Öz
Geçmişte olduğu gibi günümüzde de fiziksel olayların anlaşılması, doğru bir şekilde yorumlanabilmesi ve modellenmesi gelişmiş matematiksel yöntemlerin kullanılmasını gerektirir. Bu bağlamda, Newton'un soğuma yasası gibi ısı transferi problemlerinin çözümü, integral dönüşümü gibi güçlü matematiksel araçlarla karmaşık hesaplamalara gerek kalmadan, doğru, güvenilir ve kolaylıkla elde edilir. Newton'un soğuma yasası bir cismin sıcaklığının çevresel sıcaklıkla nasıl etkileşime girdiğini ve zaman içinde nasıl değiştiğini diferensiyel denklem modelleriyle ifade eder. Değişkenler ve değişim hızları arasındaki karmaşık ilişkileri ifade eden bu denklemler, fizikçilerin kesin matematiksel modeller formüle etmelerine olanak tanıyarak, fiziksel sistemlerin davranışlarına ilişkin doğru yorumlar yapılmasını sağlarlar. Diferensiyel denklemlerin çözümlerini elde etmeye yönelik hesaplamalar, cebirsel denklemlere ilişkin hesaplamalardan daha karmaşık olabilir. Bundan dolayı, bu denklemlerin çözümlerini elde etmek için farklı yöntemler kullanılmıştır. Bu makalede, Newton'un soğuma yasasının integral dönüşümlerinin bir çeşidi olan Kashuri Fundo dönüşümü ile çözümünü ve bu yaklaşımın fizik, biyokimya, ekonomi, finans, mühendislik vb. alanlarda yer alan farklı matematiksel modellerin çözümlerine ulaşmada kullanılabilecek etkili ve güvenilir bir yöntem olduğunu ortaya koyuyoruz.
Anahtar Kelimeler
İntegral Dönüşümü Kashuri Fundo Dönüşümü Newton’un Soğuma Yasası Diferensiyel Denklemler.
Kaynakça
- W.J. Palm, Y.A. Çengel, Differential Equations for Engineers and Scientists, McGraw Hill, New York, 2012.
- D.G. Zill, A First Course in Differential Equations with Modeling Applications, Cengage Learning, Boston, 2017.
- L.M. Jiji, Heat Conduction, Springer-Verlag, Berlin, 2009. doi: 10.1007/978-3-642-01267-9
- R.H.S. Winterton, Newton's law of cooling, Contemporary Physics. 40(3) (1999), 205–212. doi: 10.1080/001075199181549
- H.D. Baehr, K. Stephan, Heat and Mass Transfer, Springer-Verlag, Berlin, 2011. doi: 10.1007/978-3-642-20021-2
- L. Debnath, D. Bhatta, Integral Transforms and Their Applications, Chapman and Hall/CRC, New York, 2007.
- G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Dordrecht, 1994.
- H.J. He, Variational iteration method-a kind of non-linear analytical technique: some examples, International Journal of Non-Linear Mechanics. 34(4) (1999), 699–708. doi:10.1016/S0020-7462(98)00048-1
- S.J. Liao, The Proposed Homotopy Analysis Technique for The Solution of Non-Linear Problems, Ph.D. thesis, Shanghai Jiao Tong University, Shanghai, 1992.
- A. Kashuri, A. Fundo, A new integral transform, Advances in Theoretical and Applied Mathematics. 8(1) (2013), 27–43.
- A. Kashuri, A. Fundo, R. Liko, On double new integral transform and double Laplace transform, European Scientific Journal. 9(33) (2013), 82–90.
- N. Helmi, M. Kiftiah, B. Prihandono, Penyelesaian persamaan diferensial parsial linear dengan menggunakan metode transformasi Artion-Fundo, Buletin Ilmiah Matematika Statistika dan Terapannya. 5(3) (2016), 195–204.
- D.N. Dhange, A new integral transform and its applications in electric circuits and mechanics, Journal of Emerging Technologies and Innovative Research. 7 (11) (2020), 80-86.
- N. Dhange, A new integral transform for solution of convolution type Volterra integral equation of first kind, International Journal of Mathematics Trends and Technology. 66 (10) (2020), 52-57.
- H.A. Peker, F.A. Çuha, Application of Kashuri Fundo transform to decay problem, Süleyman Demirel University Journal of Natural and Applied Sciences. 26(3) (2022), 546–551. doi: 10.19113/sdufenbed.1160426
- H.A. Peker, F.A. Çuha, B. Peker, Kashuri Fundo transform for solving chemical reaction models, Internatıonal E-Conference On Mathematical And Statistical Sciences: A Selcuk Meeting, ICOMSS-22, Konya, 2022, 145–150.
