Araştırma Makalesi
BibTex RIS Kaynak Göster

CO2 AKIŞKANININ KAYNAMALI AKIŞ REJİMİNDE ISI TRANSFERİ KATSAYISININ ÇOKLU REGRESYON YÖNTEMİ İLE TAHMİNLENMESİ

Yıl 2023, , 179 - 193, 29.06.2023
https://doi.org/10.55071/ticaretfbd.1230594

Öz

Teknolojinin gelişmesi ile performansı artan ve boyutu küçülen elektronik cihazların yaydıkları ısı artmış olup ihtiyaç duyulan soğutma yükü çok yüksek değerlere ulaşmıştır. Bu soğutma yükünü karşılayabilmek için kullanılan geleneksel soğutucu akışkanların performansları, iyi olmasına rağmen küresel ısınma katsayıları ve ozon tabakası hasar potansiyel katsayıları yüksektir. Çeşitli uluslararası protokoller ve antlaşmalarla, bu geleneksel soğutucu akışkanların kullanımlarında küresel çapta kısıtlamaya gidilmiştir. Bu nedenle, araştırmacılar alternatif, çevre dostu soğutucu akışkanlar üzerine çalışmalar yapmaya başlamıştır. CO2 akışkanı zehirli olmaması, küresel ısınma katsayısının 1 olması, ozon tabakası hasar potansiyel katsayısının 0 olması ve kaynamalı akış rejiminde yüksek performans sergilemesi sebebiyle, geleneksel akışkanlara rakip olarak öne çıkmaktadır. Fakat CO2’nin diğer akışkanlardan farklı termo-fiziksel özelliklere sahip olması sebebiyle, literatürde CO2 için kaynamalı akış rejiminde ısı transfer katsayısını yüksek doğruluk oranında veren bir korelasyona rastlanmamıştır. Bu çalışmada, farklı çap borularda, kaynamalı akış rejiminde bulunan CO2 akışkanı ile yapılmış çalışmalardan alınan 1084 satır veri ile çoklu regresyon modeli ile ısı transfer katsayısı tahmini yapılmıştır. Bu amaçla 26 değişken analiz edilmiş ve aralarındaki korelasyon incelenmiştir. Sonuçlar literatüre dayalı olarak tartışılarak öneriler kısmında sunulmuştur.

Destekleyen Kurum

Marmara Üniversitesi BAP birimi

Proje Numarası

FYL-2022-10426

Teşekkür

Bu çalışma Marmara Üniversitesi BAP birimi tarafından FYL-2022-10426 kodlu proje tarafından desteklenmiştir.

