Newton'un Soğutma Yasası Denkleminin Kashuri Fundo Dönüşümü ile Analitik Çözümü

Year 2024, , 10 - 20, 30.04.2024

Bilge Peker , Fatma Aybike Çuha , Haldun Alpaslan Peker

https://doi.org/10.47112/neufmbd.2024.29

Abstract

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.

Keywords

İntegral Dönüşümü, Kashuri Fundo Dönüşümü, Newton’un Soğuma Yasası, Diferensiyel Denklemler.

Analytical Solution of Newton's Law of Cooling Equation via Kashuri Fundo Transform

Abstract

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.

Keywords

Integral Transform, Kashuri Fundo Transform, Newton’s Law of Cooling, Differential Equation

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