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İZOLE SPİRAL KANATÇIKLARDA KESİNTİLİ ISI AKISI ALTINDA SICAKLIK DAĞILIMININ SAYISAL OLARAK HESAPLANMASI

Yıl 2025, Cilt: 28 Sayı: 3, 1512 - 1525, 03.09.2025

Nurettin Şenyer , İbrahim Keles

https://doi.org/10.17780/ksujes.1702437

Öz

Bu çalışma, izole spiral kanatçıkların kesintili ısı akısı koşulları altında gösterdiği termal davranışı sayısal olarak incelemeyi amaçlamaktadır. Özellikle analitik çözümlerin elde edilmesinin zorlaştığı süreksiz ısı yüklemeleri altında, sıcaklık dağılımının belirlenmesi için Talbot Laplace dönüşüm yöntemi uygulanmıştır. Problem, önce Laplace uzayına taşınarak çözülmüş; ardından zaman uzayına dönüş, Talbot yönteminin yüksek doğruluk potansiyelinden yararlanılarak gerçekleştirilmiştir. Doğrulama amacıyla, birim basamak ve sinüzoidal sıcaklık değişimleri içeren test fonksiyonları kullanılmış, elde edilen sayısal sonuçlar literatürdeki analitik çözümlerle karşılaştırılarak yöntemin geçerliliği test edilmiştir. Sayısal analizler sonucunda, spiral kanatçık boyunca sıcaklık dağılımının zamanla değişimi ile, malzeme ve geometrik parametrelerin termal yanıt üzerindeki etkileri grafik ve tablo formatında sunulmuştur. Elde edilen bulgular, özellikle mühendislik tasarımlarında süreksiz ısı akısı koşullarının göz önüne alınmasının önemini vurgulamakta ve Talbot yöntemi temelli Laplace dönüşüm tekniğinin bu tür problemler için güvenilir bir araç olduğunu ortaya koymaktadır.

Anahtar Kelimeler

Spiral kanatçık süreksiz ısı akısı termal tepki Laplace dönüşümü geçici ısı transferi

