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TAM VE PARÇALI SİLİNDİRİK KANATÇIK KONFİGÜRASYONLARININ BİR MİNİKANALLI ISI ALICININ TERMOHİDROLİK PERFORMANSI ÜZERİNDEKİ ETKİLERİ

Year 2023, Volume: 26 Issue: Özel Sayı - 9th Uluslararası IFS Çağdaş Matematik ve Mühendislik Konferansı (IFSCOM-E) Özel Sayısı, 1156 - 1170, 12.12.2023

Buğra Sarper , Döndü Nur Türk , Kayhan Dağıdır , Orhan Aydın

https://doi.org/10.17780/ksujes.1340343

Abstract

Bu çalışmada, tam ve parçalı silindirik kanatçık konfigürasyonlarının bir minikanallı ısı alıcının termohidrolik performansına etkileri sayısal olarak incelenmiştir. Bu amaçla, 0.00265 kg/s ile 0.0045 kg/s aralığında dört farklı debi ve üç farklı kanatçık konumu için sayısal çalışmalar ANSYS Fluent yazılımı kullanılarak gerçekleştirilmiştir. Farklı konfigürasyonların hız ve sıcaklık alanlarına, ortalama Nusselt sayısına, Nusselt sayısı oranına, sürtünme katsayısına ve ısı alıcının performans katsayısına olan etkileri değerlendirilmiştir. Çalışma sonucunda, parçalı silindirik kanatçık kullanımının ısı transferi ve basınç düşümü üzerinde önemli etkilerinin olduğu, ısı transferi açısından değerlendirildiğinde MCHS-R2a’nın en iyi sonucu verdiği fakat bu konfigürasyonun akışa karşı olan direnci önemli ölçüde artırdığı belirlenmiştir. Termohidrolik performans açısından değerlendirildiğinde ise MCHS-R2c’nin önemli sonuçlar vadettiği ortaya konmuştur.