- H.A. Peker, F.A. Cuha, B. Peker, Solving steady heat transfer problems via Kashuri Fundo transform, Thermal Science. 26(4A) (2022), 3011–3017. doi: 10.2298/TSCI2204011P
- F.A. Cuha, H.A. Peker, Solution of Abel’s integral equation by Kashuri Fundo transform, Thermal Science. 26(4A) (2022), 3003–3010. doi:10.2298/TSCI2204003C
- H.A. Peker, F.A. Çuha, Application of Kashuri Fundo Transform to Population Growth and Mixing Problem, in: Hemanth D.J., Yiğit T., Köse U., Güvenç U. (Ed.), Engineering Cyber-Physical Systems and Critical Infrastructures (ECPSCI), Springer, 2023: ss. 407-414. doi:10.1007/978-3-031-31956-3
- H.A. Peker, F.A. Çuha, Exact solutions of some basic cardiovascular models by Kashuri Fundo transform, Journal of New Theory. 43 (2023), 63-72. doi:10.53570/jnt.1267202
- F.A. Çuha, H.A. Peker, Finding solutions to undamped and damped simple harmonic oscillations via Kashuri Fundo transform, MANAS Journal of Engineering. 11(1) (2023), 154-157. doi:10.51354/mjen.1186550
- A. Kashuri, A. Fundo, M. Kreku, M., Mixture of a new integral transform and homotopy perturbation method for solving nonlinear partial differential equations, Advances in Pure Mathematics. 3 (2013), 317-323.
- K. Shah, T. Singh, A Solution of the Burger’s equation arising in the longitudinal dispersion phenomenon in fluid flow through porous media by mixture of new integral transform and homotopy perturbation method, Journal of Geoscience and Environment Protection. 3 (2015), 24-30.
- K. Shah, T. Singh, The mixture of new integral transform and homotopy perturbation method for solving discontinued problems arising in nanotechnology, Open Journal of Applied Sciences. 5 (2015), 688-695.
- K. Shah, T. Singh, B. Kılıçman, Combination of integral and projected differential transform methods for time-fractional gas dynamics equations, Ain Shams Engineering Journal, 9 (2018), 1683-1688.
- K.B. Singh, Homotopy perturbation new integral transform method for numeric study of space-and time fractional (N+1)-dimensional heat and wave-like equations, Waves Wavelets and Fractals. 4 (2018), 19-36.
- I. Sumiati, Sukono, A.T. Bon, Adomian decomposition method and the new integral transform, Proceedings of the 2nd African International Conference on Industrial Engineering and Operations Management, Harare, 2020, 1882-1887.
- H.A. Peker, F.A. Cuha, Application of Kashuri Fundo transform and homotopy perturbation methods to fractional heat transfer and porous media equations, Thermal Science. 26(4A) (2022), 2877-2884. doi:10.2298/TSCI2204877P
- M.D. Johansyah, A.K. Supriatna, E. Rusyaman, J. Saputra, Solving the economic growth acceleration model with memory effects: An application of combined theorem of Adomian decomposition methods and Kashuri–Fundo transformation methods, Symmetry. 14(2) (2022), 192.
- H.J. Kadyum, A. Al-Fayadh, Solving Schrodinger equations using Kashuri and Fundo transform decomposition method, Al-Nahrain Journal of Science. 25(2) (2022), 25-28.
- H.A. Peker, F.A. Çuha, B. Peker, Kashuri Fundo decomposition method for solving Michaelis-Menten nonlinear biochemical reaction model, MATCH Communications in Mathematical and in Computer Chemistry. 90 (2023), 315-332. doi:10.46793/match.90-2.315P
- H.A. Peker, F.A. Çuha, Solving one-dimensional Bratu’s problem via Kashuri Fundo decomposition method, Romanian Journal of Physics. 68(5/6) (2023), 109.
- D.P. Patil, D.S. Shirsath, V.S. Gangurde, Application of Soham transform in Newtons law of cooling, International Journal of Research in Engineering and Science (IJRES). 10(6) (2022), 1299-1303.
- D.P. Patil, S.A. Patil, K.J. Patil, Newton’s law of cooling by “Emad–Falih transform", International Journal of Advances in Engineering and Management (IJAEM). 4(6) (2022), 1515-1519.
- D.P. Patil, J.P. Gangurde, S.N. Wagh, T.P. Bachhav, Applications of the HY transform for Newton’s law of cooling, International Journal of Research and Analytical Reviews (IJRAR). 9(2) (2022), 740-745.
