Modified time-dependent linear thermal expansion equation: using Inhomogeneous 1-D heat equation

Muhammad Rizka Taufani, Adam Hadiana Aminudin, Endah Nur Syamsiah, Keiichi Yoshua Togatorop

Abstract

The correction factor must be derived from the results of the linear thermal expansion experiment. We have two ways to address this problem: we use the form of polynomials for the linear thermal coefficient, and one must solve the one-dimensional heat diffusion equation. The temperature function that we obtained is the solution for the inhomogeneous differential equation. Using those two, then combine them into a modified linear thermal expansion equation, i.e., the infinitesimal form of the equation, so that we could find the expression for the time-dependent expansion for the metal rod, . We should attempt to reduce the higher-order terms by taking the approximation as our first step in this paper. Finally, the observer may choose a suitable boundary condition for the formula and use the resulting equation as the correction factor.

Keywords

linear expansion coefficient; heat diffusion; inhomogeneous boundary condition; Fourier series solution

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References

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DOI: https://doi.org/10.20961/jphystheor-appl.v9i2.110756

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