COMPARISON OF METHODS FOR SOLVING THE HEAT TRANSFER IN ELECTRICAL MACHINES

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1 POZNAN UNIVE RSITY OF TE CHNOLOGY ACADE MIC JOURNALS No 75 Electical Engineeing 2013 Zbynek MAKKI* Macel JANDA* Ramia DEEB* COMPARISON OF METHODS FOR SOLVING THE HEAT TRANSFER IN ELECTRICAL MACHINES This pape descibes the use of moden computational methods fo the veification of mathematical equations, to detemine the total heat flow tansmitted acoss a cetain suface. ANSYS WORKBENCH is choosen as the computational softwae fo this pupose. Calculations ae pesented fo fou models. Thee is a suface, which the total heat flow is tansmitted though is consideed as: a simple flat plate, compising with othe flat plate, and thinwalled and thickwalled tube. Fo each case, the total heat flow is calculated using numeical methods and moden compute methods (ANSYS WORBENCH). Pefomed esults of numeical methods ae compaed with the esults of ANSYS softwae. The numeical methods ae consideed as a efeent. The eo of ANSYS calculations in compaison with the the numeical is calculated. The heat tansfe by conduction is descibed fo all pesented models. Finally, the esults of tempeatue distibution and heat flux distibution fo each simulated case ae pesented Simple flat plate 1. INTRODUCTION Fo the numeical we have to use Fouie s laws. Fouie's law is an empiical law based on obsevation. It states that the ate of heat flow dq/dt, though a homogeneous solid is diectly popotional to the aea A, of the section at ight angles to the diection of heat flow, and to the tempeatue diffeence along the path of heat flow, dt/dx i.e. [1]. Fo simple flat plate applies equation = λ ( T T )A (1) Q S 1 2 x whee Qs is numeical total heat flow tansmitted acoss a cetain suface [J], λ is themal conductivity [W/m.K], x is wall thickness [m], T 1 is tempeatue of hot wall [K], T 2 is tempeatue of cold wall [K] and A is heat flow aea [m 2 ] [3]. * Bno Univesity of Technology.

2 26 Zbynek Makki, Macel Janda, Ramia Deeb Fig. 1. Case of simply flat plate [2] 1.2. Flat plate compising with othe flat plate In this case we combined two mateials (steel and cupum) with diffeent thickness. Fig. 2. Case of flat plate compising with othe flat plate [2] Fo this case applies equation Q S ( T1 T3) A = (2) x1 x2 λ + λ Thinwalled and thickwalled tube In this case is impotant atio between the adius 1 and adius 2. When is this atio lowe than 1.5 ( 1 / 2 <1.5) is it thinwalled tube and applies this equation [3]

3 Compaison of methods fo solving the heat tansfe in electical machines Q S = π λ. L( T1 T2) (3) 2 1 whee L is length of tube [m]. When is this atio uppe than 1.5 ( 1 / 2 > 1.5) is it thickwalled tube and applies this equation [3] 2π. λ. L Q S = ( T1 T2) (4) 2 ln 1 Fig. 3. Case of thinwalled and thickwalled tube [2] 2. CALCULATION PARAMETERS Each calculation of the numeical and compute have set hot wall on value K and cold wall on value K. Used mateial in case of Simple flat plate, thinwalled and thickwalled tube is steel with themal conduction 60.5 W/m.K and in case of flat plate compising with othe flat plate is steel as fist mateial with the same paametes as fist case and cupum as second mateial with themal conduction 400 W/m.K. Thinwalled and thickwalled tube is solved as decomposed simple flat plate. Simple flat plate, flat plate compising with othe flat plate, thinwalled and thickwalled tube of esults is divided into thee pats. Fist (a) is change thickness steel plate in case of simple flat plate and flat plate compise with othe flat plate fom 0.1 to 1 m. In case of thinwalled tube we change thickness fom 0.05 to 0.3. And in case of thickwalled tube fom 0.75 to 1.9 m. Second pat (b) is change tempeatue T1 fom to K fo each model. And thid pat (c) is change tempeatue T2 fom to K fo each model.

