Thermal diffusivity measurements in porous ceramics by photothermal methods

Received: 16 September 1996/Accepted: 6 January 1997     

Forced-air precooling of spherical foods in bulk: A parametric study

In this paper, a mathematical model for forced-air precooling of spherical food products in bulk is developed. The foods are arranged in horizontal layers stacked one above the other to form a rectangular parallelepiped with a vertical gap in between the product layers. The foods are cooled by chilled air blown along the height of the package. The governing equations for the conduction heat transfer in the foods, simultaneous heat and mass transfer at the food-air interface and in the air stream are solved numerically using finite-difference methods. A comprehensive numerical study is performed by varying the process parameters over a wide range. Typical results showing the variation of moist air properties along the height of the package and the effect of each parameter on the process time are presented. The ranges of parameters for advantageous operation of the precooling system are identified. Correlations are obtained for the process time based on the product center and mass-averaged temperatures in terms of process parameters.     

On Producing Multiple Solutions Using Repeated Trials

The number of trials that is required by an algorithm to produce a given fraction of the problem solutions with a specified level of confidence is analyzed. The analysis indicates that the number of trials required to find a large fraction of the solutions rapidly decreases as the number of solutions obtained on each trial by an algorithm increases. In applications where multiple solutions are sought, this decrease in the number of trials could potentially offset the additional computational cost of algorithms that produce multiple solutions on a single trial. The analysis framework presented is used to compare the efficiency of a homotopy algorithm to that of a Newton method by measuring both the number of trials and the number of calculations required to obtain a specified fraction of the solutions.     

Left versus right canonical Wiener-Hopf factorization and realization

For an arbitrary rational matrix function, not necessarily analytic at infinity, the existence of a right canonical Wiener-Hopf factorization is characterized in terms of a left canonical Wiener-Hopf factorization. Formulas for the factors in a right factorization are given in terms of the formulas for the factors in a given left factorization. All formulas are based on a special representation of a rational matrix function involving a quintet of matrices.