Abstract
This study presents a method to calculate the freezing time of multidimensional objects using a pseudo-one-dimensional method. For example, the temperature of a rectangle in (x,y,t) can be simulated from the two-dimensional heat conduction equation to obtain a pseudo-one-dimensional temperature T(x,t), using the space grid Δx=Lx/(n−1) (where n=m) and Δy=ΔxLy/Lx as references. This procedure can be used to calculate the freezing time (tcalc) at a selected point, such as the center of an object. A computer program with a runtime similar to that of a one-dimensional problem has been developed for the proposed model. The freezing times (tcalc) of 212 multidimensional objects (parallelepipeds, rectangles, and finite cylinders) were then compared with the experimental freezing times (texper). The calculations yielded the following parameters for all 212 objects: minimum error Emin=−3.9%, mean error Emean=0.2%, maximum error Emax=5.0%, standard deviation σn−1=1.4%, and mean absolute error Eabs=1.1%. The freezing times (tcalc) of 100 multidimensional objects (parallelepipeds and rectangles) were then compared with the freezing times of computational experiments (computational simulation) obtained from the literature using the finite element method (tcomput). The calculations yielded the following parameters for all 100 objects: Emin=−2.8%, Emean=0.1%, Emax=3.7%, σn−1=1.4%, and Eabs=1.1%.
Published Version
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