Keywords

Minikanallı ısı alıcı parçalı silindirik kanatçık termohidrolik performans

References

  • Abdulhaleem, A. A., Jaffal, H. M., & Khudhur, D. S. (2019). Performance optimiation of a cylindrical mini-channel heat sink using hybrid straight-wavy channel. International Journal of Thermal Sciences, 146, 106111. https://doi.org/10.1016/j.ijthermalsci.2019.106111
  • Al-Hasani, H. M., & Freegah, B. (2022). Influence of secondary flow angle and pin fin on hydro-thermal evaluation of double outlet serpentine mini-channel heat sink. Results in Engineering, 16, 100670. https://doi.org/10.1016/j.rineng.2022.100670
  • Ansys Inc. (2021). ANSYS Fluent, Release 21 R2, Theory Guide.
  • Azadi, M., Hosseinirad, E., Hormozi, F., & Rashidi, S. (2020). Second law analysis for nanofluid flow in mini-channel heat sink with finned surface: a study on fin geometries. Journal of Thermal Analysis and Calorimetry, 140(4), 1883-1895. https://doi.org/10.1007/s10973-019-08921-2
  • Bessanane, N., Si-Ameur, M., & Rebay, M. (2022). Numerical Study of the Temperature Effects on Heat Transfer Coefficient in Mini-Channel Pin-Fin Heat Sink. International Journal of Heat and Technology, 40(1), 247-257. https://doi.org/10.18280/ijht.400129
  • Bi, C., Tang, G. H., & Tao, W. Q. (2013). Heat transfer enhancement in mini-channel heat sinks with dimples and cylindrical grooves. Applied Thermal Engineering, 55(1-2), 121-132. https://doi.org/10.1016/j.applthermaleng.2013.03.007
  • Bowers, M. B., & Mudawar, I. (1994). High flux boiling in low flow rate, low pressure drop mini-channel and micro-channel heat sinks. International Journal of Heat and Mass Transfer, 37(2), 321-332. https://doi.org/10.1016/0017-9310(94)90103-1
  • Cao, X., Liu, H., Shao, X., Shen, H., & Xie, G. (2020). Thermal performance of double serpentine minichannel heat sinks: Effects of inlet-outlet arrangements and through-holes. International Journal of Heat and Mass Transfer, 153, 119575. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119575
  • Chen, Z., Feng, Z. F., Zhang, Q. Y., Zhang, J. X. & Guo, F. W. (2022). Effects of regular triangular prisms on thermal and hydraulic characteristics in a minichannel heat sink, Internatıonal Journal of Heat And Mass Transfer, 188. https://doi.org/10.1016/j.ijheatmasstransfer.2022.122583.
  • Dabrowski, P. (2020). Thermohydraulic maldistribution reduction in mini heat exchangers, Applıed Thermal Engıneerıng, 173. https://doi.org/10.1016/j.applthermaleng.2020.115271.
  • Deng, Z. Y., Shen, J., Dai, W., Liu, Y., Song, Q., Gong, W., Li, K., & Gong, M. (2020). Flow and thermal analysis of hybrid mini-channel and slot jet array heat sink. Applied Thermal Engineering, 171, 115063. https://doi.org/10.1016/j.applthermaleng.2020.115063
  • Di Maio, E., Mastrullo, R., Mauro, A. W., & Toto, D. (2014). Thermal management of a multiple mini-channel heat sink by the integration of a thermal responsive shape memory material. Applied Thermal Engineering, 62(1), 113-122. https://doi.org/10.1016/j.applthermaleng.2013.08.039
  • Ghobadi, M., & Muzychka, Y. S. (2014). Heat transfer and pressure drop in mini channel heat sinks. Heat Transfer Engineering, 36(10), 902-911. https://doi.org/10.1080/01457632.2015.965097
  • Imran, A. A., Mahmoud, N. S., & Jaffal, H. M. (2018). Numerical and experimental investigation of heat transfer in liquid cooling serpentine mini-channel heat sink with different new configuration models. Thermal Science and Engineering Progress, 6, 128-139. https://doi.org/10.1016/j.tsep.2018.03.011
  • Khdair, A. I. (2023). Numerical simulation of heat transfer of two-phase flow in mini-channel heat sink and investigation the effect of pin-fin shape on flow maldistribution. Engineering Analysis with Boundary Elements, 150, 385-393. https://doi.org/10.1016/j.enganabound.2023.02.017
  • Kilic, M., Aktas, M., Sevilgen, G., (2020). Thermal assessment of laminar flow liquid cooling blocks for led circuit boards used in automotive headlight assemblies. Energies, 13(5), 1202-1202. https://doi.org/10.3390/en13051202
  • Kim, Y., Kim, M., Ahn, C., Kim, H. U., Kang, S. W., & Kim, T. (2017). Numerical study on heat transfer and pressure drop in laminar-flow multistage mini-channel heat sink. International Journal of Heat and Mass Transfer, 108, 1197-1206. https://doi.org/10.1016/j.ijheatmasstransfer.2016.12.025
  • Kumar, S., & Singh, P. K. (2019). Effects of flow inlet angle on flow maldistribution and thermal performance of water cooled mini-channel heat sink. International Journal of Thermal Sciences, 138, 504-511. https://doi.org/10.1016/j.ijthermalsci.2019.01.014
