Jangam, Mujumdar - Basic Concepts and Definition
2008 ). Mathematical modeling allows one to test innovative designs that may be too
risky and too expensive as well as time-consuming to test experimentally.
Statistical tools have been used for years in almost all research sectors. Response
Surface Methodology (RSM) is a statistical tool which is commonly used in drying of
foods in recent years. RSM is mainly used for design of experiments and optimization of
process parameters. This tool is used to relate several input parameters with the output
parameters (also known as responses) using regression analysis. The significant para-
meters are then identified based on the relation between input and output parameters.
Recently this technique has been used to optimize various operating parameters in-
volved in drying process. Spray drying, micro-encapsulation, microwave drying are few
examples where this technique is applied. In this e-book, a whole chapter is dedicated to
this very important topic.
1.4.2. Reaction Engineering Approach in Drying
There are different ways to model drying processes, which is a necessary part for
the development of innovative and energy efficient drying techniques. There are three
different common approaches used for modeling the drying process. The concept of cha-
racteristic drying rate curve, use of empirical models: which are system specific and
cannot be generalized as these does not involve any physical basis, the most famous
model under this category is the Page model. The third approach is mechanistic models:
which are based on the drying phenomenon as well as the physics involved and can be
generalized, mainly involves coupled heat and mass diffusion equations. However, un-
der mechanistic models, there are different mechanisms proposed and generally these
models involve high mathematical complexity and determination of too many parame-
ters. It is necessary to have simple, accurate and robust mathematical model with mini-
mum mathematical complexity to reduce the computational time. Chen, 1998 has pro-
posed Reaction Engineering Approach to model the drying processes.
Some of the constraints with characteristic drying rate curve approach are: one has
to determine critical moisture content of the material which is a function of drying con-
ditions, the experimental drying data is relatively scattered and the flux which is calcu-
lated using following equation is based on the wet bulb temperature (TWB) for gas phase
and not based on the actual surface temperature (TS).
푁=푘푚 �휌푣,푠푎푡(푇푆)−휌푣,∞�≈푘푚 �휌푣,푠푎푡(푇푤푏)−휌푣,∞� (1. 13)
Where, km is the mass transfer coefficient
However, according to REA model, which was intended particularly for small case of Bi-
ot number (< 0.1), the temperature of the sample air interface TS is considered equal to
the product temperature TP.
Where biot number is defined as 퐵푖=ℎ푘^ 퐿푠퐶 (1. 14)
According to REA the drying rate can be written as
푚푆푑푋푑푡�=푘푚 퐴 �휌푣,푠(푇푆)−휌푣,∞� (1. 15)
ms is the dry mass of the solids and ρv,s is the vapor concentration at the solid-gas inter-
face. This is a unknown parameter and changes as the drying proceeds, but which is al-