2018年高教社杯全國大學生數(shù)學建模競賽題目 A題

高溫作業(yè)專用服裝設(shè)計C

2018年高教社杯全國大學生數(shù)學建模競賽題目高溫作業(yè)專用服裝設(shè)計C

（請先閱讀“全國大學生數(shù)學建模競賽論文格式規(guī)范”）

A題

在高溫環(huán)境下工作時，人們需要穿著專用服裝以避免灼傷。專用服裝通常由三層織物材料構(gòu)成，記為I、II、III層，其中I層與外界環(huán)境接觸，III層與皮膚之間還存在空隙，將此空隙記為IV層。為設(shè)計專用服裝，將體內(nèi)溫度控制在37oC的假人放置在實驗室的高溫環(huán)境中，測量假人皮膚外側(cè)的溫度。為了降低研發(fā)成本、縮短研發(fā)周期，請你們利用數(shù)學模型來確定假人皮膚外側(cè)的溫度變化情況，并解決以下問題：(1)專用服裝材料的某些參數(shù)值由附件1給出，對環(huán)境溫度為75oC、II層厚度為6mm、IV層厚度為5mm、工作時間為90分鐘的情形開展實驗，測量得到假人皮膚外側(cè)的溫度（見附件2）。建立數(shù)學模型，計算溫度分布，并生成溫度分布的Excel文件（文件名為problem1.xlsx）。(2)當環(huán)境溫度為65oC、IV層的厚度為5.5mm時，確定II層的最優(yōu)厚度，確保工作60分鐘時，假人皮膚外側(cè)溫度不超過47oC，且超過44oC的時間不超過5分鐘。

(3)當環(huán)境溫度為80時，確定II層和IV層的最優(yōu)厚度，確保工作30分

鐘時，假人皮膚外側(cè)溫度不超過47oC，且超過44oC的時間不超過5分鐘。

附件1.專用服裝材料的參數(shù)值附件2.假人皮膚外側(cè)的測量溫度

密度(kg/m3)30086274.21.18比熱熱傳導率(J/(kg·oC)密度(kg/m3)30086274.21.18比熱熱傳導率(J/(kg·oC))(W/(m·oC))13770.08221000.3717260.04510050.028厚度(mm)0.60.6-253.60.6-6.4

分層

I層II層III層IV層

附件2.假人皮膚外側(cè)的測量溫度時間(s)溫度(C)037.00137.00237.00337.00437.00537.00637.00737.00837.00937.001037.001137.001237.001337.001437.001537.001637.011737.011837.011937.012037.022137.022237.032337.032437.042537.052637.062737.072837.082937.093037.103137.123237.133337.153437.163537.183637.203737.223837.243937.264037.28

37.3137.3337.3637.3837.3137.3337.3637.3837.4137.4437.4637.4937.5237.5537.5837.6137.6537.6837.7137.7437.7837.8137.8537.8837.9137.9537.9938.0238.0638.0938.1338.1738.2038.2438.2838.3238.3538.3938.4338.4738.5038.5438.5838.6238.6538.6938.73424344454647484950515253545556575859606162636465666768697071727374757677787980818283

38.7738.8138.8438.8838.7738.8138.8438.8838.9238.9638.9939.0339.0739.1139.1439.1839.2239.2639.2939.3339.3739.4039.4439.4839.5239.5539.5939.6239.6639.7039.7339.7739.8039.8439.8739.9139.9539.9840.0240.0540.0940.1240.1540.1940.2240.2640.29858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126

40.3240.3640.3940.4340.3240.3640.3940.4340.4640.4940.5240.5640.5940.6240.6640.6940.7240.7540.7840.8240.8540.8840.9140.9440.9741.0041.0341.0741.1041.1341.1641.1941.2241.2541.2841.3141.3441.3741.4041.4241.4541.4841.5141.5441.5741.6041.63128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169

41.6541.6841.7141.7441.6541.6841.7141.7441.7741.7941.8241.8541.8841.9041.9341.9641.9842.0142.0442.0642.0942.1242.1442.1742.1942.2242.2542.2742.3042.3242.3542.3742.4042.4242.4542.4742.5042.5242.5442.5742.5942.6242.6442.6742.6942.7142.74171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212

42.7642.7842.8142.8342.7642.7842.8142.8342.8542.8742.9042.9242.9442.9742.9943.0143.0343.0543.0843.1043.1243.1443.1643.1943.2143.2343.2543.2743.2943.3143.3343.3543.3743.4043.4243.4443.4643.4843.5043.5243.5443.5643.5843.6043.6243.6443.66214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255

