MATHEMATICAL MODELING of TRANSIENT HEAT and MASS TRANSPORT IN A BAKING BISCUIT

Abstract

Drying behavior of a single baking biscuit was modeled using unsteady state, anisotropic, two dimensional, simultaneous heat and mass balances. Solutions of these equations agreed well with the experimentally determined temperature and the moisture data. Modeling revealed that in the outer sections of the baking biscuit conduction and diffusion were the dominant heat and mass transfer mechanisms, respectively. In the central section of the biscuit the gas cells cracked with the increased vapor pressure and the upward volume expansion, then air/vapor enclaves were formed among the horizontal dough layers in the radial direction. the dominant heat and mass transfer mechanisms in the central section of the biscuit were convection. Presence of two different regime zones in a baking biscuit may have important consequences concerning the strength of the commercial products against crumbling during marketing and consumption.

Mathematical modeling of bread baking process

“…Sometimes, moisture change is treated as a simple diffusion process although water evaporation and pressure driven flow may exist in reality (Ozilgen & Heil, 1994;Zanoni, Pierucci, & Peri, 1994 neglect the deformation (Tong & Lund, 1993). Studies focusing on the deformation assume that transport can be solved independently (Itaya, Kobayashi, & Hayakawa, 1995) or known beforehand (Fan et al, 1999;Shah, Campbell, McKee, & Rielly, 1998).…”

Modeling of Simultaneous Heat and Water Transport in the Baking Process

“…In the outer section of baking Unsteady state, anisotropic, Moisture dependent thermal Heil (19) biscuit heat and mass transfer by axi-symmetric 2-D heat and conductivity and specific heat, conduction and diffusion, and in water diffusion with constant constant density and latent heat of the central section by temperature and equilibrium evaporation, water and convection water content at the temperature dependent water boundaries during baking, in the diffusivity central section heat and water fluxes were taken as zero, finite difference method stage. However, prediction of the average water content deviated from experimental values after a heating time of 30 s, and this was attributed to a decrease in loaf volume as the average water content decreased, which was ignored in the development of the model.…”

“…The small difference between the experimental and model predicted values was attributed to errors in the experimental measurement of temperature for thin product and physical properties values used in the simulation model, and assumption of negligible internal resistance for heat and mass diffusion within the product. Ozilgen and Heil (19) assumed that biscuit surfaces attain boiling temperature immediately, and that water is transported to the surface mainly through diffusion during the baking process. In the inner region of the product, convection occurs in addition to diffusion due to the cracking of gas cells with increased vapor pressure and volume expansion during the baking process; therefore, temperature and moisture distribution may be uniform in the region.…”

Analysis of mass transfer parameters (changes in mass flux, diffusion coefficient and mass transfer coefficient) during baking of cookies

“…Karathanos, Villalobos, and Saravacos (1990) discussed the use of method of slopes to estimate the effective variable moisture diffusivity at various moisture contents of drying samples and concluded that the method of slopes could be used to determine the effective diffusivity. Ozilgen and Heil (1994) used an empirical expression for moisture diffusivity in their mathematical model for transient heat and mass transport in a baking biscuit. Baik and Marcotte (2002) applied an Arrhenius type of equation to model the effect of temperature on the moisture diffusivity of a baking cake.…”