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Journal of Food Engineering, Vol.36, No.2, 233-247, 1998
On the development of a ready reckoner table for evaluating surface area of general ellipsoids based on numerical techniques
Surface areas of food materials resembling general ellipsoids can be obtained from the principal dimensions by numerical techniques. Nodes were identified on the surface along the principal planes in the developed model for generating a series of flat triangular element grids and their assembly gave the surface area of the ellipsoidal material. The model was validated against simpler geometries, such as sphere, prolate spheroids and oblate spheroids, and was found to be accurate. With the combination of non-dimensional input in the model and scaling factor a two-dimensional ready reckoner table of reduced surface areas was developed, which covered the entire range of sizes and shapes of general ellipsoid. The method of obtaining the intermediate values in the table by univariate and bivariate linear interpolation was also outlined and the interpolation error was in the range of 0.0-0.57%. The nomogram representation of the table can be utilised for rough estimates. The actual surface area of the object is obtained from the reduced surface area by multiplying it by the scaling factor.