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Dikey Salınımlı Düz Bir Levhadan Karışık Taşınım Isı Transferinde Yığılmış Heterojen Topluluk Öğrenme Modeli

Yıl 2023, Cilt: 6 Sayı: 1, 635 - 654, 10.03.2023
https://doi.org/10.47495/okufbed.1100651

Öz

Bu çalışmada, hareketli dikey düz bir levhadan karışık taşınım ısı transferinin etkileri deneysel ve yığılmış heterojen topluluk öğrenme yaklaşımı ile analiz edildi. Deneysel çalışmada, boyutsuz salınım genliği (Ao), boyutsuz salınım frekansı (Wo) ve Rayleigh sayısının (Ra) doğal ve zorlanmış taşınım üzerindeki etkileri incelendi. Deneylerde, levhanın dikey hareketi volan-motor düzeneği ile sağlandı. Hareketli levha ve sabit levha yüzeyi üzerinde ortalama Nusselt sayıları (Nu) elde edildi. Ayrıca, bu çalışma, tek tabanlı algoritmalar (Gradient Boosting, AdaBoost, Multilayer Perceptron) ve yığılmış heterojen topluluk öğrenme modeli kullanarak hareketli bir düz plakanın ısı transfer tahminine odaklanmıştır. Tek tabanlı algoritmaların ve yığılmış topluluk modelinin istatistiksel performansı karışık taşınım ısı transferi tahmininde ölçülmüştür. Sonuçlar, yığılmış topluluk modelinin MSE = 2.01, RMSE = 1.42, MAE = 1.1 ve R2 = 0.99 değerlerini verdiğini göstermektedir. Genel olarak, bu çalışma, önerilen yığılmış topluluk makine öğrenme modelinin, hareketli bir levhanın taşınım ısı transferini modellemek için başarıyla kullanılabileceğini ortaya koymaktadır.