Kaynakça

  • Abate, J., & Valkó, P. P. (2004a). Multi-precision Laplace transform inversion. International Journal for Numerical Methods in Engineering, 60(5). https://doi.org/10.1002/nme.995, 979-993.
  • Abate, J., & Valkó, P. P. (2004b). Multi‐precision Laplace transform inversion. International Journal for Numerical Methods in Engineering, 60(5), 979-993.
  • Abate, J., & Whitt, W. (2006). A unified framework for numerically inverting Laplace transforms. INFORMS Journal on Computing, 18(4), 408-421.
  • Avdis, E., & Whitt, W. (2007). Power algorithms for inverting laplace transforms. INFORMS Journal on Computing, 19(3). https://doi.org/10.1287/ijoc.1060.0217, 341-355.
  • Cheng, C. Y., & Chen, C. K. (1994). Transient response of annular fins of various shapes subjected to constant base heat fluxes. Journal of Physics D: Applied Physics, 27(11). https://doi.org/10.1088/0022-3727/27/11/009, 2302.
  • Chu, H. S., Chen, C. K., & Weng, C. I. (1983). Transient response of circular pins. Journal of Heat Transfer, 105(1). https://doi.org/10.1115/1.3245547, 205-208.
  • Chu, H. Sen, Chen, C. K., & Weng, C. I. (1982). Applications of fourier series technique to transient heat trasfer problem. Chemical Engineering Communications, 16(1-6). https://doi.org/10.1080/00986448208911098, 215-225.
  • Chu, H. Sen, Weng, C. I., & Chen, C. K. (1983). Transient response of a composite straight fin. Journal of Heat Transfer, 105(2). https://doi.org/10.1115/1.3245579
  • D’Amore, L. (2014). Remarks on numerical algorithms for computing the inverse Laplace transform. Ricerche di Matematica, 63(2). https://doi.org/10.1007/s11587-013-0176-2, 239-252.
  • Das, R., & Kundu, B. (2017). Prediction of heat generation in a porous fin from surface temperature. Journal of Thermophysics and Heat Transfer, 31(4). https://doi.org/10.2514/1.T5098, 781-790.
  • Davies, B. (2002). Integral transforms and their applications (C. 41). Springer Science & Business Media. Durbin, F. (1974). Numerıcal ınversıon of laplace transforms: an effıcıent ımprovement to dubner and abate’s method. Computer Journal, 17(4). https://doi.org/10.1093/comjnl/17.4.371, 371-376.
  • Egonmwan, A. O. (2012). The numerical inversion of the Laplace transform. LAP Lambert Academic Publishing. Hoseinzadeh, S., Moafi, A., Shirkhani, A., & Chamkha, A. J. (2019). Numerical validation heat transfer of rectangular cross-section porous fins. Journal of Thermophysics and Heat Transfer, 33(3), 698-704.
  • Keller, H. B., & Keller, J. B. (1962). Exponential-Like Solutions of Systems of Linear Ordinary Differential Equations. Journal of the Society for Industrial and Applied Mathematics, 10(2). https://doi.org/10.1137/0110019, 246-259.
  • Kraus, A., Aziz, A., Welty, J., & Sekulic, D. (2001). Extended Surface Heat Transfer. Applied Mechanics Reviews, 54(5). https://doi.org/10.1115/1.1399680, B92-B92.
  • Kundu, B. (2017). Exact method for annular disc fins with heat generation and nonlinear heating. Journal of Thermophysics and Heat Transfer, 31(2). https://doi.org/10.2514/1.T4977, 337-345.
  • Li, J., Farquharson, C. G., & Hu, X. (2016). Three effective inverse Laplace transform algorithms for computing time-domain electromagnetic responses. Geophysics, 81(2). https://doi.org/10.1190/GEO2015-0174.1, E113-E128.
  • Mashayekhizadeh, V., Dejam, M., & Ghazanfari, M. H. (2011). The application of numerical Laplace inversion methods for type curve development in well testing: A comparative study. Petroleum Science and Technology, 29(7). https://doi.org/10.1080/10916460903394060, 695-707.
  • Redheffer, R. M., Rabenstein, A. L., Simmons, G. F., & Plaat, O. (1975). Introduction to Ordinary Differential Equations, Second Enlarged Edition with Applications. The American Mathematical Monthly, 82(9). https://doi.org/10.2307/2318518
  • Stehfest, H. (1970). Algorithm 368: Numerical inversion of Laplace transforms [D5]. Communications of the ACM, 13(1). https://doi.org/10.1145/361953.361969, 47-49.
  • Su, R. J., & Hwang, J. J. (1998). Analysis of transient heat transfer in a cylindrical pin fin. Journal of Thermophysics and Heat Transfer, 12(2). https://doi.org/10.2514/2.6334, 281-283.
  • Talbot, A. (1979a). The accurate numerical inversion of laplace transforms. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 23(1). https://doi.org/10.1093/imamat/23.1.97, 97-120.
  • Turkyilmazoglu, M. (2016). Exact heat-transfer solutions to radial fins of general profile. Journal of Thermophysics and Heat Transfer, 30(1). https://doi.org/10.2514/1.T4555, 89-93.
  • Valkó, P. P., & Abate, J. (2004). Comparison of sequence accelerators for the Gaver method of numerical laplace transform inversion. Computers and Mathematics with Applications, 48(3-4). https://doi.org/10.1016/j.camwa.2002.10.017, 629-636.
  • Valkó, P. P., & Vajda, S. (2002). Inversion of noise-free Laplace transforms: Towards a standardized set of test problems. Inverse Problems in Engineering, 10(5). https://doi.org/10.1080/10682760290004294, 467-483.
  • Vicente, P. G., García, A., & Viedma, A. (2004). Experimental investigation on heat transfer and frictional characteristics of spirally corrugated tubes in turbulent flow at different Prandtl numbers. International Journal of Heat and Mass Transfer, 47(4). https://doi.org/10.1016/j.ijheatmasstransfer.2003.08.005, 671-681.
  • Wang, J. S., Luo, W. J., & Hsu, S. P. (2008). Transient response of a spiral fin with its base subjected to the variation of heat flux. Journal of Applied Sciences, 8(10). https://doi.org/10.3923/jas.2008.1798.1811, 1798-1811.
  • Yontar, O., Aydin, K., & Keles, I. (2020). Practical jointed approach to thermal performance of functionally graded material annular fin. Journal of Thermophysics and Heat Transfer, 34(1), 144-149.