  • Li, R. R., Zhang, Y. H., Wang, Y. F., & Wang, L. B. (2015). Convective heat-transfer characteristics of a channel with one surface having mini-grooves in the flow direction and a plain surface located at a mini-distance. IEEE Transactions on Components, Packaging and Manufacturing Technology, 5(1), 65-74. https://doi.org/10.1109/tcpmt.2014.2373054
  • Lim, K., & Lee, J. (2019). 1-D two-phase flow analysis for interlocking double layer counter flow mini channel heat sink. International Journal of Heat and Mass Transfer, 135, 305-317. https://doi.org/10.1016/j.ijheatmasstransfer.2019.01.092
  • Liu, X. Q., & Yu, J. (2016). Numerical study on performances of mini-channel heat sinks with non-uniform inlets. Applied Thermal Engineering, 93, 856-864. https://doi.org/10.1016/j.applthermaleng.2015.09.032
  • Ma, L., Zhao, X., Sun, H., Wu, Q., & Liu, W. (2016). Experimental study of single phase flow in a closed-loop cooling system with ıntegrated mini-channel heat sink. Entropy, 18(6), 128. https://doi.org/10.3390/e18060128
  • Mahmood, H., & Freegah, B. (2022). Investigating the effect of counter flow formation, ribs and dimples on the hydrothermal performance of the serpentine Mini-Channel Heat Sink (SMCHS). International Communications in Heat and Mass Transfer, 139, 106490. https://doi.org/10.1016/j.icheatmasstransfer.2022.106490
  • Mitra, I., & Ghosh, I. (2020). Mini-channel heat sink parameter sensitivity based on precise heat flux re-distribution. Thermal Science and Engineering Progress, 20, 100717. https://doi.org/10.1016/j.tsep.2020.100717
  • Naphon, P., & Wongwises, S. (2010). Investigation on the jet liquid impingement heat transfer for the central processing unit of personal computers. International Communications in Heat and Mass Transfer, 37(7), 822-826. https://doi.org/10.1016/j.icheatmasstransfer.2010.05.004
  • Saeed, M., & Kim, M. H. (2016). Numerical study on thermal hydraulic performance of water cooled mini-channel heat sinks. International Journal of Refrigeration, 69, 147-164. https://doi.org/10.1016/j.ijrefrig.2016.05.004
  • Saeed, M., & Kim, M. H. (2017). Header design approaches for mini-channel heatsinks using analytical and numerical methods. Applied Thermal Engineering, 110, 1500-1510. https://doi.org/10.1016/j.applthermaleng.2016.09.069
  • Song, J. Y., Hah, S., Kim, D., & Kim, S. M. (2019). Enhanced flow uniformity in parallel mini-channels with pin-finned inlet header, Applied Thermal Engineering, 152, 718-733. https://doi.org/10.1016/j.applthermaleng.2019.02.069
  • Tang, B., Zhou, R., Bai, P., Fu, T., Lu, L., & Zhou, G. (2017). Heat transfer performance of a novel double-layer mini-channel heat sink. Heat and Mass Transfer, 53(3), 929-936. https://doi.org/10.1007/s00231-016-1869-3
  • Tikadar A., Paul, T. C., Oudah, S. K., Abdulrazzaq, N. M., Salman, A. S., & Khan, J. A. (2020). Enhancing thermal-hydraulic performance of counter flow mini-channel heat sinks utilizing secondary flow: Numerical study with experimental validation. International Communications in Heat and Mass Transfer, 111, 104447. https://doi.org/10.1016/j.icheatmasstransfer.2019.10444
  • Tikadar, A., Oudah, S. K., Paul, T. C., Salman, A. S., Morshed, A. K. M. M., & Khan, J. A. (2019). Parametric study on thermal and hydraulic characteristics of inter-connected parallel and counter flow mini-channel heat sink. Applied Thermal Engineering, 153, 15-28. https://doi.org/10.1016/j.applthermaleng.2019.02.007
  • Wang, H. L., Wu, H. C., Wang, S. K., Hung, T. C., & Yang, R. J. (2013). A study of mini-channel thermal module design for achieving high stability and high capability in electronic cooling. Applied Thermal Engineering, 51(1-2), 1144-1153. https://doi.org/10.1016/j.applthermaleng.2012.10.007
  • Xiao, H., Liu, Z., & Liu, W. (2020). Turbulent heat transfer enhancement in the mini-channel by enhancing the original flow pattern with v-ribs. International Journal of Heat and Mass Transfer, 163, 120378. https://doi.org/10.1016/j.ijheatmasstransfer.2020.120378
  • Xu, S., Yang, L., Li, Y., Wu, Y., & Hu, X. (2016). Experimental and numerical investigation of heat transfer for two-layered microchannel heat sink with non-uniform heat flux conditions. Heat and Mass Transfer, 52(9), 1755-1763. https://doi.org/10.1007/s00231-015-1691-3
  • Zhang, Q. Y., Li, Z. Z., Feng, Z. F, Chen, Z., Zhang, J. X. & Guo, F. W. (2023). Effects of combination modes of different cavities and ribs on performance in mini-channels - A comprehensive study. International Communications in Heat and Mass Transfer, 142, 106633. https://doi.org/10.1016/j.icheatmasstransfer.2023.106633

