Question

A cylindrical shaped potato with length 2 cm and a diameter of 0.5 cm was dried at a temperature of 65 o C in a convective oven for 24 h, if the surface temperature of the potato remained at 62 o C throughout the drying operation, describe the different changes that occurs during the constant and falling rate periods

Answer 1

The drying process is divided into the constant rate period and the falling rate period. The requirement for constant rate drying is that the potato surface layer behaves as if it were a solvent pool and, as there is always enough solvent on the surface, the drying rate is then determined by the heat transfer rate to the surface and the mass transfer rate from the surface. These are determined by what takes place in the air, and not by diffusion in the surface layer. In the constant rate period the drying rate is constant only at equilibrium, not throughout the whole constant rate period. Because the heat transfer rate is determined by the temperature driving force from the air to the outer layer (and by the heat transfer coefficient), the layer has to remain below the drying air temperature for there to be a temperature driving force. In fact, in single-sided impingement drying of aqueous coatings, the equilibrium coating temperature in the constant rate period is the so-called wet bulb air temperature. However, at the start of the dryer the equilibrium conditions have not yet been reached, but it is still in the constant rate period. There are cases where equilibration is never reached in the constant rate period and the drying rate continuously changes, yet it is still in the constant rate period. After the constant rate period is over, the surface layer no longer resembles a solvent pool. The surface appears dull and dry. Now the drying rate is determined by how fast solvent can diffuse to the surface, and not by the conditions in the air. The diffusion rate to the surface is determined by the diffusivity and by the concentration driving force (dc/dx) in the potato outer surface. The diffusivity is a function of the coating temperature and of the solvent concentration in the coating. As the coating dries and the solvent concentration decreases, the diffusivity drops rapidly, the evaporation rate and the evaporative cooling decreases, and the temperature rises to approach the drying air temperature. At higher temperatures the diffusivity is higher. The drying rate continuously decreases in the falling rate period because the effect of the lower concentration on reducing the diffusivity is much greater than the effect of the increasing temperature on increasing the diffusivity.

In the falling-rate period, the surface of the potato is no longer completely wetted and the rate of drying steadily falls. In the previous analysis, it has been assumed that the rate of drying per unit effective wetted area is a linear function of the water content, so that the rate of drying is given by:

  

Where is the water content of the potato, is the equilibrium content , m is the mass of the potato, A is the total surface area of the potato

If r and h are the height and radius of the cylindrical shape potato then we have

Here we have   ,   

Hence we have the surface area of the potato

Hence from above equation the rate of drying of the potato can be easily calculated if the other parameters are also known.