NUMERICAL DETERMINATION OF TEMPERATURE DISTRIBUTION IN ISOLATED SPIRAL FINS SUBJECTED TO INTERMITTENT HEAT FLUX

Yıl 2025, Cilt: 28 Sayı: 3, 1512 - 1525, 03.09.2025

Nurettin Şenyer , İbrahim Keles

https://doi.org/10.17780/ksujes.1702437

Öz

This study aims to numerically investigate the thermal behavior of isolated spiral fins subjected to intermittent heat flux conditions. In cases where analytical solutions become challenging due to discontinuous thermal loading, the Talbot Laplace transform method is employed to determine the temperature distribution. The problem is initially transformed into the Laplace domain, and the inverse transformation to the time domain is performed using the Talbot method, known for its high accuracy. For validation purposes, test functions involving unit step and sinusoidal temperature variations are used, and the obtained numerical results are compared with analytical solutions available in the literature to assess the method’s reliability. Numerical analyses present the time-dependent temperature distribution along the spiral fin, along with the effects of material and geometric parameters on thermal response, in both graphical and tabular formats. The findings highlight the importance of considering intermittent heat flux in engineering designs and demonstrate that the Talbot-based Laplace transform technique provides a robust approach for solving such complex thermal problems.

Anahtar Kelimeler

Spiral fin discontinuous heat flux thermal response Laplace transform transient heat transfer

