The closing valve law is a mathematical function that describes the speed variation of the fluid as it is closing. This reduction of the speed determines the shape of the pressure wave during the development of the water-hammer. A wide variety of closing modes exists, depending on the valve type and their operation, each one is mathematically given by a function. A generic function was formulated that allows to model an extensive variety of closing laws by means of a polygonal segmented structure. An algorithm has been generated that includes this closing law as boundary condition for describing the transitory. The pressure wave shape and amplitude depends on closing function in a unique relationship.

Many processes in food technology involve water migration from or into the processed product. Modeling of food water migration knowledge could result speeding up the processes, improving the quality of final products, and reducing energy costs. A mathematical formulation for mass transfer during drying and hydration of a porous solid sphere with volume change was developed in terms of the diffusion equation. The present model also provides an analytical expression for the ariation of water diffusivity with moisture content based on a simple relationship between the activation energy for diffusion and sorption energy. The non-linear diffusion equation was solved numerically, moisture profiles, the kinetics curves for drying and hydration and the moisture concentration dependence of diffusivity coefficient were calculated. Marked differences were observed in the moisture profiles for drying and hydration. The kinetic curves of both processes are strongly dependent on the range of moisture tested. Moisture diffusivity falls drastically at low moisture contents.

A model for isothermal diffusion of bound water was used to simulate the thin-layer drying kinetics of amaranth grain. The model assumes that the driving force for the transport of bound water is the gradient of spreading pressure. The gradient of spreading pressure was related to the moisture gradient using the GAB isotherm. This variation shows a relative maximum moisture content about 8% (d.b), after which the diffusion coefficient falls sharply as the moisture content is further reduced. To verify the model, drying tests of amaranth grain were conducted at 40 to 70ºC in a laboratory drier from 32.5 to 6% moisture (d.b.). Equilibrium moisture contents were also determined using an electronic hygrometer at temperatures and relative humidities corresponding to drying conditions. The applicability of the model to simulation of drying curves was satisfactory in the full range of moisture.