EFFECTS OF COMPLETE AND PARTIAL CYLINDRICAL FIN CONFIGURATIONS ON THERMOHYDRAULIC PERFORMANCE OF A MINICHANNEL HEAT SINK

Year 2023, Volume: 26 Issue: Özel Sayı - 9th Uluslararası IFS Çağdaş Matematik ve Mühendislik Konferansı (IFSCOM-E) Özel Sayısı, 1156 - 1170, 12.12.2023

Buğra Sarper , Döndü Nur Türk , Kayhan Dağıdır , Orhan Aydın

https://doi.org/10.17780/ksujes.1340343

Abstract

In this numerical investigation, the impacts of complete and partial cylindrical fin configurations on the thermohydraulic performance of a minichannel heatsink are studied. ANSYS Fluent software is used to conduct numerical analyses for four distinct mass flow rates ranging from 0.00265 kg/s to 0.0045 kg/s and three distinct fin positions. The effects of various configurations on velocity and temperature fields, average Nusselt number, Nusselt number ratio, friction coefficient, and performance evaluation coefficient are analyzed. According to the study’s findings, using partial cylindrical fins has a substantial impact on both heat transfer and pressure drop. When evaluating heat transfer, MCHS-R2a produces the greatest results, but this configuration greatly raises flow resistance. MCHS-R2c was found to have substantial potential when evaluated in terms of thermohydraulic performance.

Keywords

Minichannel heat sink partial cylindrical fin thermohydraulic performance.

