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 (Journal of Physics: Theories and Applications, 2025)
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.