Kaynakça

  • Abdelatief MA., Zamel AA., Ahmed SA. Elliptic tube free convection augmentation: an experimental and ANN numerical approach. International Communications in Heat and Mass Transfer, 2019; 108: 104296.
  • Akcay S., Akdag U., Palancioglu H. Experimental investigation of mixed convection on an oscillating vertical flat plate. International Communications in Heat and Mass Transfer 2020; 113: 104528.
  • Akdag U., Akcay S. Demiral D. Heat transfer enhancement with laminar pulsating nanofluid flow in a wavy channel. International Communications in Heat and Mass Transfer 2014; 59: 17–23.
  • Akdag U., Akcay S., Demiral D. and Palancioglu, H. Experimental investigation of heat transfer with a transversely pulsating jet on a flat plate. Journal of Thermal Science and Technology 2018; 38(2): 63-74.
  • Akdag U., Komur MA. Ozguc F. Estimation of heat transfer in oscillating annular flow using artificial neural networks. Advances in Engineering Software 2009; 40: 864–870.
  • Akdag U., Komur MA., Akcay S. Prediction of heat transfer on a flat plate subjected to a transversely pulsating jet using artificial neural networks. Applied Thermal Engineering 2016; 100: 412–420.
  • Akhgar A., Toghrai D., Sina N., Afrand M. Developing dissimilar artificial neural networks (ANNs) to prediction the thermal conductivity of MWCNT-TiO2/water-ethylene glycol hybrid nanofluid. Powder Technology 2019; 355: 602–610.
  • Alkanhal TA. Comprehensive investigation of reduced graphene oxide (rGO) in the base fuid: thermal analysis and ANN modeling. Journal of Thermal Analysis and Calorimetry 2021; 144: 2605–2614.
  • Ashafa S., Ahmed AA., Sakir AA. Analytical solution of the effect of MHD inclination and unsteady heat transfer in a laminar, transition and turbulent flow of a basic gaseous micro-flow past a vertically moving oscillating plate. American Journal of Engineering & Natural Sciences 2017; 1(2): 30–35.
  • Buyrukoğlu G., Buyrukoğlu S. Topalcengiz Z. Comparing regression models with count data to artificial neural network and ensemble models for prediction of generic escherichia coli population in agricultural ponds based on weather station measurements. Microbial Risk Analysis 2021; 100171.
  • Chicco D., Warrens MJ., Jurman G. The coefficient of determination r-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation. PeerJ Computer Science 2021; 7: e623
  • Cortell R. Flow and heat transfer in a moving fluid over a moving flat surface. Theoretical and Computational Fluid Dynamics 2007; 21(6): 435–446.
  • Ghritlahre HK., Prasad RK. Prediction of heat transfer of two different types of roughened solar air heater using artificial neural network technique. Thermal Science and Engineering Progress 2018; 8: 145-153.
  • Gomaa H., Al Taweel AM. Effect of oscillatory motion on heat transfer at vertical flat surfaces. International Journal of Heat and Mass Transfer 2005; 48(8): 1494–1504.
  • Holman JP. Experimental methods for engineers. McGraw-Hill, New York, USA; 2001.
  • Hughes MT., Fronk BM., Garimella S. Universal condensation heat transfer and pressure drop model and the role of machine learning techniques to improve predictive capabilities. International Journal of Heat and Mass Transfer 2021; 179: 121712.
  • Kalogirou SA. Prediction of flat-plate collector performance parameters using artificial neural networks. Solar Energy 2006; 80(3): 248-259.
  • Khalaj AH., Chaibakhsh A., Sayyaadi H., Nasr MRJ. Thermo-hydraulic behavior modeling of passive heat transfer enhancement techniques using a soft computing approach. Chemical Engineering Communications 2014; 201(1): 53–71.
  • Khalid A., Khan I., Shafie S. Free convection flow of micropolar fluids over an oscillating vertical plate. Malaysian Journal of Fundamental and Applied Sciences 2017; 13(4): 654–658.
  • Khan D., Khan A., Khan I., Ali F., Karim Fl., Tlili I. Effects of relative magnetic field, chemical reaction, heat generation and newtonian heating on convection flow of casson fluid over a moving vertical plate embedded in a porous medium. Scientific Reports 2019; 9:400.
  • Koffi M., Andreopoulos Y., Jiji L. Heat transfer enhancement by induced vortices in the vicinity of a rotationally oscillating heated plate. International Journal of Heat and Mass Transfer 2017; 112: 862–875.
  • Koroleva AP., Kuzmenkov NV., Frantcuzov MS. Application of machine learning methods for investigating the heat transfer enhancement performance in a circular tube with artificial roughness. In Journal of Physics: Conference Series 2020; 1675(1): 012008.
  • Lee S., Chiou J., Cyue G. Mixed convection in a square enclosure with a rotating flat plate. International Journal of Heat and Mass Transfer, 2019; 131: 807-814.
  • Malika M., Sonawane SS. Application of RSM and ANN for the prediction and optimization of thermal conductivity ratio of water based Fe2O3 coated SiC hybrid nanofluid. International Communications in Heat and Mass Transfer 2021; 126: 10535.
  • Mehta K., Mehta N., Patel V. Experimental investigation of the thermal performance of closed loop flat plate oscillating heat pipe. Experimental Heat Transfer 2021; 34(1): 85-103.
  • Mirzaei M., Mohiabadi MZ. Neural network modelling for accurate prediction of thermal efficiency of a flat plate solar collector working with nanofluids. International Journal of Ambient Energy 2021; 42(2): 227-237.
  • Mohanraj M., Jayaraj S. Muraleedharan C. Applications of Artificial Neural Networks for Thermal Analysis of Heat Exchangers: A Review. International Journal of Thermal Sciences 2015; 90: 150-172.
  • Natekin A., Knoll A. Gradient boosting machines, A tutorial. Frontiers in Neuro-Robotics 2013; 7: 21.
  • Neethu TS., Areekara S., Mathew A. Statistical approach on 3D hydromagnetic flow of water‐based nanofluid between two vertical porous plates moving in opposite directions. Heat Transfer 2021; 50: 5170–5197.
  • Pare A., Ghosh SK. A unique thermal conductivity model (ANN) for nanofluid based on experimental study. Powder Technology 2021; 377: 429-438.
  • Patil PM., Roy M., Roy S., Momoniat E. Triple diffusive mixed convection along a vertically moving surface. International Journal of Heat and Mass Transfer 2018; 117: 287–295.
  • Pradhan B., Das SS., Paul AK., Dash RC. Unsteady free convection flow of a viscous incompressible polar fluid past a semi-infinite vertical porous moving plate. International Journal of Applied Engineering Research 2017; 12(21): 10958–10963.
  • Sarhan AR., Karim MR., Kadhim ZK., Naser J. Experimental investigation on the effect of vertical vibration on thermal performances of rectangular flat plate. Experimental Thermal and Fluid Science 2019; 101: 231-240.
  • Serrano D., Golpour I. Sánchez-Delgado S. Predicting the Effect of bed materials in bubbling fluidized bed gasification using artificial neural networks (ANNs) modeling approach. Fuel 2020; 266: 117021.
  • Shah NA., Ahmed N., Elnaqeeb T., Rashidi MM. Magneto hydrodynamic free convection flows with thermal memory over a moving vertical plate in porous medium. Journal of Applied and Computational Mechanics 2019; 5(1): 150–161.
  • Sozen A. Arcaklioglu E. Exergy analysis of an ejector-absorption heat transformer using artificial neural network approach. Applied Thermal Engineering 2007; 27(2-3): 481-491.
  • Srivastava N., Hinton G., Krizhevsky A., Sutskever I., Salakhutdinov R. Dropout: A simple way to prevent neural networks from overfitting. Journal of Machine Learning Research 2014; 15(1): 1929-1958.
  • Subhashini SV., Sumathi R. Dual solutions of a mixed convection flow of nanofluids over a moving vertical plate. International Journal of Heat and Mass Transfer 2014; 71: 117–124.
  • Tafarroj MM., Mahian O., Kasaeian A., Sakamatapan K., Dalkilic AS., Wongwises, S. Artificial neural network modeling of nanofluid flow in a microchannel heat sink using experimental data. International Communications in Heat and Mass Transfer 2017; 86: 25–31
  • Tang J., Deng C. Huang GB. Extreme learning machine for multilayer perceptron. IEEE Transactions on Neural Networks and Learning Systems 2015; 27(4): 809-821.
  • Uddin MJ., Khan WA., Ismail AIM. Similarity solution of double diffusive free convective flow over a moving vertical flat plate with convective boundary condition. Ain Shams Engineering Journal 2015; 6(3): 1105–1112.
  • Yang KT. Artificial Neural Networks (ANNs): A new paradigm for thermal science and engineering. Journal of Heat Transfer 2008; 130(9): 093001.
  • Zhou ZH. Ensemble learning. In Machine Learning, Springer, Singapore, 2021; 181-210.

