Analytical solution to heat transfer in stationary wet granular mixtures with time-varying boundary conditions

Analytical solution of the temperature distribution in a stationary wet granular mixture in a heated cylindrical vessel, which is the typical geometry of an industrial filter-dryer, provides useful prediction of the wall heat flux that is needed as input to zero-dimensional heat and mass transfer models to get accurate predictions of the heating and drying time. The analytical solution can also be used for verification of numerical simulations. The derivation of such an analytical solution with time-dependent boundary conditions is important as it is a more realistic representation of experimental conditions. In this work, we derive an analytical solution for the transient axisymmetric temperature distribution in a cylindrical geometry with time-varying boundary conditions, which extends our previous result for constant-temperature boundary conditions [1]. We analyze two cases using the analytical solution: (1) when the vessel jacket temperature Td,b is linearly ramped up to a target temperature below the boiling point Tboil of the solvent, and (2) when the target temperature is above Tboil. In both cases, the ambient air temperature above the top surface of the mixture is also time-dependent, and is modeled as a similar linear ramp function at a fixed offset below the jacket temperature. A parametric study to assess the effect of the Biot number on the spatial variation of temperature is also performed.