2025 ASEE Annual Conference & Exposition

The introductory thermodynamics course in undergraduate mechanical engineering programs teaches students the fundamental principles, laws of physics, and the application of these principles to solve real-world problems. Solving thermodynamic problems not only helps students understand the science of energy but also strengthens their critical thinking skills. However, as problems become more complex and realistic, analyzing them can become tedious, often requiring the derivation and solution of numerous simultaneous equations. This complexity is especially evident in transient systems where mass, energy, and entropy balances can lead to a combination of linear and non-linear equations, depending on the system's parameters.

Despite the widespread use of MATLAB in engineering education for various applications, there is a notable lack of literature focusing on its use for non-linear analysis of thermodynamic systems. This gap highlights the need for resources and studies that demonstrate how MATLAB can be effectively employed to simplify and solve complex thermodynamic problems involving non-linearities. By addressing this gap, educators and students can leverage MATLAB's powerful computational capabilities to enhance understanding and efficiency in thermodynamic analyses. In this paper, we present a comprehensive demonstration of using MATLAB for teaching and learning thermodynamics, specifically targeting the solution of complex problems involving non-linear equations. We provide a detailed solution process that includes a flowchart and an illustrative example problem, complete with derived governing equations. MATLAB's Symbolic Math Toolbox is utilized for linear interpolation of thermodynamic property values and for solving non-linear equations involving variables such as the quality factor. By solving the non-linear parameters and related dependent variables first, the remaining equations are iteratively transformed into a linear system, which can then be efficiently arranged into a matrix form for solution.

This approach not only simplifies the computational process but also facilitates optimization studies by allowing the examination of varying key parameters that influence the thermodynamic system's behavior. The findings from this study enhance the understanding and solving of complex thermodynamic problems in an educational setting. Furthermore, this methodology can be beneficial for industry practitioners involved in the design and optimization of large-scale energy systems, providing a practical tool for handling the complexities inherent in non-linear thermodynamic analyses.