43.6743.6943.7143.7343.6743.6943.7143.7343.7543.7743.7943.8143.8343.8543.8643.8843.9043.9243.9443.9643.9743.9944.0144.0344.0544.0644.0844.1044.1244.1344.1544.1744.1844.2044.2244.2444.2544.2744.2944.3044.3244.3444.3544.3744.3844.4044.42257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298

44.4344.4544.4644.4844.4344.4544.4644.4844.5044.5144.5344.5444.5644.5744.5944.6144.6244.6444.6544.6744.6844.7044.7144.7344.7444.7544.7744.7844.8044.8144.8344.8444.8644.8744.8844.9044.9144.9344.9444.9544.9744.9844.9945.0145.0245.0345.05300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341

45.0645.0745.0945.1045.0645.0745.0945.1045.1145.1345.1445.1545.1745.1845.1945.2045.2245.2345.2445.2545.2745.2845.2945.3045.3145.3345.3445.3545.3645.3845.3945.4045.4145.4245.4345.4545.4645.4745.4845.4945.5045.5145.5345.5445.5545.5645.57343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384

45.5845.5945.6045.6145.5845.5945.6045.6145.6245.6445.6545.6645.6745.6845.6945.7045.7145.7245.7345.7445.7545.7645.7745.7845.7945.8045.8145.8245.8345.8445.8545.8645.8745.8845.8945.9045.9145.9245.9345.9445.9545.9645.9745.9745.9845.9946.00386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427

46.0146.0246.0346.0446.0146.0246.0346.0446.0546.0646.0746.0746.0846.0946.1046.1146.1246.1346.1346.1446.1546.1646.1746.1846.1946.1946.2046.2146.2246.2346.2346.2446.2546.2646.2746.2746.2846.2946.3046.3146.3146.3246.3346.3446.3546.3546.36429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470

46.3746.3846.3846.3946.3746.3846.3846.3946.4046.4146.4146.4246.4346.4346.4446.4546.4646.4646.4746.4846.4846.4946.5046.5146.5146.5246.5346.5346.5446.5546.5546.5646.5746.5746.5846.5946.5946.6046.6146.6146.6246.6346.6346.6446.6446.6546.66472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513

46.6646.6746.6846.6846.6646.6746.6846.6846.6946.6946.7046.7146.7146.7246.7246.7346.7446.7446.7546.7546.7646.7746.7746.7846.7846.7946.7946.8046.8146.8146.8246.8246.8346.8346.8446.8446.8546.8546.8646.8746.8746.8846.8846.8946.8946.9046.90515516517518519520521522523524525526527528529530531532533534535536537538539540541542543544545546547548549550551552553554555556

46.9146.9146.9246.9246.9146.9146.9246.9246.9346.9346.9446.9446.9546.9546.9646.9646.9746.9746.9846.9846.9946.9947.0047.0047.0147.0147.0247.0247.0347.0347.0347.0447.0447.0547.0547.0647.0647.0747.0747.0847.0847.0847.0947.0947.1047.1047.11558559560561562563564565566567568569570571572573574575576577578579580581582583584585586587588589590591592593594595596597598599

47.1147.1147.1247.1247.1147.1147.1247.1247.1347.1347.1447.1447.1447.1547.1547.1647.1647.1647.1747.1747.1847.1847.1847.1947.1947.2047.2047.2047.2147.2147.2247.2247.2247.2347.2347.2347.2447.2447.2547.2547.2547.2647.2647.2647.2747.2747.27601602603604605606607608609610611612613614615616617618619620621622623624625626627628629630631632633634635636637638639640641642

47.2847.2847.2847.2947.2847.2847.2847.2947.2947.3047.3047.3047.3147.3147.3147.3247.3247.3247.3347.3347.3347.3447.3447.3447.3547.3547.3547.3647.3647.3647.3647.3747.3747.3747.3847.3847.3847.3947.3947.3947.4047.4047.4047.4047.4147.4147.41644645646647648649650651652653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683684685

47.4247.4247.4247.4347.4247.4247.4247.4347.4347.4347.4347.4447.4447.4447.4547.4547.4547.4547.4647.4647.4647.4647.4747.4747.4747.4847.4847.4847.4847.4947.4947.4947.4947.5047.5047.5047.5047.5147.5147.5147.5147.5247.5247.5247.5247.5347.53687688689690691692693694695696697698699700701702703704705706707708709710711712713714715716717718719720721722723724725726727728

47.5347.5347.5447.5447.5347.5347.5447.5447.5447.5447.5547.5547.5547.5547.5647.5647.5647.5647.5647.5747.5747.5747.5747.5847.5847.5847.5847.5847.5947.5947.5947.5947.6047.6047.6047.6047.6047.6147.6147.6147.6147.6147.6247.6247.6247.6247.62730731732733734735736737738739740741742743744745746747748749750751752753754755756757758759760761762763764765766767768769770771