Stacked Heterogeneous Ensemble Learning Model in Mixed Convection Heat Transfer from a Vertically Oscillating Flat Plate

Yıl 2023, Cilt: 6 Sayı: 1, 635 - 654, 10.03.2023
https://doi.org/10.47495/okufbed.1100651

Öz

In this study, the effects of mixed convection heat transfer from a moving vertical flat plate with an experimental and stacked heterogeneous ensemble learning approach are analyzed. In the experimental work, the effects on both natural and forced convection of dimensionless oscillation amplitude (Ao), dimensionless oscillation frequency (Wo) and Rayleigh number (Ra) are investigated. In the experiments, the vertical movement of the plate is provided by a flywheel-motor assembly. The average Nusselt numbers (Nu) on the fixed plate and the moving plate surface were obtained. Additionally, this study is focused on the prediction of heat transfer of a moving flat plate using single-based algorithms (Gradient Boosting, AdaBoost, Multilayer Per-ceptron) and a stacked heterogeneous ensemble learning model. The statistical per-formance of the single-based algorithms and the stacked ensemble model is meas-ured in the prediction of mixed convection heat transfer. The results show that the stacked-based ensemble learning model yielded the MSE = 2.01, RMSE = 1.42, MAE = 1.1 and R2 = 0.99 values. Overall, this study reveals that the proposed stacked en-semble machine learning model can be used successfully for modeling convection heat transfer of a moving plate.