4 28 Zbynek Makki, Macel Janda, Ramia Deeb 3. RESULTS 3.1. Simple flat plate Table 3.1. Simple flat plate, (a) change thickness steel plate, (b) change tempeatue T 1 and (c) change tempeatue T 2 Eo Eo Eo , ,00 0, , ,00 0, , ,00 0, , ,00 0, , ,00 0, , ,00 0, , ,00 0, , ,00 0, , ,00 0, , ,15 0, , ,00 0, , ,00 0, , ,00 0, , ,00 0, , ,00 0, , ,39 0, , ,00 0,00 Fig. 4. Change thickness steel plate fo simply flat plate

5 Compaison of methods fo solving the heat tansfe in electical machines 29 Fig. 5. Change tempeatue T 1 and T 2 fo simply flat plate 3.2. Flat plate compising with othe flat plate Table 3.2. Flat plate compising with othe flat plate, (a) change thickness steel plate, (b) change tempeatue T 1 and (c) change tempeatue T 2 Eo Eo Eo , ,1 6 0, , ,60 0, , ,60 0, , ,06 0, , ,49 0, , ,49 0, , ,34 0, , ,39 0, , ,39 0, , ,75 0, , ,29 0, , ,29 0, , ,07 0, , ,19 0, , ,19 0, , ,33 0, , ,48 0,01

6 30 Zbynek Makki, Macel Janda, Ramia Deeb 3.3. Thinwalled tube Table 3.3. Thinwalled tube, (a) change thickness steel plate, (b) change tempeatue T 1 and (c) change tempeatue T 2 Eo Numeica l Eo Numeica l , ,41 1, , , , , , , , , , ,47 1, , , , , , , , , , , , ,87 0, , , , , , ,54 0, , , , , Thickwalled tube Table 3.4. Thickwalled tube, (a) change thickness steel plate, (b) change tempeatue T 1 and (c) change tempeatue T 2 Eo 1,11 Eo Eo Eo 19024, ,90 1, , ,86 2, , ,86 2, , ,03 1, , ,67 2, , ,67 2, , ,48 2, , ,48 2, , ,48 2, , ,18 3, , ,28 2, , ,28 2, , ,72 1, , ,09 2, , ,09 2, , , ,02

7 Compaison of methods fo solving the heat tansfe in electical machines CONCLUSION When changing thickness of the mateial in case is obtained simple flat plate diffeence between the values calculated using the numeical method and ANSYS Wokbench 0% (in fact, this diffeence is about 1x106%). In the second case fo flat plate compising with othe flat plate is obtained the diffeence between the values calculated using the numeical method and ANSYS Wokbench maximum 0.05%. In this case we can see the effect of two mateials with diffeent themal conductivities. In the thid case fo thinwalled tube is the diffeence maximum 1.32%. And in the last case fo Thickwalled tube maximum eo was 3.34%. All esults show that with inceasing thickness of the mateial deceases nonlinealy heat flow. When changing tempeatue T 1 o T 2 we can see linea change in heat flow with tempeatue. All eos between the numeical and the compute came out small, so we can say that ANSYS Wokbench is a suitable to these poblems. ACKNOWLEDGEMENTS Reseach descibed in this pape was financed by the Gant agency CR No. GACR: 102/09/18775 and Ministy of industy and tade of the Czech Republic unde pojects No. FRTI1/067 and FRTI3/073. The wok was suppoted by Cente fo Reseach and utilization of enewable enegy CZ.1.05/2.1.00/ REFERENCES [1] Fouie's Law of Conduction. In: Fouie's Law of Conduction [online] [cit ]. Dostupné z: [2] Sdílení tepla a poudění. Ostava: Ediční středisko VŠBTU, ISBN [3] Přenos tepla a látky. Bno: Akademické nakladatelství CERM, ISBN [4] ASHGRIZ, N. Handbook of Atomization and Spays: Theoy and Applications. Canada: Spinge. ISBN [5] BURGESS, William, Michael ELLENBECKER a Robet TREITMAN. VENTILATION FOR CONTROL OF THE WORK ENVIRONMENT. ISBN X. [6] KREITH, Fank. The CRC Handbook of Themal Engineeing. CRC Pess LLC, ISBN X.

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