- P. Naresh, Newton's law of cooling-Laplace transform, Journal of Global Research in Mathematical Archives. 4(12) (2017), 28-34.
Öz
As in the past, understanding, correctly interpreting and modeling physical phenomena requires the use of advanced mathematical methods. In this context, the solution of heat transfer problems such as Newton's cooling law is obtained accurately, reliably and easily without the need for complex calculations with powerful mathematical tools such as integral transform. Newton's law of cooling expresses how the temperature of a body interacts with the environmental temperature and changes over time by differential equation models. These equations, expressing the complex relationships between variables and rates of change, provides accurate interpretations of the behavior of physical systems by allowing physicist formulating precise mathematical models. Calculations to obtain solutions of differential equations can be more complex than calculations for algebraic equations. Therefore, different methods have been used to get the solutions of these equations. In this article, we present the solution of Newton's cooling law with Kashuri Fundo transformation, which is a type of integral transformations, and that this approach is an effective and reliable method that can be used to reach solutions of different mathematical models in the fields of physics, biochemistry, economics, finance, engineering, etc.
Anahtar Kelimeler
Integral Transform Kashuri Fundo Transform Newton’s Law of Cooling Differential Equation
Kaynakça
- W.J. Palm, Y.A. Çengel, Differential Equations for Engineers and Scientists, McGraw Hill, New York, 2012.
- D.G. Zill, A First Course in Differential Equations with Modeling Applications, Cengage Learning, Boston, 2017.
- L.M. Jiji, Heat Conduction, Springer-Verlag, Berlin, 2009. doi: 10.1007/978-3-642-01267-9
- R.H.S. Winterton, Newton's law of cooling, Contemporary Physics. 40(3) (1999), 205–212. doi: 10.1080/001075199181549
- H.D. Baehr, K. Stephan, Heat and Mass Transfer, Springer-Verlag, Berlin, 2011. doi: 10.1007/978-3-642-20021-2
- L. Debnath, D. Bhatta, Integral Transforms and Their Applications, Chapman and Hall/CRC, New York, 2007.
- G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Dordrecht, 1994.
- H.J. He, Variational iteration method-a kind of non-linear analytical technique: some examples, International Journal of Non-Linear Mechanics. 34(4) (1999), 699–708. doi:10.1016/S0020-7462(98)00048-1
- S.J. Liao, The Proposed Homotopy Analysis Technique for The Solution of Non-Linear Problems, Ph.D. thesis, Shanghai Jiao Tong University, Shanghai, 1992.
- A. Kashuri, A. Fundo, A new integral transform, Advances in Theoretical and Applied Mathematics. 8(1) (2013), 27–43.
- A. Kashuri, A. Fundo, R. Liko, On double new integral transform and double Laplace transform, European Scientific Journal. 9(33) (2013), 82–90.
- N. Helmi, M. Kiftiah, B. Prihandono, Penyelesaian persamaan diferensial parsial linear dengan menggunakan metode transformasi Artion-Fundo, Buletin Ilmiah Matematika Statistika dan Terapannya. 5(3) (2016), 195–204.
- D.N. Dhange, A new integral transform and its applications in electric circuits and mechanics, Journal of Emerging Technologies and Innovative Research. 7 (11) (2020), 80-86.
- N. Dhange, A new integral transform for solution of convolution type Volterra integral equation of first kind, International Journal of Mathematics Trends and Technology. 66 (10) (2020), 52-57.
- H.A. Peker, F.A. Çuha, Application of Kashuri Fundo transform to decay problem, Süleyman Demirel University Journal of Natural and Applied Sciences. 26(3) (2022), 546–551. doi: 10.19113/sdufenbed.1160426
- H.A. Peker, F.A. Çuha, B. Peker, Kashuri Fundo transform for solving chemical reaction models, Internatıonal E-Conference On Mathematical And Statistical Sciences: A Selcuk Meeting, ICOMSS-22, Konya, 2022, 145–150.
