserveAspect; endGroup] 12 ;[o] 12 :[font = input; preserveAspect; startGroup] gtempbeitzke = { 5.8, 7.9, 10, 13.8, 20, 20.6, 22.4, 22.3, 15.6, 8, 5, 5} :[font = output; output; inactive; preserveAspect; endGroup] {5.8, 7.900000000000001, 10, 13.8, 20, 20.6, 22.4, 22.3, 15.6, 8, 5, 5} ;[o] {5.8, 7.9, 10, 13.8, 20, 20.6, 22.4, 22.3, 15.6, 8, 5, 5} :[font = input; preserveAspect; startGroup] Length[gtempbeitzke] :[font = output; output; inactive; preserveAspect; endGroup] 12 ;[o] 12 :[font = input; preserveAspect; startGroup] (*Differenztemperatur*) ListPlot[Table[gtempbeitzke[[i]] - mtempbeitzke[[i]], {i, 12}], PlotRange->{{1, 12}, {0, 5}}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.0909091 0.0909091 0 0.123607 [ [(2)] .09091 0 0 2 Msboxa [(4)] .27273 0 0 2 Msboxa [(6)] .45455 0 0 2 Msboxa [(8)] .63636 0 0 2 Msboxa [(10)] .81818 0 0 2 Msboxa [(12)] 1 0 0 2 Msboxa [(1)] .07841 .12361 1 0 Msboxa [(2)] .07841 .24721 1 0 Msboxa [(3)] .07841 .37082 1 0 Msboxa [(4)] .07841 .49443 1 0 Msboxa [(5)] .07841 .61803 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .09091 0 m .09091 .00625 L s P [(2)] .09091 0 0 2 Mshowa p .002 w .27273 0 m .27273 .00625 L s P [(4)] .27273 0 0 2 Mshowa p .002 w .45455 0 m .45455 .00625 L s P [(6)] .45455 0 0 2 Mshowa p .002 w .63636 0 m .63636 .00625 L s P [(8)] .63636 0 0 2 Mshowa p .002 w .81818 0 m .81818 .00625 L s P [(10)] .81818 0 0 2 Mshowa p .002 w 1 0 m 1 .00625 L s P [(12)] 1 0 0 2 Mshowa p .001 w .12727 0 m .12727 .00375 L s P p .001 w .16364 0 m .16364 .00375 L s P p .001 w .2 0 m .2 .00375 L s P p .001 w .23636 0 m .23636 .00375 L s P p .001 w .30909 0 m .30909 .00375 L s P p .001 w .34545 0 m .34545 .00375 L s P p .001 w .38182 0 m .38182 .00375 L s P p .001 w .41818 0 m .41818 .00375 L s P p .001 w .49091 0 m .49091 .00375 L s P p .001 w .52727 0 m .52727 .00375 L s P p .001 w .56364 0 m .56364 .00375 L s P p .001 w .6 0 m .6 .00375 L s P p .001 w .67273 0 m .67273 .00375 L s P p .001 w .70909 0 m .70909 .00375 L s P p .001 w .74545 0 m .74545 .00375 L s P p .001 w .78182 0 m .78182 .00375 L s P p .001 w .85455 0 m .85455 .00375 L s P p .001 w .89091 0 m .89091 .00375 L s P p .001 w .92727 0 m .92727 .00375 L s P p .001 w .96364 0 m .96364 .00375 L s P p .001 w .05455 0 m .05455 .00375 L s P p .001 w .01818 0 m .01818 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w .09091 .12361 m .09716 .12361 L s P [(1)] .07841 .12361 1 0 Mshowa p .002 w .09091 .24721 m .09716 .24721 L s P [(2)] .07841 .24721 1 0 Mshowa p .002 w .09091 .37082 m .09716 .37082 L s P [(3)] .07841 .37082 1 0 Mshowa p .002 w .09091 .49443 m .09716 .49443 L s P [(4)] .07841 .49443 1 0 Mshowa p .002 w .09091 .61803 m .09716 .61803 L s P [(5)] .07841 .61803 1 0 Mshowa p .001 w .09091 .02472 m .09466 .02472 L s P p .001 w .09091 .04944 m .09466 .04944 L s P p .001 w .09091 .07416 m .09466 .07416 L s P p .001 w .09091 .09889 m .09466 .09889 L s P p .001 w .09091 .14833 m .09466 .14833 L s P p .001 w .09091 .17305 m .09466 .17305 L s P p .001 w .09091 .19777 m .09466 .19777 L s P p .001 w .09091 .22249 m .09466 .22249 L s P p .001 w .09091 .27193 m .09466 .27193 L s P p .001 w .09091 .29666 m .09466 .29666 L s P p .001 w .09091 .32138 m .09466 .32138 L s P p .001 w .09091 .3461 m .09466 .3461 L s P p .001 w .09091 .39554 m .09466 .39554 L s P p .001 w .09091 .42026 m .09466 .42026 L s P p .001 w .09091 .44498 m .09466 .44498 L s P p .001 w .09091 .46971 m .09466 .46971 L s P p .001 w .09091 .51915 m .09466 .51915 L s P p .001 w .09091 .54387 m .09466 .54387 L s P p .001 w .09091 .56859 m .09466 .56859 L s P p .001 w .09091 .59331 m .09466 .59331 L s P p .002 w .09091 0 m .09091 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p .008 w 0 .30902 Mdot .09091 .4079 Mdot .18182 .43262 Mdot .27273 .61803 Mdot .36364 .51915 Mdot .45455 .44498 Mdot .54545 .29666 Mdot .63636 .2843 Mdot .72727 .32138 Mdot .81818 0 Mdot .90909 0 Mdot 1 0 Mdot P % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect; endGroup] Graphics["<<>>"] ;[o] -Graphics- :[font = input; preserveAspect; startGroup] 0.6 2.5 :[font = output; output; inactive; preserveAspect; endGroup] 1.5 ;[o] 1.5 :[font = input; preserveAspect; endGroup] :[font = input; preserveAspect; endGroup; endGroup] :[font = subsubtitle; inactive; dontPreserveAspect; startGroup] Ohne Einheiten datao, so, areao, qso, dataso, mtempno, mtempko ;[s] 2:0,0;15,1;64,-1; 2:1,20,14,Times,1,18,0,0,0;1,17,12,Times,0,14,0,0,0; :[font = section; inactive; dontPreserveAspect; startGroup] Wärmeleitfähigkeiten, Erdreich-Temp. (datao) :[font = input; preserveAspect; endGroup] Clear[datao]; datao := ( Clear[alphai, alphaa, alphi, lambda,ts, kf]; alphai = 1/0.13 (*W/(m^2 K), DIN 4701, Teil 2*); alphaa = Infinity; alphi = 1/0.04 (*W/(m^2 K), mittlere Windgeschwindigkeit, Ihle 176.5*); Cst = 5.67; Clear[lambda]; {lambda[1], lambda[2], lambda[3], lambda[4]} = {2.1, 0.035, 1.4, 1.0}(*W/(m K)*); ts = 5; lambdav := Array[lambda, 4]; kf[kv_] := 0.7 kv + 0.3 2.5 (*W/(m^2 K)*)); datao; :[font = section; inactive; Cclosed; preserveAspect; startGroup] Glasdaten - ich brauche Glas senkrecht: F6/16/F6, schräg: 6/16/VSG8 - ;[s] 2:0,0;12,1;70,-1; 2:1,17,12,Times,1,14,0,0,0;1,14,9,Times,0,12,0,0,0; :[font = input; dontPreserveAspect] (*{g, en, SZR, kv}*) glasdata = {{1 (* - Infrastop Silber 48/43, Ar*) g, 0.11, 12, 1.7}, {2 (*- Infrastop Neutral 51/37, Ar*), g, 0.10, 12, 1.6}, {3 (*- Infrastop Neutral 51/37, Ar*), g, 0.10, 14, 1.5}, {4 (*- Infrastop Neutral 51/37, Ar*), g, 0.10, 16, 1.4}, {5 (*- Infrastop Grün 37/20, Ar*), g, 0.02, 12, 1.4}, {6 (*- Infrastop Brilliant 66/33, Ar*), g, 0.02, 12, 1.4}, {7 (*- Infrastop Brilliant 66/33, Ar*), g, 0.02, 14, 1.2}, {8 (*- Infrastop Brilliant 66/33, Ar*), g, 0.02, 16, 1.1}, {9 (* - Thermopane Comfort 37/20, Ar*), g, 0.02, 12, 1.4}, {10 (*- Thermopane Comfort 37/20, Ar*), g, 0.02, 14, 1.2}, {11 (*- Thermopane Comfort 37/20, Ar*), g, 0.02, 16, 1.1}, {214 (*- Semcosafe S.1.1 VSG8/16/4, Ar*), 0.52, 0.04, 16, 1.2}, {213 (*- Semcosafe S.1.4.L, VSG8/16/4, Luft*), 0.53, 0.04, 16, 1.5}, {125 (*- Semcoplus S 1.0, 4/16/4, Ar50Kr50*), 0.58, 0.04, 16, 1.1}, {196 (*- Semcoplus S 1.0, 4/16/4, Kr*), 0.58, 0.04, 16, 1.1}, {123 (*- Semcoplus S1.4L 4/16/4, Luft*), 0.59, 0.04, 16, 1.5}, {129 (*- Semcoplus S1.4L 6/16/6, Luft*), 0.58, 0.04, 16, 1.5}, {284 (*- Semcostar 0.9 4/16/4, Ar50Kr50*), 0.50, 0.04, 16, 1.0}, {155 (*- Semcophone S 35/26 6/16/4, Ar*), 0.58, 0.04, 