Kaynakça

  • Al-Zaidi, A. H., Mahmoud, M. M., & Karayiannis, T. G. (2022). Flow boiling in copper and aluminium microchannels. International Journal of Heat and Mass Transfer, 194, 123101, 1-18. https://doi.org/10.1016/j.ijheatmasstransfer.2022.123101.
  • Arslan, B., & Ertuğrul, İ. (2022). Çoklu Regresyon, arima ve yapay sinir ağı yöntemleri ile türkiye elektrik piyasasında fiyat tahmin ve analizi. Journal of Management and Economics Research, 20(1), 331-353. http://dx.doi.org/10.11611/yead.988146.
  • Ayvaz, B., & Kusakci, A. O. (2017). Electricity consumption forecasting for Turkey with nonhomogeneous discrete grey model. Energy Sources, Part B: Economics, Planning, and Policy, 12(3), 260-267. http://dx.doi.org/10.1080/15567249.2015.1089337.
  • Bansal, P. K., & Zhao, X. (2007, Mayıs, 28-31). Flow boiling heat transfer of CO2 at low temperatures-a critical review. 7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim. Norveç.
  • Bruno, F., Belusko, M., & Halawa, E. (2019). CO2 refrigeration and heat pump systems—a comprehensive review. Energies, 12(15), 2959. https://doi.org/10.3390/en12152959.
  • Chen, S., Mao, J., & Han, X. (2016). Heat transfer analysis of a vertical ground heat exchanger using numerical simulation and multiple regression model. Energy and Buildings, 129, 81-91. https://doi.org/10.1016/j.enbuild.2016.07.010
  • Cheng, L., Ribatski, G., & Thome, J. R. (2008). New prediction methods for CO2 evaporation inside tubes: Part II—An updated general flow boiling heat transfer model based on flow patterns. International Journal of Heat and Mass Transfer, 51(1-2), 125-135. https://doi.org/10.1016/j.ijheatmasstransfer.2007.04.001.
  • Cheng, L., Xia, G., & Thome, J. R. (2021). Flow boiling heat transfer and two-phase flow phenomena of CO2 in macro-and micro-channel evaporators: Fundamentals, applications and engineering design. Applied Thermal Engineering, 195, 117070. https://doi.org/10.1016/j.applthermaleng.2021.117070.
  • Di Filippo, R., Bursi, O. S., & Di Maggio, R. (2022). Global warming and ozone depletion potentials caused by emissions from HFC and CFC banks due to structural damage. Energy and Buildings, 273, 112385. https://doi.org/10.1016/j.enbuild.2022.112385.
  • Dönmez, N.P. (2012). In tube evaporation of carbon dioxide with and without oil [Doktora tezi]. İstanbul Teknik Üniversitesi Fen Bilimleri Enstitüsü. İstanbul.
  • Eygü, H. & Kılınç, A. (2020). Oecd Ülkelerinin Lojistik Performans Endekslerinin Ridge Regresyon Analizi ile Araştırılması. Trakya Üniversitesi Sosyal Bilimler Dergisi, 22(2), 899-919. https://doi.org/10.26468/trakyasobed.688737.
  • Fang, X., Zhou, Z., & Li, D. (2013a). Review of correlations of flow boiling heat transfer coefficients for carbon dioxide. International Journal of Refrigeration, 36(8), 2017-2039. http://dx.doi.org/10.1016/j.ijrefrig.2013.05.015.
  • Fang, X. (2013b). A new correlation of flow boiling heat transfer coefficients for carbon dioxide. International Journal of Heat and Mass Transfer, 64, 802-807. https://doi.org/10.1016/j.ijheatmasstransfer.2013.05.024.
  • Grauso, S., Mastrullo, R., Mauro, A. W., & Vanoli, G. P. (2011). CO2 and propane blends: Experiments and assessment of predictive methods for flow boiling in horizontal tubes. International Journal of Refrigeration, 34(4), 1028-1039. https://doi.org/10.1016/j.ijrefrig.2011.03.001.
  • Jiang, L., Liu, J., Zhang, L., Liu, Q., & Xu, X. (2017). Characteristics of heat transfer for CO2 flow boiling at low temperature in mini-channel. International Journal of Heat and Mass Transfer, 108, 2120-2129. https://doi.org/10.1016/j.ijheatmasstransfer.2016.12.113.
  • Jianxin, P., & Yigang, L. (2009). Estimation of the surface tension of liquid carbon dioxide. Physics and Chemistry of Liquids, 47(3), 267-273. https://doi.org/10.1080/00319100701824389.
  • Kalayci, S. (2014). SPSS uygulamali cok degiskenli istatistik teknikleri (6. Baski). Asil Yayın Dağıtım, Ankara.
  • Kayakuş, M., & Terzioğlu, M. (2021). Yapay sinir ağları ve çoklu doğrusal regresyon kullanarak emeklilik fonu net varlık değerlerinin tahmin edilmesi. Bilişim Teknolojileri Dergisi, 14(1), 95-103. https://doi.org/10.17671/gazibtd.742995.
  • Kim, S., & Hrnjak, P. S. (2012, Temmuz, 16-19). Effect of oil on flow boiling heat transfer and flow patterns of CO2 in 11.2 mm horizontal smooth and enhanced tube, International Refrigeration and Air Conditioning Conference. Indiana. 2519-2528.
  • Li, W., Zheng, B., Lv, T., & Ayub, Z. (2020). A modified correlation for flow boiling heat transfer in plate heat exchangers. Journal of Thermal Science and Engineering Applications, 12(6), 6-14. https://doi.org/10.1115/1.4046786.
  • Mastrullo, R., Mauro, A. W., Rosato, A., & Vanoli, G. P. (2010). Carbon dioxide heat transfer coefficients and pressure drops during flow boiling: Assessment of predictive methods. International Journal of Refrigeration, 33(6), 1068-1085. https://doi.org/10.1016/j.ijrefrig.2010.04.005.
  • Mistral (2022). Mistral Programs for Refrigeration & Air Conditioning Professionals başlığı ile https://www.mistralassociates.com/co2_temperature_pressure_enthalpy_entropy_viscosity.html adresinden 21 Aralık 2022 tarihinde alınmıştır.
  • Oh, H. K., & Son, C. H. (2011). Flow boiling heat transfer and pressure drop characteristics of CO2 in horizontal tube of 4.57-mm inner diameter. Applied Thermal Engineering, 31(2-3), 163-172. https://doi.org/10.1016/j.applthermaleng.2010.08.026.
  • Oh, J. T., Pamitran, A. S., Choi, K. I., & Hrnjak, P. (2011). Experimental investigation on two-phase flow boiling heat transfer of five refrigerants in horizontal small tubes of 0.5, 1.5 and 3.0 mm inner diameters. International Journal of Heat and Mass Transfer. 54(9-10), 2080-2088. https://doi.org/10.1016/j.ijheatmasstransfer.2010.12.021.
  • Özdemir, M.R. (2016). Single-phase flow and flow boiling of water in rectangular metallic microchannels [Doktora tezi]. Brunel University London Graduate School. London.
  • Parahovnik, A., & Peles, Y. (2022). High pressure saturated flow boiling of CO2 at the micro scale. International Journal of Heat and Mass Transfer, 86, 122449. https://doi.org/10.1016/j.ijheatmasstransfer.2021.1224490017-9310.
  • Park, C. Y., & Hrnjak, P. S. (2007). CO2 and R410A flow boiling heat transfer, pressure drop, and flow pattern at low temperatures in a horizontal smooth tube. International Journal of Refrigeration. 30(1), 166-178. https://doi.org/10.1016/j.ijrefrig.2006.08.007.
  • Scalabrin, G., Marchi, P., Finezzo, F., & Span, R. (2006). A reference multiparameter thermal conductivity equation for carbon dioxide with an optimized functional form. Journal of Physical and Chemical Reference data, 35(4), 1549-1575. https://doi.org/10.1063/1.2213631.
  • Span, R., & Wagner, W. (1996). A new equation of state for carbon dioxide covering the fluid region from the triple‐point temperature to 1100 K at pressures up to 800 MPa. Journal of Physical and Chemical Reference Data. 25(6), 1509-1596. https://doi.org/10.1063/1.555991.
  • Tabachnick, B.G., Fidell, L.S. (2013). Using multivariate statistics (6th Edn.). Pearson Education, Boston.
  • Yun, R., Kim, Y., Kim, M.S. (2005). Convective boiling heat transfer characteristics of CO2 in microchannels, Int. J. Heat Mass Transfer, 48, 235–242.
  • Zhang, L., Liu, J., Yang, J., & Ge, Q. (2012, Mart, 27-29). Study of Heat Transfer for CO2 Flow Boiling in Horizontal Small Diameter Tubes, IEEE Asia-Pacific Power and Energy Engineering Conference. Şangay.1-4.
  • Zhang, J., Elmegaard, B., & Haglind, F. (2021). Condensation heat transfer and pressure drop correlations in plate heat exchangers for heat pump and organic Rankine cycle systems. Applied Thermal Engineering. 183, 116231. https://doi.org/10.1016/j.applthermaleng.2020.116231.