Kaynakça

  • Abdelatief MA., Zamel AA., Ahmed SA. Elliptic tube free convection augmentation: an experimental and ANN numerical approach. International Communications in Heat and Mass Transfer, 2019; 108: 104296.
  • Akcay S., Akdag U., Palancioglu H. Experimental investigation of mixed convection on an oscillating vertical flat plate. International Communications in Heat and Mass Transfer 2020; 113: 104528.
  • Akdag U., Akcay S. Demiral D. Heat transfer enhancement with laminar pulsating nanofluid flow in a wavy channel. International Communications in Heat and Mass Transfer 2014; 59: 17–23.
  • Akdag U., Akcay S., Demiral D. and Palancioglu, H. Experimental investigation of heat transfer with a transversely pulsating jet on a flat plate. Journal of Thermal Science and Technology 2018; 38(2): 63-74.
  • Akdag U., Komur MA. Ozguc F. Estimation of heat transfer in oscillating annular flow using artificial neural networks. Advances in Engineering Software 2009; 40: 864–870.
  • Akdag U., Komur MA., Akcay S. Prediction of heat transfer on a flat plate subjected to a transversely pulsating jet using artificial neural networks. Applied Thermal Engineering 2016; 100: 412–420.
  • Akhgar A., Toghrai D., Sina N., Afrand M. Developing dissimilar artificial neural networks (ANNs) to prediction the thermal conductivity of MWCNT-TiO2/water-ethylene glycol hybrid nanofluid. Powder Technology 2019; 355: 602–610.
  • Alkanhal TA. Comprehensive investigation of reduced graphene oxide (rGO) in the base fuid: thermal analysis and ANN modeling. Journal of Thermal Analysis and Calorimetry 2021; 144: 2605–2614.
  • Ashafa S., Ahmed AA., Sakir AA. Analytical solution of the effect of MHD inclination and unsteady heat transfer in a laminar, transition and turbulent flow of a basic gaseous micro-flow past a vertically moving oscillating plate. American Journal of Engineering & Natural Sciences 2017; 1(2): 30–35.
  • Buyrukoğlu G., Buyrukoğlu S. Topalcengiz Z. Comparing regression models with count data to artificial neural network and ensemble models for prediction of generic escherichia coli population in agricultural ponds based on weather station measurements. Microbial Risk Analysis 2021; 100171.
  • Chicco D., Warrens MJ., Jurman G. The coefficient of determination r-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation. PeerJ Computer Science 2021; 7: e623
  • Cortell R. Flow and heat transfer in a moving fluid over a moving flat surface. Theoretical and Computational Fluid Dynamics 2007; 21(6): 435–446.
  • Ghritlahre HK., Prasad RK. Prediction of heat transfer of two different types of roughened solar air heater using artificial neural network technique. Thermal Science and Engineering Progress 2018; 8: 145-153.
  • Gomaa H., Al Taweel AM. Effect of oscillatory motion on heat transfer at vertical flat surfaces. International Journal of Heat and Mass Transfer 2005; 48(8): 1494–1504.
  • Holman JP. Experimental methods for engineers. McGraw-Hill, New York, USA; 2001.
  • Hughes MT., Fronk BM., Garimella S. Universal condensation heat transfer and pressure drop model and the role of machine learning techniques to improve predictive capabilities. International Journal of Heat and Mass Transfer 2021; 179: 121712.
  • Kalogirou SA. Prediction of flat-plate collector performance parameters using artificial neural networks. Solar Energy 2006; 80(3): 248-259.
  • Khalaj AH., Chaibakhsh A., Sayyaadi H., Nasr MRJ. Thermo-hydraulic behavior modeling of passive heat transfer enhancement techniques using a soft computing approach. Chemical Engineering Communications 2014; 201(1): 53–71.
  • Khalid A., Khan I., Shafie S. Free convection flow of micropolar fluids over an oscillating vertical plate. Malaysian Journal of Fundamental and Applied Sciences 2017; 13(4): 654–658.
  • Khan D., Khan A., Khan I., Ali F., Karim Fl., Tlili I. Effects of relative magnetic field, chemical reaction, heat generation and newtonian heating on convection flow of casson fluid over a moving vertical plate embedded in a porous medium. Scientific Reports 2019; 9:400.
  • Koffi M., Andreopoulos Y., Jiji L. Heat transfer enhancement by induced vortices in the vicinity of a rotationally oscillating heated plate. International Journal of Heat and Mass Transfer 2017; 112: 862–875.