References

  • Abdulhaleem, A. A., Jaffal, H. M., & Khudhur, D. S. (2019). Performance optimiation of a cylindrical mini-channel heat sink using hybrid straight-wavy channel. International Journal of Thermal Sciences, 146, 106111. https://doi.org/10.1016/j.ijthermalsci.2019.106111
  • Al-Hasani, H. M., & Freegah, B. (2022). Influence of secondary flow angle and pin fin on hydro-thermal evaluation of double outlet serpentine mini-channel heat sink. Results in Engineering, 16, 100670. https://doi.org/10.1016/j.rineng.2022.100670
  • Ansys Inc. (2021). ANSYS Fluent, Release 21 R2, Theory Guide.
  • Azadi, M., Hosseinirad, E., Hormozi, F., & Rashidi, S. (2020). Second law analysis for nanofluid flow in mini-channel heat sink with finned surface: a study on fin geometries. Journal of Thermal Analysis and Calorimetry, 140(4), 1883-1895. https://doi.org/10.1007/s10973-019-08921-2
  • Bessanane, N., Si-Ameur, M., & Rebay, M. (2022). Numerical Study of the Temperature Effects on Heat Transfer Coefficient in Mini-Channel Pin-Fin Heat Sink. International Journal of Heat and Technology, 40(1), 247-257. https://doi.org/10.18280/ijht.400129
  • Bi, C., Tang, G. H., & Tao, W. Q. (2013). Heat transfer enhancement in mini-channel heat sinks with dimples and cylindrical grooves. Applied Thermal Engineering, 55(1-2), 121-132. https://doi.org/10.1016/j.applthermaleng.2013.03.007
  • Bowers, M. B., & Mudawar, I. (1994). High flux boiling in low flow rate, low pressure drop mini-channel and micro-channel heat sinks. International Journal of Heat and Mass Transfer, 37(2), 321-332. https://doi.org/10.1016/0017-9310(94)90103-1
  • Cao, X., Liu, H., Shao, X., Shen, H., & Xie, G. (2020). Thermal performance of double serpentine minichannel heat sinks: Effects of inlet-outlet arrangements and through-holes. International Journal of Heat and Mass Transfer, 153, 119575. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119575
  • Chen, Z., Feng, Z. F., Zhang, Q. Y., Zhang, J. X. & Guo, F. W. (2022). Effects of regular triangular prisms on thermal and hydraulic characteristics in a minichannel heat sink, Internatıonal Journal of Heat And Mass Transfer, 188. https://doi.org/10.1016/j.ijheatmasstransfer.2022.122583.
  • Dabrowski, P. (2020). Thermohydraulic maldistribution reduction in mini heat exchangers, Applıed Thermal Engıneerıng, 173. https://doi.org/10.1016/j.applthermaleng.2020.115271.
  • Deng, Z. Y., Shen, J., Dai, W., Liu, Y., Song, Q., Gong, W., Li, K., & Gong, M. (2020). Flow and thermal analysis of hybrid mini-channel and slot jet array heat sink. Applied Thermal Engineering, 171, 115063. https://doi.org/10.1016/j.applthermaleng.2020.115063
  • Di Maio, E., Mastrullo, R., Mauro, A. W., & Toto, D. (2014). Thermal management of a multiple mini-channel heat sink by the integration of a thermal responsive shape memory material. Applied Thermal Engineering, 62(1), 113-122. https://doi.org/10.1016/j.applthermaleng.2013.08.039
  • Ghobadi, M., & Muzychka, Y. S. (2014). Heat transfer and pressure drop in mini channel heat sinks. Heat Transfer Engineering, 36(10), 902-911. https://doi.org/10.1080/01457632.2015.965097
  • Imran, A. A., Mahmoud, N. S., & Jaffal, H. M. (2018). Numerical and experimental investigation of heat transfer in liquid cooling serpentine mini-channel heat sink with different new configuration models. Thermal Science and Engineering Progress, 6, 128-139. https://doi.org/10.1016/j.tsep.2018.03.011
  • Khdair, A. I. (2023). Numerical simulation of heat transfer of two-phase flow in mini-channel heat sink and investigation the effect of pin-fin shape on flow maldistribution. Engineering Analysis with Boundary Elements, 150, 385-393. https://doi.org/10.1016/j.enganabound.2023.02.017
  • Kilic, M., Aktas, M., Sevilgen, G., (2020). Thermal assessment of laminar flow liquid cooling blocks for led circuit boards used in automotive headlight assemblies. Energies, 13(5), 1202-1202. https://doi.org/10.3390/en13051202
  • Kim, Y., Kim, M., Ahn, C., Kim, H. U., Kang, S. W., & Kim, T. (2017). Numerical study on heat transfer and pressure drop in laminar-flow multistage mini-channel heat sink. International Journal of Heat and Mass Transfer, 108, 1197-1206. https://doi.org/10.1016/j.ijheatmasstransfer.2016.12.025
  • Kumar, S., & Singh, P. K. (2019). Effects of flow inlet angle on flow maldistribution and thermal performance of water cooled mini-channel heat sink. International Journal of Thermal Sciences, 138, 504-511. https://doi.org/10.1016/j.ijthermalsci.2019.01.014
  • Li, R. R., Zhang, Y. H., Wang, Y. F., & Wang, L. B. (2015). Convective heat-transfer characteristics of a channel with one surface having mini-grooves in the flow direction and a plain surface located at a mini-distance. IEEE Transactions on Components, Packaging and Manufacturing Technology, 5(1), 65-74. https://doi.org/10.1109/tcpmt.2014.2373054
  • Lim, K., & Lee, J. (2019). 1-D two-phase flow analysis for interlocking double layer counter flow mini channel heat sink. International Journal of Heat and Mass Transfer, 135, 305-317. https://doi.org/10.1016/j.ijheatmasstransfer.2019.01.092
