Freezing time of an infinite cylinder and sphere using the method of lines |
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| Affiliation: | 1. Department of Chemical Engineering, UFRN – University Federal of the Rio Grande do Norte, Campus Universitário, 59078-970 Natal, RN, Brazil;2. Department of Chemical Engineering, UFPb – University Federal of the Paraíba, João Pessoa, PB, Brazil;1. Chair of Building Physics, Swiss Federal Institute of Technology of Zurich, ETHZ, Zurich, Switzerland;2. Laboratory for Multiscale Studies in Building Physics, Swiss Federal Laboratories for Material Testing and Research, Empa, Dbendorf, Switzerland;1. UPMC Univ. Paris 06, CNRS (UMR 8190), LATMOS-IPSL, Paris, France;2. UPS Univ. Toulouse 03, CNRS (UMR 5560), LA (Laboratoire d''Aérologie), Toulouse, France;3. Univ. Littoral Côte d''Opale & Univ. Lille Nord de France, CNRS (UMR 8101), LPCA (Laboratoire de Physico-Chimie de l''Atmosphère), Dunkerque, France;4. Ecole Polytechnique, CNRS (UMR 8539), LMD-IPSL, Palaiseau, France;5. Met Office, Exeter, United Kingdom |
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| Abstract: | An energy balance model has been developed to simulate freezing processes for infinite cylinders and spheres. The mathematical model (1) was numerically solved using the method of lines. In this method, spatial derivatives are discretized by the finite difference method and the resulting system of ordinary differential equations in time is integrated using an appropriate solver. Freezing times obtained with the proposed model were compared to experimental data and results calculated by different published methods. The freezing times predicted by the proposed model agreed well with the published experimental results and predictions by other published methods. Model (1) gives a percentage error in the range −4.61 ≤ E (%) ≤ 6.81, which includes the experimental data for the 123 spheres analyzed and 30 infinite cylinders, within range −2.96 ≤ E (%) ≤ 3.34. |
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