47.6347.6347.6347.6347.6347.6347.6347.6347.6347.6447.6447.6447.6447.6447.6547.6547.6547.6547.6547.6647.6647.6647.6647.6647.6747.6747.6747.6747.6747.6747.6847.6847.6847.6847.6847.6847.6947.6947.6947.6947.6947.7047.7047.7047.7047.7047.70773774775776777778779780781782783784785786787788789790791792793794795796797798799800801802803804805806807808809810811812813814

47.7147.7147.7147.7147.7147.7147.7147.7147.7147.7147.7247.7247.7247.7247.7247.7247.7247.7347.7347.7347.7347.7347.7347.7447.7447.7447.7447.7447.7447.7447.7547.7547.7547.7547.7547.7547.7647.7647.7647.7647.7647.7647.7647.7747.7747.7747.77816817818819820821822823824825826827828829830831832833834835836837838839840841842843844845846847848849850851852853854855856857

47.7747.7747.7747.7747.7747.7747.7747.7747.7847.7847.7847.7847.7847.7847.7847.7947.7947.7947.7947.7947.7947.7947.7947.8047.8047.8047.8047.8047.8047.8047.8047.8147.8147.8147.8147.8147.8147.8147.8147.8247.8247.8247.8247.8247.8247.8247.82859860861862863864865866867868869870871872873874875876877878879880881882883884885886887888889890891892893894895896897898899900

47.8247.8347.8347.8347.8247.8347.8347.8347.8347.8347.8347.8347.8347.8347.8447.8447.8447.8447.8447.8447.8447.8447.8447.8547.8547.8547.8547.8547.8547.8547.8547.8547.8547.8647.8647.8647.8647.8647.8647.8647.8647.8647.8647.8747.8747.8747.87902903904905906907908909910911912913914915916917918919920921922923924925926927928929930931932933934935936937938939940941942943

47.8747.8747.8747.8747.8747.8747.8747.8747.8747.8747.8747.8847.8847.8847.8847.8847.8847.8847.8847.8847.8847.8847.8947.8947.8947.8947.8947.8947.8947.8947.8947.8947.8947.9047.9047.9047.9047.9047.9047.9047.9047.9047.9047.9047.9047.9047.91945946947948949950951952953954955956957958959960961962963964965966967968969970971972973974975976977978979980981982983984985986

47.9147.9147.9147.9147.9147.9147.9147.9147.9147.9147.9147.9147.9147.9147.9147.9147.9247.9247.9247.9247.9247.9247.9247.9247.9247.9247.9247.9247.9247.9347.9347.9347.9347.9347.9347.9347.9347.9347.9347.9347.9347.9347.9347.9347.9447.9447.94988989990991992993994995996997998999100010011002100310041005100610071008100910101011101210131014101510161017101810191020102110221023102410251026102710281029

47.9447.9447.9447.9447.9447.9447.9447.9447.9447.9447.9447.9447.9447.9447.9447.9447.9447.9547.9547.9547.9547.9547.9547.9547.9547.9547.9547.9547.9547.9547.9547.9547.9547.9547.9647.9647.9647.9647.9647.9647.9647.9647.9647.9647.9647.9647.96103110321033103410351036103710381039104010411042104310441045104610471048104910501051105210531054105510561057105810591060106110621063106410651066106710681069107010711072

47.9647.9647.9647.9647.9647.9647.9647.9647.9647.9747.9747.9747.9747.9747.9747.9747.9747.9747.9747.9747.9747.9747.9747.9747.9747.9747.9747.9747.9747.9847.9847.9847.9847.9847.9847.9847.9847.9847.9847.9847.9847.9847.9847.9847.9847.9847.98107410751076107710781079108010811082108310841085108610871088108910901091109210931094109510961097109810991100110111021103110411051106110711081109111011111112111311141115

47.9847.9847.9847.9847.9847.9847.9847.9847.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9947.9948.0048.0048.0048.0048.0048.0048.0048.0048.0048.0048.0048.0048.0048.0048.00111711181119112011211122112311241125112611271128112911301131113211331134113511361137113811391140114111421143114411451146114711481149115011511152115311541155115611571158

48.0048.0048.0048.0048.0048.0048.0048.0048.0048.0048.0048.0048.0048.0048.0048.0048.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.0148.02116011611162116311641165116611671168116911701171117211731174117511761177117811791180118111821183118411851186118711881189119011911192119311941195119611971198119912001201

48.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0248.0348.0348.0348.0348.0348.0348.0348.0348.03120312041205120612071208120912101211121212131214121512161217121812191220122112221223122412251226122712281229123012311232123312341235123612371238123912401241124212431244

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