Kaynakça

  • Abate, J., & Valkó, P. P. (2004a). Multi-precision Laplace transform inversion. International Journal for Numerical Methods in Engineering, 60(5). https://doi.org/10.1002/nme.995, 979-993.
  • Abate, J., & Valkó, P. P. (2004b). Multi‐precision Laplace transform inversion. International Journal for Numerical Methods in Engineering, 60(5), 979-993.
  • Abate, J., & Whitt, W. (2006). A unified framework for numerically inverting Laplace transforms. INFORMS Journal on Computing, 18(4), 408-421.
  • Avdis, E., & Whitt, W. (2007). Power algorithms for inverting laplace transforms. INFORMS Journal on Computing, 19(3). https://doi.org/10.1287/ijoc.1060.0217, 341-355.
  • Cheng, C. Y., & Chen, C. K. (1994). Transient response of annular fins of various shapes subjected to constant base heat fluxes. Journal of Physics D: Applied Physics, 27(11). https://doi.org/10.1088/0022-3727/27/11/009, 2302.
  • Chu, H. S., Chen, C. K., & Weng, C. I. (1983). Transient response of circular pins. Journal of Heat Transfer, 105(1). https://doi.org/10.1115/1.3245547, 205-208.
  • Chu, H. Sen, Chen, C. K., & Weng, C. I. (1982). Applications of fourier series technique to transient heat trasfer problem. Chemical Engineering Communications, 16(1-6). https://doi.org/10.1080/00986448208911098, 215-225.
  • Chu, H. Sen, Weng, C. I., & Chen, C. K. (1983). Transient response of a composite straight fin. Journal of Heat Transfer, 105(2). https://doi.org/10.1115/1.3245579
  • D’Amore, L. (2014). Remarks on numerical algorithms for computing the inverse Laplace transform. Ricerche di Matematica, 63(2). https://doi.org/10.1007/s11587-013-0176-2, 239-252.
  • Das, R., & Kundu, B. (2017). Prediction of heat generation in a porous fin from surface temperature. Journal of Thermophysics and Heat Transfer, 31(4). https://doi.org/10.2514/1.T5098, 781-790.
  • Davies, B. (2002). Integral transforms and their applications (C. 41). Springer Science & Business Media. Durbin, F. (1974). Numerıcal ınversıon of laplace transforms: an effıcıent ımprovement to dubner and abate’s method. Computer Journal, 17(4). https://doi.org/10.1093/comjnl/17.4.371, 371-376.
  • Egonmwan, A. O. (2012). The numerical inversion of the Laplace transform. LAP Lambert Academic Publishing. Hoseinzadeh, S., Moafi, A., Shirkhani, A., & Chamkha, A. J. (2019). Numerical validation heat transfer of rectangular cross-section porous fins. Journal of Thermophysics and Heat Transfer, 33(3), 698-704.
  • Keller, H. B., & Keller, J. B. (1962). Exponential-Like Solutions of Systems of Linear Ordinary Differential Equations. Journal of the Society for Industrial and Applied Mathematics, 10(2). https://doi.org/10.1137/0110019, 246-259.
  • Kraus, A., Aziz, A., Welty, J., & Sekulic, D. (2001). Extended Surface Heat Transfer. Applied Mechanics Reviews, 54(5). https://doi.org/10.1115/1.1399680, B92-B92.
  • Kundu, B. (2017). Exact method for annular disc fins with heat generation and nonlinear heating. Journal of Thermophysics and Heat Transfer, 31(2). https://doi.org/10.2514/1.T4977, 337-345.
  • Li, J., Farquharson, C. G., & Hu, X. (2016). Three effective inverse Laplace transform algorithms for computing time-domain electromagnetic responses. Geophysics, 81(2). https://doi.org/10.1190/GEO2015-0174.1, E113-E128.
  • Mashayekhizadeh, V., Dejam, M., & Ghazanfari, M. H. (2011). The application of numerical Laplace inversion methods for type curve development in well testing: A comparative study. Petroleum Science and Technology, 29(7). https://doi.org/10.1080/10916460903394060, 695-707.
  • Redheffer, R. M., Rabenstein, A. L., Simmons, G. F., & Plaat, O. (1975). Introduction to Ordinary Differential Equations, Second Enlarged Edition with Applications. The American Mathematical Monthly, 82(9). https://doi.org/10.2307/2318518
  • Stehfest, H. (1970). Algorithm 368: Numerical inversion of Laplace transforms [D5]. Communications of the ACM, 13(1). https://doi.org/10.1145/361953.361969, 47-49.
  • Su, R. J., & Hwang, J. J. (1998). Analysis of transient heat transfer in a cylindrical pin fin. Journal of Thermophysics and Heat Transfer, 12(2). https://doi.org/10.2514/2.6334, 281-283.
  • Talbot, A. (1979a). The accurate numerical inversion of laplace transforms. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 23(1). https://doi.org/10.1093/imamat/23.1.97, 97-120.
  • Turkyilmazoglu, M. (2016). Exact heat-transfer solutions to radial fins of general profile. Journal of Thermophysics and Heat Transfer, 30(1). https://doi.org/10.2514/1.T4555, 89-93.
  • Valkó, P. P., & Abate, J. (2004). Comparison of sequence accelerators for the Gaver method of numerical laplace transform inversion. Computers and Mathematics with Applications, 48(3-4). https://doi.org/10.1016/j.camwa.2002.10.017, 629-636.
  • Valkó, P. P., & Vajda, S. (2002). Inversion of noise-free Laplace transforms: Towards a standardized set of test problems. Inverse Problems in Engineering, 10(5). https://doi.org/10.1080/10682760290004294, 467-483.
  • Vicente, P. G., García, A., & Viedma, A. (2004). Experimental investigation on heat transfer and frictional characteristics of spirally corrugated tubes in turbulent flow at different Prandtl numbers. International Journal of Heat and Mass Transfer, 47(4). https://doi.org/10.1016/j.ijheatmasstransfer.2003.08.005, 671-681.
  • Wang, J. S., Luo, W. J., & Hsu, S. P. (2008). Transient response of a spiral fin with its base subjected to the variation of heat flux. Journal of Applied Sciences, 8(10). https://doi.org/10.3923/jas.2008.1798.1811, 1798-1811.
  • Yontar, O., Aydin, K., & Keles, I. (2020). Practical jointed approach to thermal performance of functionally graded material annular fin. Journal of Thermophysics and Heat Transfer, 34(1), 144-149.
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Makine Mühendisliğinde Sayısal Yöntemler
Bölüm Makine Mühendisliği
Yazarlar

Nurettin Şenyer 0000-0002-2324-9285

İbrahim Keles 0000-0001-8252-2635

Yayımlanma Tarihi 3 Eylül 2025
Gönderilme Tarihi 20 Mayıs 2025
Kabul Tarihi 7 Ağustos 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 28 Sayı: 3

Kaynak Göster

APA Şenyer, N., & Keles, İ. (2025). İZOLE SPİRAL KANATÇIKLARDA KESİNTİLİ ISI AKISI ALTINDA SICAKLIK DAĞILIMININ SAYISAL OLARAK HESAPLANMASI. Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi, 28(3), 1512-1525. https://doi.org/10.17780/ksujes.1702437
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