Given the temperature of the dryers, the model simulates the profile of the velocity and temperature of the air. This is done in the steady case, meaning that there is no time dependency, and the temperature at the bottom of the dryers is extracted.
The model has no time dependency because it is interesting to investigate the distribution of the air in the steady case. There will not occur any paper drying in the oven when it is cold or during it is being heated up. That is why the model is in steady case or preheated mode as it can be expressed in a bit less formal way.
As seen in the model, the density and the viscosity is set to constant. This is done because of simplicity. To get a more accurate model, the density should depend on the temperature of the air. The viscosity of the air is dependent on the temperature, though it is between: \((1.12 - 15.1) \cdot 10^{-4} \text{ft}^2/\text{s}\). So it does not affect that much and was therefore set as a constant for simplicity. The Navier Stokes equations were never used in the final results. Though there was a lot of time spent on this equation, it had to be a part of the paper. As explained above, both the density and the viscosity were put as constants. This meant that the compressible Navier Stokes equations could not be used, which is a very good model to simulate fluid, but our problem gets much more complicated. So the incompressible Navier Stokes equations were used instead. Even though the compressible Navier Stokes were used instead of the incompressible Navier Stokes, the solution was not stable. A reason for this could be that there is no proof there exist a stationary solution, but even the time depended problem was numerically unstable. Refining the mesh helped, but the numerical error was still dominant. Problably this problem could be solved by using iterative methods like a modified CG-Method for non symmetric problems. After some discussion with the supervisor, the conclusion was, that a part of the problem occured because of the very low viscosity that air have. With this in mind, Navier Stokes where dropped, and the regular Stokes were used. The approximation of the problem works even though it is not completely accurate.
A very important part of the boundary conditions, on the Stokes equation, of a dryer is the air extraction of humid air which was neglected. The problem with the boundary condition was that it has to be a closed system. So the moisture had to go somewhere, and because it’s a closed system, it could not just vanish.
This model’s purpose was to model the temperature distribution in a dryer. Although this was completed, the intend of it, was to use it for a real problem. An attempt to model the drying process of a paper that went through the oven was made. The problem was that there were a lot of physics behind the actual drying process that was not fully understood. And that is why only the temperature profile of the dryers bottom and the temperature distribution of the air was simulated and plotted.
Overall the model simulates the temperature distribution and the temperature profile quite good and the result seems plausible with the approximations in mind.