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