PREDICTION OF HEAT TRANSFER COEFFICIENT OF CO2 IN FLOW BOILING REGIME USING MULTIPLE REGRESSION METHOD

Yıl 2023, , 179 - 193, 29.06.2023
https://doi.org/10.55071/ticaretfbd.1230594

Öz

With the development of technology, the performance of electric devices has increased, and their sizes have been miniaturized. Therefore, the heat emitted by these devices has elevated, and this increased required cooling load rates. Although the cooling performance of conventional refrigerants could meet these cooling load rates, their global warming potential and ozone layer depletion coefficients are high. Accordingly, international protocols and agreements have started to restrict these traditional refrigerants globally. Therefore, researchers have begun to work on alternative, environmentally friendly refrigerants. At this point, CO2 refrigerant stands out as a competitor to conventional refrigerants due to its non-toxic feature, low global warming potential value (1), zero ozone layer depletion coefficient, and high performance in the flow boiling regime. However, there is no high-accuracy flow boiling heat transfer coefficient in the literature due to the unique thermophysical properties of CO2. In the current study, 1084 flow boiling heat transfer coefficient data of CO2 for pipes having different diameters were taken from the literature studies. The collected flow boiling heat transfer coefficient data were tried to be predicted with the multiple regression model. For this purpose, 26 variables were analyzed and the correlation between them was examined. The results were discussed based on the literature, and suggestions were presented.