  • Koroleva AP., Kuzmenkov NV., Frantcuzov MS. Application of machine learning methods for investigating the heat transfer enhancement performance in a circular tube with artificial roughness. In Journal of Physics: Conference Series 2020; 1675(1): 012008.
  • Lee S., Chiou J., Cyue G. Mixed convection in a square enclosure with a rotating flat plate. International Journal of Heat and Mass Transfer, 2019; 131: 807-814.
  • Malika M., Sonawane SS. Application of RSM and ANN for the prediction and optimization of thermal conductivity ratio of water based Fe2O3 coated SiC hybrid nanofluid. International Communications in Heat and Mass Transfer 2021; 126: 10535.
  • Mehta K., Mehta N., Patel V. Experimental investigation of the thermal performance of closed loop flat plate oscillating heat pipe. Experimental Heat Transfer 2021; 34(1): 85-103.
  • Mirzaei M., Mohiabadi MZ. Neural network modelling for accurate prediction of thermal efficiency of a flat plate solar collector working with nanofluids. International Journal of Ambient Energy 2021; 42(2): 227-237.
  • Mohanraj M., Jayaraj S. Muraleedharan C. Applications of Artificial Neural Networks for Thermal Analysis of Heat Exchangers: A Review. International Journal of Thermal Sciences 2015; 90: 150-172.
  • Natekin A., Knoll A. Gradient boosting machines, A tutorial. Frontiers in Neuro-Robotics 2013; 7: 21.
  • Neethu TS., Areekara S., Mathew A. Statistical approach on 3D hydromagnetic flow of water‐based nanofluid between two vertical porous plates moving in opposite directions. Heat Transfer 2021; 50: 5170–5197.
  • Pare A., Ghosh SK. A unique thermal conductivity model (ANN) for nanofluid based on experimental study. Powder Technology 2021; 377: 429-438.
  • Patil PM., Roy M., Roy S., Momoniat E. Triple diffusive mixed convection along a vertically moving surface. International Journal of Heat and Mass Transfer 2018; 117: 287–295.
  • Pradhan B., Das SS., Paul AK., Dash RC. Unsteady free convection flow of a viscous incompressible polar fluid past a semi-infinite vertical porous moving plate. International Journal of Applied Engineering Research 2017; 12(21): 10958–10963.
  • Sarhan AR., Karim MR., Kadhim ZK., Naser J. Experimental investigation on the effect of vertical vibration on thermal performances of rectangular flat plate. Experimental Thermal and Fluid Science 2019; 101: 231-240.
  • Serrano D., Golpour I. Sánchez-Delgado S. Predicting the Effect of bed materials in bubbling fluidized bed gasification using artificial neural networks (ANNs) modeling approach. Fuel 2020; 266: 117021.
  • Shah NA., Ahmed N., Elnaqeeb T., Rashidi MM. Magneto hydrodynamic free convection flows with thermal memory over a moving vertical plate in porous medium. Journal of Applied and Computational Mechanics 2019; 5(1): 150–161.
  • Sozen A. Arcaklioglu E. Exergy analysis of an ejector-absorption heat transformer using artificial neural network approach. Applied Thermal Engineering 2007; 27(2-3): 481-491.
  • Srivastava N., Hinton G., Krizhevsky A., Sutskever I., Salakhutdinov R. Dropout: A simple way to prevent neural networks from overfitting. Journal of Machine Learning Research 2014; 15(1): 1929-1958.
  • Subhashini SV., Sumathi R. Dual solutions of a mixed convection flow of nanofluids over a moving vertical plate. International Journal of Heat and Mass Transfer 2014; 71: 117–124.
  • Tafarroj MM., Mahian O., Kasaeian A., Sakamatapan K., Dalkilic AS., Wongwises, S. Artificial neural network modeling of nanofluid flow in a microchannel heat sink using experimental data. International Communications in Heat and Mass Transfer 2017; 86: 25–31
  • Tang J., Deng C. Huang GB. Extreme learning machine for multilayer perceptron. IEEE Transactions on Neural Networks and Learning Systems 2015; 27(4): 809-821.
  • Uddin MJ., Khan WA., Ismail AIM. Similarity solution of double diffusive free convective flow over a moving vertical flat plate with convective boundary condition. Ain Shams Engineering Journal 2015; 6(3): 1105–1112.
  • Yang KT. Artificial Neural Networks (ANNs): A new paradigm for thermal science and engineering. Journal of Heat Transfer 2008; 130(9): 093001.
  • Zhou ZH. Ensemble learning. In Machine Learning, Springer, Singapore, 2021; 181-210.
Toplam 43 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Bilgisayar Yazılımı, Makine Mühendisliği
Bölüm Araştırma Makaleleri (RESEARCH ARTICLES)
Yazarlar

