Freezing time of an infinite cylinder and sphere using the method of lines

• A mathematical model has been developed to simulate freezing processes.
• The model is solved by the method of lines, and can predict the freezing time.
• The method of lines is easy to program, accurate and requires a shorter run time.
• The freezing times predicted were close to those published experimental results.
• The freezing times predicted were close to those predictions by other methods.

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.