Proje Numarası

FYL-2022-10426

Kaynakça

  • Al-Zaidi, A. H., Mahmoud, M. M., & Karayiannis, T. G. (2022). Flow boiling in copper and aluminium microchannels. International Journal of Heat and Mass Transfer, 194, 123101, 1-18. https://doi.org/10.1016/j.ijheatmasstransfer.2022.123101.
  • Arslan, B., & Ertuğrul, İ. (2022). Çoklu Regresyon, arima ve yapay sinir ağı yöntemleri ile türkiye elektrik piyasasında fiyat tahmin ve analizi. Journal of Management and Economics Research, 20(1), 331-353. http://dx.doi.org/10.11611/yead.988146.
  • Ayvaz, B., & Kusakci, A. O. (2017). Electricity consumption forecasting for Turkey with nonhomogeneous discrete grey model. Energy Sources, Part B: Economics, Planning, and Policy, 12(3), 260-267. http://dx.doi.org/10.1080/15567249.2015.1089337.
  • Bansal, P. K., & Zhao, X. (2007, Mayıs, 28-31). Flow boiling heat transfer of CO2 at low temperatures-a critical review. 7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim. Norveç.
  • Bruno, F., Belusko, M., & Halawa, E. (2019). CO2 refrigeration and heat pump systems—a comprehensive review. Energies, 12(15), 2959. https://doi.org/10.3390/en12152959.
  • Chen, S., Mao, J., & Han, X. (2016). Heat transfer analysis of a vertical ground heat exchanger using numerical simulation and multiple regression model. Energy and Buildings, 129, 81-91. https://doi.org/10.1016/j.enbuild.2016.07.010
  • Cheng, L., Ribatski, G., & Thome, J. R. (2008). New prediction methods for CO2 evaporation inside tubes: Part II—An updated general flow boiling heat transfer model based on flow patterns. International Journal of Heat and Mass Transfer, 51(1-2), 125-135. https://doi.org/10.1016/j.ijheatmasstransfer.2007.04.001.
  • Cheng, L., Xia, G., & Thome, J. R. (2021). Flow boiling heat transfer and two-phase flow phenomena of CO2 in macro-and micro-channel evaporators: Fundamentals, applications and engineering design. Applied Thermal Engineering, 195, 117070. https://doi.org/10.1016/j.applthermaleng.2021.117070.
  • Di Filippo, R., Bursi, O. S., & Di Maggio, R. (2022). Global warming and ozone depletion potentials caused by emissions from HFC and CFC banks due to structural damage. Energy and Buildings, 273, 112385. https://doi.org/10.1016/j.enbuild.2022.112385.
  • Dönmez, N.P. (2012). In tube evaporation of carbon dioxide with and without oil [Doktora tezi]. İstanbul Teknik Üniversitesi Fen Bilimleri Enstitüsü. İstanbul.
  • Eygü, H. & Kılınç, A. (2020). Oecd Ülkelerinin Lojistik Performans Endekslerinin Ridge Regresyon Analizi ile Araştırılması. Trakya Üniversitesi Sosyal Bilimler Dergisi, 22(2), 899-919. https://doi.org/10.26468/trakyasobed.688737.
  • Fang, X., Zhou, Z., & Li, D. (2013a). Review of correlations of flow boiling heat transfer coefficients for carbon dioxide. International Journal of Refrigeration, 36(8), 2017-2039. http://dx.doi.org/10.1016/j.ijrefrig.2013.05.015.
  • Fang, X. (2013b). A new correlation of flow boiling heat transfer coefficients for carbon dioxide. International Journal of Heat and Mass Transfer, 64, 802-807. https://doi.org/10.1016/j.ijheatmasstransfer.2013.05.024.
  • Grauso, S., Mastrullo, R., Mauro, A. W., & Vanoli, G. P. (2011). CO2 and propane blends: Experiments and assessment of predictive methods for flow boiling in horizontal tubes. International Journal of Refrigeration, 34(4), 1028-1039. https://doi.org/10.1016/j.ijrefrig.2011.03.001.
  • Jiang, L., Liu, J., Zhang, L., Liu, Q., & Xu, X. (2017). Characteristics of heat transfer for CO2 flow boiling at low temperature in mini-channel. International Journal of Heat and Mass Transfer, 108, 2120-2129. https://doi.org/10.1016/j.ijheatmasstransfer.2016.12.113.
  • Jianxin, P., & Yigang, L. (2009). Estimation of the surface tension of liquid carbon dioxide. Physics and Chemistry of Liquids, 47(3), 267-273. https://doi.org/10.1080/00319100701824389.
  • Kalayci, S. (2014). SPSS uygulamali cok degiskenli istatistik teknikleri (6. Baski). Asil Yayın Dağıtım, Ankara.
