Publicação
Physics-Based Model of Solid CO$_2$ Sublimation—Transient Homothetic Approach for Timescale Optimization
| Resumo: | This study develops a rigorous analytical formulation to predict the evolution of the mass of solid carbon dioxide (dry ice) over time, under natural or forced convection conditions. Starting from the fundamental principles of energy conservation and convective heat transfer, and assuming a homothetic geometric evolution of the solid, the following analytical solution is deduced:$$m_s(t) = \left[m_{s,0}^{1-\gamma} - (1-\gamma) K_s t\right]^{1/(1-\gamma)} \, , \quad t \in [0,\, t_{\text{sub}}]\,.$$ The parameters \(K_s\) and \(\gamma\) are explicitly defined as functions of the fluid properties, the temperature difference between the environment and the sublimating surface, the geometry, the heat transfer conditions, and the physical characteristics of the solid. This expression enables an accurate description of the solid mass evolution throughout the sublimation process. Three representative geometries — sphere, cylinder (with height equal to diameter), and cube — were analyzed and optimized to assess the influence of the surface-to-volume ratio on the sublimation rate. The sphere was found to be the most efficient shape for mass conservation, followed by the cylinder and, lastly, the cube. The model also predicts the effect of the initial mass, ambient temperature, and airflow velocity, showing that the sublimation time increases with mass and decreases with higher temperature and velocity. The model is validated through comparison with experimental data from the literature, showing consistent agreement with the observed mass evolution profiles. |
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| Autores principais: | Ferreira, Pedro Gabriel Fazenda |
| Assunto: | Dry Ice CO2 Sólido Sublimation Physical Model Gelo Seco Solid CO2 Sublimação Modelo Físico |
| Ano: | 2025 |
| País: | Portugal |
| Tipo de documento: | dissertação de mestrado |
| Tipo de acesso: | acesso embargado |
| Instituição associada: | Universidade de Coimbra |
| Idioma: | inglês |
| Origem: | Estudo Geral - Universidade de Coimbra |
| Resumo: | This study develops a rigorous analytical formulation to predict the evolution of the mass of solid carbon dioxide (dry ice) over time, under natural or forced convection conditions. Starting from the fundamental principles of energy conservation and convective heat transfer, and assuming a homothetic geometric evolution of the solid, the following analytical solution is deduced:$$m_s(t) = \left[m_{s,0}^{1-\gamma} - (1-\gamma) K_s t\right]^{1/(1-\gamma)} \, , \quad t \in [0,\, t_{\text{sub}}]\,.$$ The parameters \(K_s\) and \(\gamma\) are explicitly defined as functions of the fluid properties, the temperature difference between the environment and the sublimating surface, the geometry, the heat transfer conditions, and the physical characteristics of the solid. This expression enables an accurate description of the solid mass evolution throughout the sublimation process. Three representative geometries — sphere, cylinder (with height equal to diameter), and cube — were analyzed and optimized to assess the influence of the surface-to-volume ratio on the sublimation rate. The sphere was found to be the most efficient shape for mass conservation, followed by the cylinder and, lastly, the cube. The model also predicts the effect of the initial mass, ambient temperature, and airflow velocity, showing that the sublimation time increases with mass and decreases with higher temperature and velocity. The model is validated through comparison with experimental data from the literature, showing consistent agreement with the observed mass evolution profiles. |
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