Conveyor-Belt Dryers with Tangential Flow for Food Drying: Mathematical Modeling and Design Guidelines for Final Moisture Content Higher Than the Critical Value

Abstract

The mathematical modeling presented in this work concerns the conveyor-belt dryer with the tangential flow of air with respect to food. This dryer, if operating in co-current, has the advantage of well preserving the organoleptic and nutritional qualities of the dried product. In fact, it has a low air temperature in the final stretch where the product has low moisture content and is therefore more temperature sensitive. It is a bulkier dryer than the continuous through-circulation conveyor dryer with a perforated belt. The latter is therefore more frequently used and has received greater study attention from researchers and designers of the industry. With the aim to propose guidelines for a rational design of the conveyor-belt dryer with tangential flow, a mathematical model was developed here through the differentiation of the drying rate equation followed by its integration performed along the dryer belt. Consequently, and with the assumption that the final moisture content XF of the product is higher than the critical moisture content XC, the relationships between the intensive quantities (temperatures, humidity and enthalpies), the extensive quantities (air and product flow rates) and the dimensional ones (length and width of the belt), were obtained. Finally, on the basis of these relationships, the rules for an optimized design for XF > XC were obtained and experimentally evaluated.

Conveyor-Belt Dryers with Tangential Flow for Food Drying: Development of Drying ODEs Useful to Design and Process Adjustment

“…Therefore, a relationship exists between the final moisture content of the product and the air temperature at the dryer exit, so that the easy and precise measurement of this temperature can be the starting point of the feed-back control chain. Figure 2 [63] represents the scheme of a conveyor-belt dryer with tangential flow completed by the diagram of the temperatures of the air T A and the product T P . This one, T P , was assumed to be equal to the wet bulb temperature T WB .…”

“…; where: GAI is the mass flow rate of dry air coinciding with the mass flow rate of hot air entering the dryer; cA is the specific heat of dry air; dA is the infinitesimal area; dTA is the infinitesimal variation of the air temperature when it touches the area dA. In the conveyor-belt dryer, the drying process takes place along the direction of the belt, i.e., following a variable called z linked to the area A by the relation derived from (18) of the previous work [63]: = ⋅ ; therefore for an infinitesimal length dz, we have: = ⋅ ( Figure 3). By equating the quantities dq, the first ordinary differential equation ODE is obtained: Figure 2 shows that the initial temperature of the product TPI is already equal to the wet bulb temperature TWB.…”

“…In a previous work [63] a conveyor-belt dryer with tangential flow was studied ( Figure 1). This dryer has a lower air temperature in the terminal area of drying thus allowing greater respect for the product, with reduced denaturation of proteins and of polyphenols.…”

“…As result of the mathematical model, among the design guidelines proposed by [63], the last one concerned adjustment with the dryer feedback system. The mathematical model had indicated, for the feedback control chain, the need to start from an instant measurement of the final moisture content of the product.…”

“…Its operation is shown in Figure 1 where a unperforated belt carries the product which is lapped by the air in co-current. Therefore, the air has a continuous variation of its characteristics of temperature T A and humidity x, along the dryer and this required a special mathematical modeling developed in the previous work [63], under the condition that the final moisture content of the product was higher than the critical one (X F > X C ).…”