  • Liu, X. Q., & Yu, J. (2016). Numerical study on performances of mini-channel heat sinks with non-uniform inlets. Applied Thermal Engineering, 93, 856-864. https://doi.org/10.1016/j.applthermaleng.2015.09.032
  • Ma, L., Zhao, X., Sun, H., Wu, Q., & Liu, W. (2016). Experimental study of single phase flow in a closed-loop cooling system with ıntegrated mini-channel heat sink. Entropy, 18(6), 128. https://doi.org/10.3390/e18060128
  • Mahmood, H., & Freegah, B. (2022). Investigating the effect of counter flow formation, ribs and dimples on the hydrothermal performance of the serpentine Mini-Channel Heat Sink (SMCHS). International Communications in Heat and Mass Transfer, 139, 106490. https://doi.org/10.1016/j.icheatmasstransfer.2022.106490
  • Mitra, I., & Ghosh, I. (2020). Mini-channel heat sink parameter sensitivity based on precise heat flux re-distribution. Thermal Science and Engineering Progress, 20, 100717. https://doi.org/10.1016/j.tsep.2020.100717
  • Naphon, P., & Wongwises, S. (2010). Investigation on the jet liquid impingement heat transfer for the central processing unit of personal computers. International Communications in Heat and Mass Transfer, 37(7), 822-826. https://doi.org/10.1016/j.icheatmasstransfer.2010.05.004
  • Saeed, M., & Kim, M. H. (2016). Numerical study on thermal hydraulic performance of water cooled mini-channel heat sinks. International Journal of Refrigeration, 69, 147-164. https://doi.org/10.1016/j.ijrefrig.2016.05.004
  • Saeed, M., & Kim, M. H. (2017). Header design approaches for mini-channel heatsinks using analytical and numerical methods. Applied Thermal Engineering, 110, 1500-1510. https://doi.org/10.1016/j.applthermaleng.2016.09.069
  • Song, J. Y., Hah, S., Kim, D., & Kim, S. M. (2019). Enhanced flow uniformity in parallel mini-channels with pin-finned inlet header, Applied Thermal Engineering, 152, 718-733. https://doi.org/10.1016/j.applthermaleng.2019.02.069
  • Tang, B., Zhou, R., Bai, P., Fu, T., Lu, L., & Zhou, G. (2017). Heat transfer performance of a novel double-layer mini-channel heat sink. Heat and Mass Transfer, 53(3), 929-936. https://doi.org/10.1007/s00231-016-1869-3
  • Tikadar A., Paul, T. C., Oudah, S. K., Abdulrazzaq, N. M., Salman, A. S., & Khan, J. A. (2020). Enhancing thermal-hydraulic performance of counter flow mini-channel heat sinks utilizing secondary flow: Numerical study with experimental validation. International Communications in Heat and Mass Transfer, 111, 104447. https://doi.org/10.1016/j.icheatmasstransfer.2019.10444
  • Tikadar, A., Oudah, S. K., Paul, T. C., Salman, A. S., Morshed, A. K. M. M., & Khan, J. A. (2019). Parametric study on thermal and hydraulic characteristics of inter-connected parallel and counter flow mini-channel heat sink. Applied Thermal Engineering, 153, 15-28. https://doi.org/10.1016/j.applthermaleng.2019.02.007
  • Wang, H. L., Wu, H. C., Wang, S. K., Hung, T. C., & Yang, R. J. (2013). A study of mini-channel thermal module design for achieving high stability and high capability in electronic cooling. Applied Thermal Engineering, 51(1-2), 1144-1153. https://doi.org/10.1016/j.applthermaleng.2012.10.007
  • Xiao, H., Liu, Z., & Liu, W. (2020). Turbulent heat transfer enhancement in the mini-channel by enhancing the original flow pattern with v-ribs. International Journal of Heat and Mass Transfer, 163, 120378. https://doi.org/10.1016/j.ijheatmasstransfer.2020.120378
  • Xu, S., Yang, L., Li, Y., Wu, Y., & Hu, X. (2016). Experimental and numerical investigation of heat transfer for two-layered microchannel heat sink with non-uniform heat flux conditions. Heat and Mass Transfer, 52(9), 1755-1763. https://doi.org/10.1007/s00231-015-1691-3
  • Zhang, Q. Y., Li, Z. Z., Feng, Z. F, Chen, Z., Zhang, J. X. & Guo, F. W. (2023). Effects of combination modes of different cavities and ribs on performance in mini-channels - A comprehensive study. International Communications in Heat and Mass Transfer, 142, 106633. https://doi.org/10.1016/j.icheatmasstransfer.2023.106633
There are 35 citations in total.

Details

Primary Language English
Subjects Energy Generation, Conversion and Storage (Excl. Chemical and Electrical), Numerical Methods in Mechanical Engineering
Journal Section Mechanical Engineering
Authors

Buğra Sarper 0000-0001-7554-6575

Döndü Nur Türk 0009-0004-4144-5361

Kayhan Dağıdır 0000-0003-0499-1764

Orhan Aydın 0000-0002-2492-8212

Publication Date December 12, 2023
Submission Date August 9, 2023
Published in Issue Year 2023Volume: 26 Issue: Özel Sayı - 9th Uluslararası IFS Çağdaş Matematik ve Mühendislik Konferansı (IFSCOM-E) Özel Sayısı

Cite

APA Sarper, B., Türk, D. N., Dağıdır, K., Aydın, O. (2023). EFFECTS OF COMPLETE AND PARTIAL CYLINDRICAL FIN CONFIGURATIONS ON THERMOHYDRAULIC PERFORMANCE OF A MINICHANNEL HEAT SINK. Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi, 26(Özel Sayı), 1156-1170. https://doi.org/10.17780/ksujes.1340343
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