- H.A. Peker, F.A. Cuha, B. Peker, Solving steady heat transfer problems via Kashuri Fundo transform, Thermal Science. 26(4A) (2022), 3011–3017. doi: 10.2298/TSCI2204011P
- F.A. Cuha, H.A. Peker, Solution of Abel’s integral equation by Kashuri Fundo transform, Thermal Science. 26(4A) (2022), 3003–3010. doi:10.2298/TSCI2204003C
- H.A. Peker, F.A. Çuha, Application of Kashuri Fundo Transform to Population Growth and Mixing Problem, in: Hemanth D.J., Yiğit T., Köse U., Güvenç U. (Ed.), Engineering Cyber-Physical Systems and Critical Infrastructures (ECPSCI), Springer, 2023: ss. 407-414. doi:10.1007/978-3-031-31956-3
- H.A. Peker, F.A. Çuha, Exact solutions of some basic cardiovascular models by Kashuri Fundo transform, Journal of New Theory. 43 (2023), 63-72. doi:10.53570/jnt.1267202
- F.A. Çuha, H.A. Peker, Finding solutions to undamped and damped simple harmonic oscillations via Kashuri Fundo transform, MANAS Journal of Engineering. 11(1) (2023), 154-157. doi:10.51354/mjen.1186550
- A. Kashuri, A. Fundo, M. Kreku, M., Mixture of a new integral transform and homotopy perturbation method for solving nonlinear partial differential equations, Advances in Pure Mathematics. 3 (2013), 317-323.
- K. Shah, T. Singh, A Solution of the Burger’s equation arising in the longitudinal dispersion phenomenon in fluid flow through porous media by mixture of new integral transform and homotopy perturbation method, Journal of Geoscience and Environment Protection. 3 (2015), 24-30.
- K. Shah, T. Singh, The mixture of new integral transform and homotopy perturbation method for solving discontinued problems arising in nanotechnology, Open Journal of Applied Sciences. 5 (2015), 688-695.
- K. Shah, T. Singh, B. Kılıçman, Combination of integral and projected differential transform methods for time-fractional gas dynamics equations, Ain Shams Engineering Journal, 9 (2018), 1683-1688.
- K.B. Singh, Homotopy perturbation new integral transform method for numeric study of space-and time fractional (N+1)-dimensional heat and wave-like equations, Waves Wavelets and Fractals. 4 (2018), 19-36.
- I. Sumiati, Sukono, A.T. Bon, Adomian decomposition method and the new integral transform, Proceedings of the 2nd African International Conference on Industrial Engineering and Operations Management, Harare, 2020, 1882-1887.
- H.A. Peker, F.A. Cuha, Application of Kashuri Fundo transform and homotopy perturbation methods to fractional heat transfer and porous media equations, Thermal Science. 26(4A) (2022), 2877-2884. doi:10.2298/TSCI2204877P
- M.D. Johansyah, A.K. Supriatna, E. Rusyaman, J. Saputra, Solving the economic growth acceleration model with memory effects: An application of combined theorem of Adomian decomposition methods and Kashuri–Fundo transformation methods, Symmetry. 14(2) (2022), 192.
- H.J. Kadyum, A. Al-Fayadh, Solving Schrodinger equations using Kashuri and Fundo transform decomposition method, Al-Nahrain Journal of Science. 25(2) (2022), 25-28.
- H.A. Peker, F.A. Çuha, B. Peker, Kashuri Fundo decomposition method for solving Michaelis-Menten nonlinear biochemical reaction model, MATCH Communications in Mathematical and in Computer Chemistry. 90 (2023), 315-332. doi:10.46793/match.90-2.315P
- H.A. Peker, F.A. Çuha, Solving one-dimensional Bratu’s problem via Kashuri Fundo decomposition method, Romanian Journal of Physics. 68(5/6) (2023), 109.
- D.P. Patil, D.S. Shirsath, V.S. Gangurde, Application of Soham transform in Newtons law of cooling, International Journal of Research in Engineering and Science (IJRES). 10(6) (2022), 1299-1303.
- D.P. Patil, S.A. Patil, K.J. Patil, Newton’s law of cooling by “Emad–Falih transform", International Journal of Advances in Engineering and Management (IJAEM). 4(6) (2022), 1515-1519.
- D.P. Patil, J.P. Gangurde, S.N. Wagh, T.P. Bachhav, Applications of the HY transform for Newton’s law of cooling, International Journal of Research and Analytical Reviews (IJRAR). 9(2) (2022), 740-745.
- P. Naresh, Newton's law of cooling-Laplace transform, Journal of Global Research in Mathematical Archives. 4(12) (2017), 28-34.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Adi Diferansiyel Denklemler, Fark Denklemleri ve Dinamik Sistemler, Akışkan Akışı, Isı ve Kütle Transferinde Hesaplamalı Yöntemler (Hesaplamalı Akışkanlar Dinamiği Dahil) |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Nisan 2024 |
| Gönderilme Tarihi | 9 Kasım 2023 |
| Kabul Tarihi | 24 Aralık 2023 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 6 Sayı: 1 |
Kaynak Göster