Selma Akçay 0000-0003-2654-0702

Selim Buyrukoğlu

Ünal Akdağ

Yayımlanma Tarihi 10 Mart 2023
Gönderilme Tarihi 8 Nisan 2022
Kabul Tarihi 21 Eylül 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 1

Kaynak Göster

APA Akçay, S., Buyrukoğlu, S., & Akdağ, Ü. (2023). Stacked Heterogeneous Ensemble Learning Model in Mixed Convection Heat Transfer from a Vertically Oscillating Flat Plate. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 6(1), 635-654. https://doi.org/10.47495/okufbed.1100651
AMA Akçay S, Buyrukoğlu S, Akdağ Ü. Stacked Heterogeneous Ensemble Learning Model in Mixed Convection Heat Transfer from a Vertically Oscillating Flat Plate. OKÜ Fen Bil. Ens. Dergisi ((OKU Journal of Nat. & App. Sci). Mart 2023;6(1):635-654. doi:10.47495/okufbed.1100651
Chicago Akçay, Selma, Selim Buyrukoğlu, ve Ünal Akdağ. “Stacked Heterogeneous Ensemble Learning Model in Mixed Convection Heat Transfer from a Vertically Oscillating Flat Plate”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 6, sy. 1 (Mart 2023): 635-54. https://doi.org/10.47495/okufbed.1100651.
EndNote Akçay S, Buyrukoğlu S, Akdağ Ü (01 Mart 2023) Stacked Heterogeneous Ensemble Learning Model in Mixed Convection Heat Transfer from a Vertically Oscillating Flat Plate. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 6 1 635–654.
IEEE S. Akçay, S. Buyrukoğlu, ve Ü. Akdağ, “Stacked Heterogeneous Ensemble Learning Model in Mixed Convection Heat Transfer from a Vertically Oscillating Flat Plate”, OKÜ Fen Bil. Ens. Dergisi ((OKU Journal of Nat. & App. Sci), c. 6, sy. 1, ss. 635–654, 2023, doi: 10.47495/okufbed.1100651.
ISNAD Akçay, Selma vd. “Stacked Heterogeneous Ensemble Learning Model in Mixed Convection Heat Transfer from a Vertically Oscillating Flat Plate”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 6/1 (Mart 2023), 635-654. https://doi.org/10.47495/okufbed.1100651.
JAMA Akçay S, Buyrukoğlu S, Akdağ Ü. Stacked Heterogeneous Ensemble Learning Model in Mixed Convection Heat Transfer from a Vertically Oscillating Flat Plate. OKÜ Fen Bil. Ens. Dergisi ((OKU Journal of Nat. & App. Sci). 2023;6:635–654.
MLA Akçay, Selma vd. “Stacked Heterogeneous Ensemble Learning Model in Mixed Convection Heat Transfer from a Vertically Oscillating Flat Plate”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 6, sy. 1, 2023, ss. 635-54, doi:10.47495/okufbed.1100651.
Vancouver Akçay S, Buyrukoğlu S, Akdağ Ü. Stacked Heterogeneous Ensemble Learning Model in Mixed Convection Heat Transfer from a Vertically Oscillating Flat Plate. OKÜ Fen Bil. Ens. Dergisi ((OKU Journal of Nat. & App. Sci). 2023;6(1):635-54.

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