  • Kayakuş, M., & Terzioğlu, M. (2021). Yapay sinir ağları ve çoklu doğrusal regresyon kullanarak emeklilik fonu net varlık değerlerinin tahmin edilmesi. Bilişim Teknolojileri Dergisi, 14(1), 95-103. https://doi.org/10.17671/gazibtd.742995.
  • Kim, S., & Hrnjak, P. S. (2012, Temmuz, 16-19). Effect of oil on flow boiling heat transfer and flow patterns of CO2 in 11.2 mm horizontal smooth and enhanced tube, International Refrigeration and Air Conditioning Conference. Indiana. 2519-2528.
  • Li, W., Zheng, B., Lv, T., & Ayub, Z. (2020). A modified correlation for flow boiling heat transfer in plate heat exchangers. Journal of Thermal Science and Engineering Applications, 12(6), 6-14. https://doi.org/10.1115/1.4046786.
  • Mastrullo, R., Mauro, A. W., Rosato, A., & Vanoli, G. P. (2010). Carbon dioxide heat transfer coefficients and pressure drops during flow boiling: Assessment of predictive methods. International Journal of Refrigeration, 33(6), 1068-1085. https://doi.org/10.1016/j.ijrefrig.2010.04.005.
  • Mistral (2022). Mistral Programs for Refrigeration & Air Conditioning Professionals başlığı ile https://www.mistralassociates.com/co2_temperature_pressure_enthalpy_entropy_viscosity.html adresinden 21 Aralık 2022 tarihinde alınmıştır.
  • Oh, H. K., & Son, C. H. (2011). Flow boiling heat transfer and pressure drop characteristics of CO2 in horizontal tube of 4.57-mm inner diameter. Applied Thermal Engineering, 31(2-3), 163-172. https://doi.org/10.1016/j.applthermaleng.2010.08.026.
  • Oh, J. T., Pamitran, A. S., Choi, K. I., & Hrnjak, P. (2011). Experimental investigation on two-phase flow boiling heat transfer of five refrigerants in horizontal small tubes of 0.5, 1.5 and 3.0 mm inner diameters. International Journal of Heat and Mass Transfer. 54(9-10), 2080-2088. https://doi.org/10.1016/j.ijheatmasstransfer.2010.12.021.
  • Özdemir, M.R. (2016). Single-phase flow and flow boiling of water in rectangular metallic microchannels [Doktora tezi]. Brunel University London Graduate School. London.
  • Parahovnik, A., & Peles, Y. (2022). High pressure saturated flow boiling of CO2 at the micro scale. International Journal of Heat and Mass Transfer, 86, 122449. https://doi.org/10.1016/j.ijheatmasstransfer.2021.1224490017-9310.
  • Park, C. Y., & Hrnjak, P. S. (2007). CO2 and R410A flow boiling heat transfer, pressure drop, and flow pattern at low temperatures in a horizontal smooth tube. International Journal of Refrigeration. 30(1), 166-178. https://doi.org/10.1016/j.ijrefrig.2006.08.007.
  • Scalabrin, G., Marchi, P., Finezzo, F., & Span, R. (2006). A reference multiparameter thermal conductivity equation for carbon dioxide with an optimized functional form. Journal of Physical and Chemical Reference data, 35(4), 1549-1575. https://doi.org/10.1063/1.2213631.
  • Span, R., & Wagner, W. (1996). A new equation of state for carbon dioxide covering the fluid region from the triple‐point temperature to 1100 K at pressures up to 800 MPa. Journal of Physical and Chemical Reference Data. 25(6), 1509-1596. https://doi.org/10.1063/1.555991.
  • Tabachnick, B.G., Fidell, L.S. (2013). Using multivariate statistics (6th Edn.). Pearson Education, Boston.
  • Yun, R., Kim, Y., Kim, M.S. (2005). Convective boiling heat transfer characteristics of CO2 in microchannels, Int. J. Heat Mass Transfer, 48, 235–242.
  • Zhang, L., Liu, J., Yang, J., & Ge, Q. (2012, Mart, 27-29). Study of Heat Transfer for CO2 Flow Boiling in Horizontal Small Diameter Tubes, IEEE Asia-Pacific Power and Energy Engineering Conference. Şangay.1-4.
  • Zhang, J., Elmegaard, B., & Haglind, F. (2021). Condensation heat transfer and pressure drop correlations in plate heat exchangers for heat pump and organic Rankine cycle systems. Applied Thermal Engineering. 183, 116231. https://doi.org/10.1016/j.applthermaleng.2020.116231.
Toplam 33 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Araştırma Makaleleri
Yazarlar

