Mathematical Modeling of High Intensity Infrared Heating of a Food Matrix

Abstract

Infrared heating has been used by the food industry for many years. Some of the advantages of infrared heating are its high intensity, ability to penetrate the product, and precise control. While infrared heating has unique advantages over convective and conductive heating, the complex mathematics and lack of optical property data associated with the radiant process have hindered extensive numerical simulation for process design and optimization.

The objectives of this research were to develop a mathematical model to predict temperature change and crust formation during high intensity infrared heating of a food matrix, and to perform parametric analysis of process variables.

A series of equations for unsteady state heat transfer, internal heat generation, and a moving boundary demarked by a phase change interface were developed. Beer's law was assumed to describe subsurface radiant energy absorption. The equations were solved numerically using explicit finite differences and MATLAB.

Russet potato was used in a series of radiant heating experiments designed to test the output of the mathematical model. Surface and center temperatures and crust thickness were measured for a range of radiant flux intensities, and the data compared to the simulation output. Simulated surface temperatures agreed well with measured surface temperature during the initial 150 s of heating. Towards the end of the heating time, higher incident radiant flux (26,900 and 22,500 W⁄m2) resulted in higher simulated surface temperature than laboratory data. A lower flux setting (17,500 W⁄m2) resulted in lower simulated temperatures than measured. The model was able to predict center temperature for the first 150 s of heating for the higher flux settings, followed by higher measured temperature for 26,900 W⁄m2 incident flux. Measured center temperature for the lowest flux setting was lower than simulated temperatures throughout the duration of heating. Experimental crust thickness determination was based on sample mass loss. The model did not account for evaporation of moisture at temperatures less than 100 °C, resulting in lower crust thickness predictions for initial stages of heating. It was hypothesized that variable optical and thermal properties of the matrix, as well as moisture diffusion, and internal pressure build up, were possible causes for deviation of predicted temperatures and crust thickness from laboratory data.

The simulation was used as a tool to evaluate parameters that affect radiant heating of products. The affects of radiant flux intensity, matrix reflectance and dissipation coefficient, ambient air temperature, and convective heat transfer coefficient on matrix temperature and crust thickness were tested. Radiant flux intensity and surface reflectance were found to have a large affect on surface temperature, center temperature, and crust thickness. Ambient air temperature and convective heat transfer coefficient were shown to have a direct affect on surface temperature and crust thickness, and an indirect affect on center temperature. Dissipation coefficient parametric analysis revealed the large affect long wavelength dissipation coefficient had on surface temperature. It was concluded that short wavelength radiation had a relatively small affect on simulated temperatures and crust thickness. This was due to the small percentage of short wavelength infrared energy emitted by a 2,000 K emitter, high reflectance, and small generation term associated with short wavelengths infrared energy.

Future work should include measurements of optical properties as a function of wavelength, matrix composition, and sample thickness; an addition of a mass diffusion term and an internal pressure term as a function of temperature and time; and expansion of the model to a two-dimensional configuration with variable radiant flux.