Non-steady state heat transport: a practical case of a microscopic energy balance in a vegetable

In this paper, the analytical and numerical solutions of a non-steady state mathematical model are developed and analyzed. The mathematical model development of a non-steady state heat transport for a one-dimensional system is shown, and the analytical solution of the model is presented. The numerical solution of the model, using the finite element method (FEM), is compared to its analytical solution, proving its consistency. One of the advantages of using numerical tools is that more complex solutions can be obtained, even if the corresponding analytical solution does not exist or is not known, which is useful for engineering students. To demonstrate the applications and possibilities of this work, it is shown that changing the boundary conditions, geometry, or dimension in the system and the mathematical model, it can be solved through a numerical solution method. This is easier and more comprehensive for students rather than facing the complexity of the analytical solutions. The paper shows that it is possible to use the FEM in a university teaching context to complementarily explain the underlying physical phenomena of an engineering problem, here applied to a heat transfer problem in a vegetable.

Automated summary

This paper develops and analyzes the analytical and numerical solutions of a non-steady state mathematical model. It demonstrates the consistency between the analytical solution and the numerical solution obtained using the finite element method (FEM). The use of numerical tools allows for obtaining complex solutions even when an analytical solution is not available, which is advantageous for engineering students. The paper also showcases the application of numerical solution method in solving system and mathematical model variations.