A mathematical model of simultaneous heat and mass transfer in a rigid porous material during the falling rate period of drying
A mathematical model of the drying process in porous media has been
developed. When translated into a computer model written in Fortran
code it displayed good agreement with published experimental work.
Numerical algorithms were devised to overcome certain problematical
features of the model equations. The model proved capable of describing
the variation with respect to time of temperature, pressure and moisture
content throughout a rigid homogeneous semi-infinite porous slab
subjected to identical boundary conditions on each of its two sides.
Unlike the simple diffusion model which predicts parabolic moisture
content profiles, the model predicts s-shaped moisture content profiles;
these are reported in the literature for a wide variety of porous
Migration of moisture to the surface has been assumed to take place
only in the vapour phase. The model is therefore limited to the falling
rate period, by which time liquid phase transport has become extinct.
The gaseous phase is treated as binary mixture of two constituents,
watervapour and air. The flux of each of these components is described
by the dusty gas model which has been the subject of recent improvement
by a number of workers in the USA.
This work has demonstrated that the dusty gas model may be applicable to
porous media when the void fraction is continually changing, though it
is recognised that experimental verification is required before this can
be stated categorically. An experiment is suggested which would address
itself to this question, it would also resolve the controversy surrounding the somewhat ambiguous definition of the porous medium
inherent in the dusty gas model itself.
The suitability of the model as a basis for a computer study in optimal
dryer design was evaluated. The most rigorous optimisation method - the
classical variational technique - is an iterative procedure wherein the
control strategy is improved stepwise over each major iteration forwards
and backwards in time. A given control strategy determines a forward
trajectory in the real system, a slightly improved strategy is then
determined by working backwards in time given the complete history of
the forward trajectory. Repetition of this procedure eventually
produces an optimal control strategy. The model proved too large,
requiring excessive computer storage for a complete history of the
forward trajectory. Moreover, the application of the variational
technique is complicated enormously by non-linear partial derivatives,
and it is clear that its use is limited to fairly simple systems of