A numerical method and graphs of generulized solutions are presented for a moving interface problem of freezing a saturated liquid inside a cylindrical or a spherical container with a constant heat transfer coefficient, as well as melting a saturated solid. The frozen solid phase has a constant heat cupacity.The moving interface problem of freezing a liquid inside a container is of interest in industrial processes such as consumable electrode melting of reactive metals, casting thermoplastics or metals, freezing foods, and producing ice. A brief review was made by Longwell (6). The fundamental transport process can be rigorously formulated by a set of partial differential equations, but the generalized analytical solutions are not readily available for cylinders and spheres.Using an analog computer, Kreith and Romie ( 3 ) studied the changes of heat transfer coefficient to maintain a constant interface velocity in a slab, a cylinder, or a sphere. London and Seban ( 5 , 7) gave analytic solutions of freezing a liquid in a cylinder or a sphere with negligible heat capacity of solid phase, and Longwell (6) proposed a graphical method to include the heat capacity.Baxter (1) computed the time required to freeze all the liquid inside a cylinder by using an analog computer. He divided the radius into five increments and the temperature profiles on the time coordinate appeared wavy. Springer and Olson (8) proposed a numerical method to solve solidification of materials with heat capacities and in an annular space between two concentric cylinders of finite length. They illustrated the movement of an interface within an annular space but the dimensionless groups were assigned such that finite solutions could not be obtained by letting the inside radius approach zero. The graphic method of reference 6 cannot be used for numerical computation when the interface approaches the vicinity of the center. Also, the usual initial step of assuming a constant temperature gradient in the solid phase could introduce some significant error which may not damp out in a finite radial distance. Therefore, it appears that a complete set of numerical solutions in terms of dimensionless parameters would be useful in that once computed they may serve many practical problems or design work. This paper presents a numerical method and its solutions of interface position as a function of time during freezing a saturated liquid inside a cylinder or .a sphere. The thermal conductivity and heat capacity of solid phase and the convective heat transfer coefficient are assumed to be constants. The temperature profiles at the instant of freezing at the center are also tabulated. The dimensionless groups were chosen so that the numerical solutions can be examined in their convergence toward their respective asymptotic solution? of negligible sensible heat. Also, the computation errors of these solutions given here have been analyzed and were minimized by choosing an optimum increment size. From these generalized solutions the interface position at any give...

Correlations of enthalpies of food systems containing water fraction from 0.74-0.94 are presented for a temperature range 230-310°K (-50 to 95°F). with these correlations, energy requirement in freezing and thawing foods within the limits of data base used for this work may be computed by providing the identity of food group (meat, juice or vegetable/fruits), water content, initial, and final temperatures.

A numerical method is developed to simulate the temperature progression of freezing a food system. It is assumed to have a constant density and to be macroscopically homogeneous during the freezing operation. The simulated results are compared with the measured temperature progression in the center of a beef slab immersed in a‐39°F bath.

No abstract

No abstract