16, 1.2}, {155 (*- Semcophone S 35/27 6/16/5, Ar*), 0.58, 0.04, 16, 1.2}, {159 (*- Semcophone S 36/27 6/16/5, Ar50/Kr50*), 0.58, 0.04, 16, 1.1}, {161 (*- Semcophone S36/28 8/16/4, Ar*), 0.57, 0.04, 16, 1.2}, {162 (*- Semcophone S36/28 6/16/4, Ar50/Kr50*), 0.57, 0.04, 16, 1.1}, {6 (*- Semcoplus N 4/18/4, Luft*), 0.64, 0.07, 18, 1.5}, {15 (*- Semcoplus N 4/18/4, Ar*), 0.64, 0.07, 18, 1.3}, {173 (*- Semcoplus N w6/12/w6, Kr*), 0.68, 0.07, 12, 1.2}, (*{275 (*- Semcoplus N 2.V.1.1 w6/12/6, Kr*), 0.68, 0.07, 12, 1.2}, *) {16 (* - Semcoplus N 4/20/4, Ar*), 0.64, 0.07, 20, 1.3}, {514 (* or 14- Semcoplus N 1.1, 6/16/6, Ar*), 0.63, 0.07, 16, 1.3}, {505 (*or 5- Semcoplus N 15.L, 6/16/6, Luft*), 0.63, 0.07, 16, 1.6}, {185 (*- Semcophone S 36/29 8/16/5, Ar50/Kr50*), 0.57, 0.04, 16, 1.1}, {52 (*- Semcosafe N VSG8/16/4, Luft*), 0.57, 0.07, 16, 1.6}, {59 (*- Semcosafe N VSG8/16/4, Ar*), 0.59, 0.07, 16, 1.3}, {63 (* - Semcosafe N VSG8/16/4, Ar*), 0.56, 0.07, 16, 1.3}, {53 (*- Semcosafe N VSG8/16/4, Ar70/SF630*), 0.57, 0.07, 16, 1.6}, {535 (*or 35 - Semcophone N37/27 6/16/5, Ar70/SF630*), 0.63, 0.07, 16, 1.6}, {536 (*or 36 - Semcophone N38/28 8/16/4, Ar70/SF630*), 0.62, 0.07, 16, 1.6}, {537 (*or 37 - Semcophone N38/29 8/16/5, Ar70/SF630*), 0.62, 0.07, 16, 1.6}, {539 (*or 39 - Semcophone N40/28 10/14/4, Ar70/SF630*), 0.61, 0.07, 14, 1.6}, {RWE3 (*- Wärmeschutzglas 4/14/4, Ar*), 0.70, 0.16, 14, 2.0} }; :[font = input; preserveAspect] (*luftgefüllte Scheiben, Auerbachs-Keller.com/sciences/wintergarten.htm, Abb. 4.1, Abb. 4.2, Abb. 4.3 *) glasdata = {{123 (*- Semcoplus S1.4L 4/16/4, Luft*), 0.59, 0.04, 16, 1.5 }, {129 (*- Semcoplus S1.4L 6/16/6, Luft*), 0.58, 0.04, 16, 1.5}, {213 (*- Semcosafe S.1.4.L, VSG8/16/4, Luft*), 0.53, 0.04, 16, 1.5}, {N20 (*- IsolarNeutralux 1.8/20, 4/12/4, Luft*), 0.64, 0.04, 12, 1.8}, {N24 (*- IsolarNeutralux 1.6/24, 4/15...16/4, Luft*), 0.64, 0.04, 16, 1.5}, {6 (*- Semcoplus N 4/18/4, Luft*), 0.64, 0.07, 18, 1.5 }, {52 (*- Semcosafe N VSG8/16/4, Luft*), 0.57, 0.07, 16, 1.6}, {505 (*or 5- Semcoplus N 15.L, 6/16/6, Luft*), 0.63, 0.07, 16, 1.6 }, {N20 (*- IsolarNeutralux 1.8/20, 4/12/4, Luft*), 0.64, 0.07, 12, 1.8 }, {N24 (*- IsolarNeutralux 1.6/24, 4/15...16/4, ?*), 0.64, 0.07, 16, 1.6}, {TP6 (*- Transplus 1.6 6*/16/VSG8 oder 6/16/6*, Luft*), 0.65, 0.08, 16, 1.6 }}; :[font = input; preserveAspect] (*Argon-gefüllte Scheiben Auerbachs-Keller.com/sciences/wintergarten.htm, Abb. 4.4, Abb. 4.5, Abb. 4.6 *) glasdata = {{155 (*- Semcophone S 35/26 6/16/4, Ar*), 0.58, 0.04, 16, 1.2 }, {155 (*- Semcophone S 35/27 6/16/5, Ar*), 0.58, 0.04, 16, 1.2}, {161 (*- Semcophone S36/28 8/16/4, Ar*), 0.57, 0.04, 16, 1.2}, {214 (*- Semcosafe S.1.1 VSG8/16/4, Ar*), 0.52, 0.04, 16, 1.2}, {N24 (*- IsolarNeutralux 1.3/24, 4/15 ...16/4, Ar*), 0.64, 0.04, 16, 1.2}, (* {N18 (*- IsolarNeutralux 1.3/18, 4/10/4, Ar*), 0.64, 0.04, 10, 1.1}, *) {N20 (*- IsolarNeutralux 1.5/20, 4/12/4, Ar*), 0.64, 0.04, 12, 1.5}, {SN1 (*Semco Plus SN 1.1, 4/15/4, Ar*), 0.64, 0.04, 15, 1.1}, {15 (*- Semcoplus N 4/18/4, Ar*), 0.64, 0.07, 18, 1.3 }, {16 (* - Semcoplus N 4/20/4, Ar*), 0.64, 0.07, 20, 1.3}, {53 (*- Semcosafe N VSG8/16/4, Ar70/SF630*), 0.57, 0.07, 16, 1.6 }, {59 (*- Semcosafe N VSG8/16/4, Ar*), 