An Analytical Solution Applied to Heat and Mass Transfer in a Vibrated Fluidised Bed Dryer
Abstract: A mathematical model for the drying of particulate solids in a continuous vibrated fluidised bed dryer was developed and applied to the drying of grain wetted with a single liquid and porous particles containing multicomponent liquid mixtures. Simple equipment and material models were applied to describe the process. In the plug-flow equipment model, a thin layer of particles moving forward and well mixed in the direction of the gas flow was regarded; thus, only the longitudinal changes of particle moisture content and composition as well as temperature along the dryer were considered. Concerning the material model, mass and heat transfer in a single isolated particle was studied. For grain wetted with a single liquid, mass and heat transfer within the particles was described by effective transfer coefficients. Assuming a constant effective mass transport coefficient and effective thermal conductivity of the wet particles, analytical solutions of the mass and energy balances were obtained. The variation of both transport coefficients along the dryer was taken into account by a stepwise application of the analytical solution in space intervals with non-uniform inlet conditions and averaged coefficients from previous locations in the dryer. Calculation results were verified by comparison with experimental data from the literature. There was fairly good agreement between experimental data and simulation but the results depend strongly on the correlation used to calculate heat and mass transfer coefficients. For the case of particles containing a multicomponent liquid mixture dried in the vibrated fluidised bed dryer, interactive diffusion and heat conduction were considered the main mechanisms for mass and heat transfer within the particles. Assuming a constant matrix of effective multicomponent diffusion coefficients and thermal conductivity of the wet particles, analytical solutions of the diffusion and conduction equations were obtained. The equations for mass transfer were decoupled by a similarity transformation and solved simultaneously with conduction equation by the variable separation method. Simulations gave a good insight into the selectivity of the drying process and can be used to find conditions to improve aroma retention during drying. Also, analytical solutions of the diffusion and conduction equations applied to liquid-side-controlled convective drying of a multicomponent liquid film were developed. Assuming constant physical properties of the liquid, the equations describing interactive mass transfer are decoupled by a similarity transformation and solved simultaneously with conduction equation and the ordinary differential equation that describes the changes in the liquid film thickness. Variations of physical properties along the process trajectory were taken into account as in the previous cases. Simulation results were compared with experimental data from the literature and a fairly good agreement was obtained. Simulations performed with ternary liquid mixtures containing only volatile components and ternary mixtures containing components of negligible volatility showed that it is difficult to obtain an evaporation process that is completely controlled by the liquid-side mass transfer. This occurs irrespective of the initial drying conditions. Despite simplifications, the analytical solution of the material model gives a good insight into the selectivity of the drying process and is computationally fast. The solution can be a useful tool for process exploration and optimisation. It can also be used to accelerate convergence and reduce tedious and time-consuming calculations when more rigorous models are solved numerically.
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