Ahmet Korkmaz 0000-0002-8930-9316

Semih Özel 0000-0001-8281-2704

Mehmed Rafet Özdemir 0000-0002-3832-9659

Proje Numarası FYL-2022-10426
Erken Görünüm Tarihi 12 Haziran 2023
Yayımlanma Tarihi 29 Haziran 2023
Gönderilme Tarihi 6 Ocak 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Korkmaz, A., Özel, S., & Özdemir, M. R. (2023). CO2 AKIŞKANININ KAYNAMALI AKIŞ REJİMİNDE ISI TRANSFERİ KATSAYISININ ÇOKLU REGRESYON YÖNTEMİ İLE TAHMİNLENMESİ. İstanbul Commerce University Journal of Science, 22(43), 179-193. https://doi.org/10.55071/ticaretfbd.1230594
AMA Korkmaz A, Özel S, Özdemir MR. CO2 AKIŞKANININ KAYNAMALI AKIŞ REJİMİNDE ISI TRANSFERİ KATSAYISININ ÇOKLU REGRESYON YÖNTEMİ İLE TAHMİNLENMESİ. İstanbul Commerce University Journal of Science. Haziran 2023;22(43):179-193. doi:10.55071/ticaretfbd.1230594
Chicago Korkmaz, Ahmet, Semih Özel, ve Mehmed Rafet Özdemir. “CO2 AKIŞKANININ KAYNAMALI AKIŞ REJİMİNDE ISI TRANSFERİ KATSAYISININ ÇOKLU REGRESYON YÖNTEMİ İLE TAHMİNLENMESİ”. İstanbul Commerce University Journal of Science 22, sy. 43 (Haziran 2023): 179-93. https://doi.org/10.55071/ticaretfbd.1230594.
EndNote Korkmaz A, Özel S, Özdemir MR (01 Haziran 2023) CO2 AKIŞKANININ KAYNAMALI AKIŞ REJİMİNDE ISI TRANSFERİ KATSAYISININ ÇOKLU REGRESYON YÖNTEMİ İLE TAHMİNLENMESİ. İstanbul Commerce University Journal of Science 22 43 179–193.
IEEE A. Korkmaz, S. Özel, ve M. R. Özdemir, “CO2 AKIŞKANININ KAYNAMALI AKIŞ REJİMİNDE ISI TRANSFERİ KATSAYISININ ÇOKLU REGRESYON YÖNTEMİ İLE TAHMİNLENMESİ”, İstanbul Commerce University Journal of Science, c. 22, sy. 43, ss. 179–193, 2023, doi: 10.55071/ticaretfbd.1230594.
ISNAD Korkmaz, Ahmet vd. “CO2 AKIŞKANININ KAYNAMALI AKIŞ REJİMİNDE ISI TRANSFERİ KATSAYISININ ÇOKLU REGRESYON YÖNTEMİ İLE TAHMİNLENMESİ”. İstanbul Commerce University Journal of Science 22/43 (Haziran 2023), 179-193. https://doi.org/10.55071/ticaretfbd.1230594.
JAMA Korkmaz A, Özel S, Özdemir MR. CO2 AKIŞKANININ KAYNAMALI AKIŞ REJİMİNDE ISI TRANSFERİ KATSAYISININ ÇOKLU REGRESYON YÖNTEMİ İLE TAHMİNLENMESİ. İstanbul Commerce University Journal of Science. 2023;22:179–193.
MLA Korkmaz, Ahmet vd. “CO2 AKIŞKANININ KAYNAMALI AKIŞ REJİMİNDE ISI TRANSFERİ KATSAYISININ ÇOKLU REGRESYON YÖNTEMİ İLE TAHMİNLENMESİ”. İstanbul Commerce University Journal of Science, c. 22, sy. 43, 2023, ss. 179-93, doi:10.55071/ticaretfbd.1230594.
Vancouver Korkmaz A, Özel S, Özdemir MR. CO2 AKIŞKANININ KAYNAMALI AKIŞ REJİMİNDE ISI TRANSFERİ KATSAYISININ ÇOKLU REGRESYON YÖNTEMİ İLE TAHMİNLENMESİ. İstanbul Commerce University Journal of Science. 2023;22(43):179-93.