0.59, 0.07, 16, 1.3 }, {63 (* - Semcosafe N VSG8/16/4, Ar*), 0.56, 0.07, 16, 1.3 }, {514 (* or 14- Semcoplus N 1.1, 6/16/6, Ar*), 0.63, 0.07, 16, 1.3 }, {535 (*or 35 - Semcophone N37/27 6/16/5, Ar70/SF630*), 0.63, 0.07, 16, 1.6}, {536 (*or 36 - Semcophone N38/28 8/16/4, Ar70/SF630*), 0.62, 0.07, 16, 1.6 }, {537 (*or 37 - Semcophone N38/29 8/16/5, Ar70/SF630*), 0.62, 0.07, 16, 1.6}, {539 (*or 39 - Semcophone N40/28 10/14/4, Ar70/SF630*), 0.61, 0.07, 14, 1.6}, {N24 (*- IsolarNeutralux 1.3/24, 4/15 ...16/4, Ar*), 0.64, 0.07, 16, 1.3 }, {N20 (*- IsolarNeutralux 1.5/20, 4/12/4, Ar*), 0.64, 0.07, 12, 1.5 }, {TP3 (*- Transplus 1.3 6*/16/VSG8 oder 6/16/6*, Ar*), 0.64, 0.08, 16, 1.3 }}; :[font = input; preserveAspect] (*Argon-Krypton-gefüllte Scheiben Auerbachs-Keller.com/sciences/wintergarten.htm, Abb. 4.7 *) glasdata = {{125 (*- Semcoplus S 1.0, 4/16/4, Ar50Kr50*), 0.58, 0.04, 16, 1.1}, {159 (*- Semcophone S 36/27 6/16/5, Ar50/Kr50*), 0.58, 0.04, 16, 1.1}, {185 (*- Semcophone S 36/29 8/16/5, Ar50/Kr50*), 0.57, 0.04, 16, 1.1}, {284 (*- Semcostar 0.9 4/16/4, Ar50Kr50*), 0.50, 0.04, 16, 1.0}}; :[font = input; preserveAspect] (*Krypton-gefüllte Scheiben Auerbachs-Keller.com/sciences/wintergarten.htm, Abb. 4.8, Abb. 4.9 *) glasdata = {{196 (*- Semcoplus S 1.0, 4/16/4, Kr*), 0.58, 0.04, 16, 1.1}, {173 (*- Semcoplus N w6/12/w6, Kr*), 0.68, 0.07, 12, 1.2 }, {275 (*- Semcoplus N 2.V.1.1 w6/12/6, Kr*), 0.68, 0.07, 12, 1.2}}; :[font = smalltext; inactive; preserveAspect; startGroup] en = f[g] :[font = input; preserveAspect; startGroup] Table[{glasdata[[i, 1]], glasdata[[i, 2]], glasdata[[i, 3]]}, {i, 12, Count[glasdata, _._]}] :[font = output; output; inactive; preserveAspect; endGroup] {} ;[o] {} :[font = input; preserveAspect; startGroup] Table[ Text[glasdata[[i, 1]], {glasdata[[i, 2]], glasdata[[i, 3]]}, {0, 0}, {0, 1}], {i, 12, 37}] :[font = message; inactive; preserveAspect] Part::partw: Part 12 of {{196, 0.58, 0.04, 16, 1.1}, {173, 0.68, 0.07, 12, 1.2}, {275, 0.68, 0.07, 12, 1.2}} does not exist. :[font = message; inactive; preserveAspect] Part::partw: Part 12 of {{196, 0.58, 0.04, 16, 1.1}, {173, 0.68, 0.07, 12, 1.2}, {275, 0.68, 0.07, 12, 1.2}} does not exist. :[font = message; inactive; preserveAspect] Part::partw: Part 12 of {{196, 0.58, 0.04, 16, 1.1}, {173, 0.68, 0.07, 12, 1.2}, {275, 0.68, 0.07, 12, 1.2}} does not exist. :[font = message; inactive; preserveAspect; endGroup] General::stop: Further output of Part::partw will be suppressed during this calculation. :[font = input; Cclosed; preserveAspect; startGroup] Show[Graphics[Table[ Text[glasdata[[i, 1]], {glasdata[[i, 2]], glasdata[[i, 3]]}, {0, 0}, {0, -1}], {i, 12, Count[glasdata, _._]}]], Axes->True, PlotRange->{{0.4, 0.71}, {0.03, 0.17}}, Frame->True, GridLines->Automatic] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 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(*m^2*); fd1to2 = 1/2 1.95 6.5 (*m^2*); fs1 = 1/4 4.7 7 (*m^2*); fs2to3 = 1/4 13 2.5 (*m^2*); fw = 1/4 (8.5 2.5 + (7.5 2.5)/2 + 4 2) (*m^2*); fo = fw; fdach = fd1 + fd2 + fd3; fg = fn3 + fn1to3 + fd1to2 + fdach + fs1 + fs2to3 + fw + fo; fwand = fg - fdach; fb = 1/4 (9 20 - 6 7 - 1.7 7) (*m^2*)); (*Glashausfußbodenfläche*) areao; :[font = section; inactive; dontPreserveAspect; startGroup] Jahresgang der Sonneneinstrahlung (dataso) und Temperatur (mtempno, mtempko) :[font = smalltext; inactive; Cclosed; preserveAspect; startGroup] RWE Energie Bau-Handbuch, 12. Ausgabe, RWE Energie AG, Bereich Anwendungstechnik, D-45117 Essen, Tel.:(0201) 12 - 01, Fax: (0201) 12 - 2 45 43, www.rweenergie.de :[font = smalltext; inactive; preserveAspect] (*max. Strahlungsleistung auf senkrecht bestrahlte Fläche*) qs[1] = 1000 (*W/m^2*); (*Strahlungsleistung bei sehr dichter Bevölkung*) qs[2] = 20 (*W/m^2*); (*min. diff. Strahlungsleistung bei vollständig verdeckter Sonne*) qs[3] = 20 (*W/m^2*); (*max. diff. Strahlungsleistung bei vollständig verdeckter Sonne*) qs[4] = 250 (*W/m^2*); :[font = input; preserveAspect; endGroup] qso := ( (*jährl. Einstrahlung auf horiz. Meckl.Ebene, dividiert durch 24h/d 365d*) qs[5] = 10.^6 (*W h /(m^2 24 h/d 365 d)*); (*durchschn. Globalstrahlung, Meckl., April-Sept.*) qs[6] = 8. 10^5 (*W h/(m^2 24 h/d 365/2 d)*); (*max. tägl. Einstrahlg., sehr klares Sommerwetter*) qs[7] = 8. 10^3 (*W h/(m^2 24 h)*); (*mittl. tägl. Einstrahlg. an den besten 100 Sonnentagen des Jahres*) qs[8] = 5500 (*W h/(m^2 24 h)*); (*mittl. tägl. Einstrahlg. an den 100 ungünstigsten Tagen des Jahres*) qs[9] = 10^3 (*W h/(m^2 24. h)*); (*min. tägl. Einstrahlg., sehr trübes Winterwetter*) qs[10] = 100. (*W h/(m^2 24 h)*); (*Sonnenscheindauer pro Jahr, min*) Tamin = 1300 h/(365 d 24. h/d); (*Sonnenscheindauer pro Jahr, max*) Tamax = 1900 h/(365 d 24. h/d); (*Sonnenscheindauer April-Sept., min*) Tamin = 1000 h/(365/2 d 24. h/d); (*Sonnenscheindauer April-Sept., max*) Tamax = 1400 h/(365/2 d 24. h/d); (*Sonnenscheindauer Okt.-März, min*) Tamin = 300 h/(365/2 d 24. h/d); (*Sonnenscheindauer Okt.-März, max*) Tamax = 500 h/(365/2 d 24. h/d) ); qso; :[font = smalltext; inactive; dontPreserveAspect; startGroup] Die tägliche Sonneneinstrahlung in eine 45 Grad geneigte nach Süden ausgerichtete Fläche ist nach Ihle, Bader, Golla, 221.5 :[font = input; dontPreserveAspect] sonneno = 1000 (*W/kW*) /(24 (*h/d*)){0.8 (*kWh/(m^2 d*), 1.55, 2.7, 4.25, 4.8, 4.3, 3.8, 3.75, 3.5, 1.9, 1.1, 0.4}(*W h/(m^2 h)*); (*Komponente 1 = Januar, 2 = Februar, etc.*) :[font = input; preserveAspect; startGroup] ListPlot[sonneno, PlotJoined->True, Frame->True, GridLines->Automatic] :[font = postscript; PostScript; 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output; inactive; preserveAspect; endGroup] Graphics["<<>>"] ;[o] -Graphics- :[font = smalltext; inactive; preserveAspect; startGroup] Veränderung dieser Sonneneinstrahlung: Einstrahlung auf eine horizontale Fläche nach RWE-Energie, Seite 17/19 :[font = input; preserveAspect; startGroup] Clear[dataso]; dataso := ( sonnenqo = {55/95 sonneno[[1]], 55/95 sonneno[[2]], 55/95 sonneno[[3]], sonneno[[4]], sonneno[[5]], sonneno[[6]], sonneno[[7]], sonneno[[8]], sonneno[[9]], 55/95 sonneno[[10]], 55/95 sonneno[[11]], 55/95 sonneno[[12]]}); dataso; :[font = message; inactive; preserveAspect] General::spell1: Possible spelling error: new symbol name "dataso" is similar to existing symbol "datao". :[font = message; inactive; preserveAspect; endGroup; endGroup] General::spell1: Possible spelling error: new symbol name "sonnenqo" is similar to existing symbol "sonneno". :[font = input; dontPreserveAspect; startGroup] (*Jahresgang der mittleren Außenluft-Temperatur, kalte/normale Winter*) mtempko = {-8, -10, -3, 0, 8, 15, 20, 20, 15, 8, 5, 0.2} (*C*); mtempno = {1.7, 2.7, 5.4, 5.5, 12, 16, 18, 17, 14, 7.7, 4, 1.6} (*C*); mtemppo = {-2, 2, 6.5, 11.5, 17, 19.5, 21, 20.5, 17, 12.5, 6.5, 0.5} (*C*); :[font = message; inactive; preserveAspect] General::spell1: Possible spelling error: new symbol name "mtempno" is similar to existing symbol "mtempko". :[font = message; inactive; preserveAspect; endGroup; endGroup; endGroup] General::spell: Possible spelling error: new symbol name "mtemppo" is similar to existing symbols {mtempko, mtempno}. :[font = input; preserveAspect; endGroup] :[font = subsubtitle; inactive; Cclosed; dontPreserveAspect; startGroup] datax :[font = input; dontPreserveAspect; startGroup] datax := ( alphai =.; alphaa =.; alphi =.; ts =.; fg =.; fb = .; g =.; fn3 = .; fn1to3 = .; fd3 = .; fd2 = .; fd1 = .; fs1 = .; fs2to3 = .; fw = .; fo = .; fb=.; fg=.; Clear[kv, lambda, lambdav, s, sv, sov]; tin=.; tout=.; tf=.; ta=.; ts =.; ); :[font = message; inactive; preserveAspect; endGroup; endGroup] General::spell1: Possible spelling error: new symbol name "datax" is similar to existing symbol "datao". :[font = subtitle; inactive; dontPreserveAspect; startGroup] Definitionen :[font = input; preserveAspect] defw := ( (*------------------------------------------------------------------- Wärmeströme bei gegebenen Temperaturdifferenzen (W/m^2 Fußboden) ----------------------------------------------------------------------*) Clear[wbodenup, wbodendown, wbodendwn, qst, qg, wglas]; (**) wbodenup[tf_, tin_] := (tf - tin)/(1/alphai + s[4]/lambda[4]); wbodendown[tf_, ts_] := (tf - ts) /(s[1]/lambda[1] + s[2] / lambda[2]); wbodendwn[{tf_, ts_}] := (tf - ts)/(s[1]/lambda[1] + s2 / lambda[2]); (*-------------------------für analytische Lösung---------------------------------------------- wbodenup[tf_, tin_] := (tf - tin) alphai; wbodendown[tf_, ts_] := (tf - ts) ki; -------------------------für analytische Lösung----------------------------------------------*) (*wglas ist die durch das Glas verschwindende Wärme, qg ist der Transmissionswärmeverlust durch die Glasfläche, qst ist der Strahlungsverlust aus dem Glashaus*) qst[{tin_, tout_}] := (fdach/fb) Cst/(1/e1 + 1/e2 - 1) (((tin + 273)/100)^4 - ((tout + 273)/100)^4); (**) qg[{tin_, tout_}] := (tin - tout) ((fdach/fb)/(1/alphi + 1/kf[kv]) + (fwand/fb)/(1/alphi + 1/kf[kv] + s[2]/lambda[2])); (*-------------------------für analytische Lösung---------------------------------------------- qg[{tin_, tout_}] := (tin - tout) (fg/fb) kf[kv]; -------------------------für analytische Lösung----------------------------------------------*) wglas[tin_, tout_] := qg[{tin, tout}] + qst[{tin, tout}]; (* ------------------------------------------------------------------- berechnet bei Stationarität die Fußboden- (tf) und Innenlufttemperatur (tin) bei gegebener Energiezufuhr (Sonne (sonnenqo)) Außen- (tout) und Erdreichtemperatur (ts) -------------------------------------------------------------------*) Clear[solve]; solve[{q_, tout_}] := Solve[ {wbodendown[tf, ts] + wbodenup[tf, tin] == g q, wbodenup[tf, tin] == wglas[tin, tout]}, {tf, tin}]; Clear[temps]; (*temps-Vektor ist {tout, tf, tin}*) temps[{q_, tout_}] := (temps[{q, tout}] = If[Cst == 0, Flatten[{tout, tf, tin}/.solve[{q, tout}]], Clear[V]; V = {}; los = {tf, tin} /. solve[{q, tout}] ; For[l = 1, l <=4, l++, If[Head[los[[l, 1]]] == Complex, V = Append[V, {l}],]]; Prepend[Delete[los, V][[2]], tout ] ] ); Clear[maptemps]; (*temps-Vektoren für alle 12 Monate des Jahres*) maptemps:= ( maptemps = Map[temps, Table[{sonnenqo[[ii]], mtempo[[ii]]}, {ii, 12}]]); plottemps := Show[ ListPlot[Table[maptemps[[i, 1]], {i, 12}], PlotJoined->True], ListPlot[Table[maptemps[[i, 2]], {i, 12}], PlotJoined->True], ListPlot[Table[maptemps[[i, 3]], {i, 12}], PlotJoined->True], PlotRange->{Automatic, {-10, 30}}, Frame->True, GridLines->Automatic ]; (* ------------------------------------------------------------------- berechnet im Glashaus pro m^2 anfallende Wärme (kWh/d) bei Bodentemp. tf = 32 C, Innenlufttemp. tin = 19 C außer Jan/Feb: tf = 2 C, tin = 2 C März, Okt., Nov., Dez.: tf = 22 C, Innenlufttemp. tin = 19 C -------------------------------------------------------------------*) Clear[wbil, wbilv, BCwbilv]; wbil[{ii_, tout_}] := ( If[flag == -1, If[ii < 4 || ii > 9, 0, 24/1000 (g sonnenqo[[ii]] - (wbodendown[32, ts] + wglas[19, tout])) ], If[flag == 0, 24/1000 (g sonnenqo[[ii]] - (wbodendown[32, ts] + wglas[19, tout])), If[ii < 3, 24/1000 (g sonnenqo[[ii]] - (wbodendown[2, ts] + wglas[2, tout])), If[ii < 4 || ii > 9, 24/1000 (g sonnenqo[[ii]] - (wbodendown[22, ts] + wglas[19, tout])), 24/1000 (g sonnenqo[[ii]] - (wbodendown[32, ts] + wglas[19, tout])) ]]]] ); wbilv := Map[wbil, Table[{i, mtempo[[i]]}, {i, 12}]]; BCwbilv := BarChart[fb wbilv, PlotRange->{Automatic, {0, 100}}, Frame->True, GridLines->{None, Automatic}]; (* ------------------------------------------------------------------- bei Temp. des Fußbodens tF, was ist tin bei gegebenen tout? -------------------------------------------------------------------*) Clear[solv] ; solv[tout_] := Solve[wbodenup[tfu, tin] == wglas[tin, tout], tin]; Clear[mtin]; mtin[tF_] := ( tfu = tF; Flatten[ Map[solv, Table[mtemp[[i]], {i, 12}]], 1]); plottin[tf_] := ListPlot[tin/C /.mtin[tf], PlotRange->{Automatic, {-10, 90}}] (*Daten mit Einheiten verwenden*) ); defw; ;[s] 11:0,0;484,2;756,0;1144,2;1385,0;1954,1;1959,0;2786,1;2791,0;3042,1;3046,0;4201,-1; 3:6,14,9,Times,0,12,0,0,0;3,14,9,Times,1,12,0,0,0;2,13,9,Times,0,10,0,0,0; :[font = smalltext; inactive; Cclosed; dontPreserveAspect; startGroup] Näherung für tin bei festem tF (tin/.solv[tout] :[font = input; dontPreserveAspect; startGroup] Clear[tina]; tina[tF_, tout_] := (tF fb/fg(1/alphai + 1/kf[kv]) + tout/alphai)/((fb/fg + 1)/alphai + (fb/fg)/kf[kv]) :[font = message; inactive; preserveAspect; endGroup] General::spell1: Possible spelling error: new symbol name "tina" is similar to existing symbol "tin". :[font = input; dontPreserveAspect; startGroup] datax; tina[tF, tout] :[font = output; output; inactive; dontPreserveAspect; endGroup] ((fb*(alphai^(-1) + (0.75 + 0.7*kv)^(-1))*tF)/fg + tout/alphai)/((1 + fb/fg)/alphai + fb/(fg*(0.75 + 0.7*kv))) ;[o] 1 1 fb (------ + -------------) tF alphai 0.75 + 0.7 kv tout ------------------------------ + ------ fg alphai --------------------------------------- fb 1 + -- fg fb ------ + ------------------ alphai fg (0.75 + 0.7 kv) :[font = smalltext; inactive; dontPreserveAspect; endGroup; endGroup] Erklärung: (1/alphai + 1/kf[kv]) ..... Wärmeübergangs-Widerstand am Fenster = Wärmedurchgangs-Widerstand durch Grenzschicht Luft am Glas + Wärmedurchgangs-Widerstand durch Glasscheibe. Quantitativ: = 1/6 + 1/1.3 m^2 K/W für kf[kv] = 1.3 W/(m^2 K): Durchgangswiderstand durch Scheibe ist etwa 5 mal größer als der durch die Luft-Grenzschicht. = 1/6 + 1/3 m^2 K/W für kf[kv] = 3 W/(m^2 K): Durchgangswiderstand durch Scheibe ist doppelt so groß wie der durch Luft-Grenzschicht. 1/alphai ................................ Wärmedurchgangs-Widerstand am Boden = Wärmedurchgangs-Widerstand durch Grenzschicht Luft am Boden + Durchgangswiderstand durch Fliesen (letzterer ist gegenüber Grenzschichtwiderstand vernachlässigbar). fg/fb ..................................... Wärmeabgabe durch Glas- und Bodenfläche ist bezogen auf 1 m^2 Bodenfläche. Im Glashaus ist etwa 3 mal soviel Glasfläche wie Bodenfläche. ;[s] 2:0,0;12,1;1946,-1; 2:1,14,10,Geneva,4,10,0,0,0;1,14,10,Geneva,0,10,0,0,0; :[font = subtitle; inactive; Cclosed; preserveAspect; fontSize = 15; startGroup] Alt: Kurven in {g, kv} mit konstanten wbil - neu siehe Wärmestrom, Wärmeleistung - ;[s] 3:0,0;55,1;80,0;83,-1; 2:2,21,15,Geneva,3,15,0,0,0;1,25,17,Times,1,23,0,0,0; :[font = input; preserveAspect] tout=.; e1=.; e2=.; :[font = input; Cclosed; preserveAspect; startGroup] 24/1000 (g 200 - (wbodendown[32, ts] + wglas[19, tout])) :[font = output; output; inactive; preserveAspect; endGroup] (3*(-11.57142857142857 + 200*g - (1.166534496431403/(0.04 + (0.75 + 0.7*kv)^(-1)) + 1.775574940523394/(2.325714285714286 + (0.75 + 0.7*kv)^(-1)))* (19 - tout) - (6.614250594766059* (28398241/390625 - (273 + tout)^4/100000000))/ (-1 + e1^(-1) + e2^(-1))))/125 ;[o] 1.16653 1.77557 (3 (-11.5714 + 200 g - (-------------------- + -----------------------) 1 1 0.04 + ------------- 2.32571 + ------------- 0.75 + 0.7 kv 0.75 + 0.7 kv 4 28398241 (273 + tout) 6.61425 (-------- - -------------) 390625 100000000 (19 - tout) - ----------------------------------)) / 125 1 1 -1 + -- + -- e1 e2 :[font = input; preserveAspect] Clear[wbilf]; wbilf[g_, e1_, kv_] := (3*(-11.57142857142857 + 200*g - (1.166534496431403/(0.04 + (0.75 + 0.7*kv)^(-1)) + 1.775574940523394/(2.325714285714286 + (0.75 + 0.7*kv)^(-1)))* (19 - tout) - (6.614250594766059* (28398241/390625 - (273 + tout)^4/100000000))/ (-1 + e1^(-1) + e2^(-1))))/125 :[font = input; preserveAspect] Clear[cplot]; cplot[eps_] := ContourPlot[ wbilf[g, eps, kv], {g, 0.4, 0.71}, {kv, 1, 2.1}, Contours->{0.5, 0.7, 0.9, 1.1, 1.3, 1.5}]; :[font = input; preserveAspect; startGroup] tout = mtempko[[1]]; e2 = 0.96; wbilf[0.68, 0.04, 1.2] :[font = output; output; inactive; preserveAspect; endGroup] 1.318606793389441 ;[o] 1.31861 :[font = input; Cclosed; preserveAspect; startGroup] Show[cplot[0.04], kvofg[1,5]] :[font = postscript; PostScript; 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