(156b) Boundary Conditions In Multiphase, Porous Media, Transport Models of Thermal Food Processes with Rapid Evaporation

In modeling of thermal food processes with rapid evaporation, like frying, baking and microwave cooking, it is critical to provide boundary conditions consistent with the phenomena happening at the surface to accurately predict spatial temperature and moisture content for quality and safety assurance. Boundary conditions in a mathematical model are as important as governing equations itself and describe how the heat and mass transfer takes place at the boundary. Until now, the exchange at the boundary has been implemented as a convective heat and mass transfer with constant transfer coefficients. Such a boundary condition is valid for situations where there is no bulk flow and migration of moisture is only due to diffusion. But in thermal processes where rapid evaporation exists, there is significant pressure driven flow inside the porous food and a constant transfer coefficient cannot represent the physics at the surface accurately. A transfer coefficient in such processes is a lumped parameter containing effects of both bulk flow and diffusion and it should change as bulk flow at the surface increases or decreases. In case of frying it was observed during experiments that the rate of moisture loss decreases over time which can only be explained if the mass transfer coefficient is varying with time.

To investigate the exchange of heat and moisture at the porous media surface, we solved heat and mass transfer during microwave heating for a conjugate domain including both the porous media food and the outside environment. As a conjugate domain was solved, there was no need to provide separate boundary conditions at the porous media surface. Information about the exchange at the porous media surface was obtained from solving the heat, mass and momentum (Navior-Stokes equation) balances of the surrounding air. It was observed from the simulations that the diffusion of vapor into air at the surface is significant and cannot be ignored at any time. Bulk flow of moisture is insignificant in the starting but as pressure builds up inside the food, it becomes significant. The mass transfer coefficient increases with the bulk flow and reaches a peak value and stays around this value for rest of the heating time. The mass transfer boundary condition in these situations can be broken into two parts: one due to diffusion and another due to convection. One due to diffusion experiences resistance at the surface and while the other due to convection leaves the surface without experiencing any further resistance just like the outlet condition in case of pipe flow.

The conclusions regarding boundary conditions from the conjugate problem can be used in formulating the boundary conditions for a non-conjugate problem. Such boundary conditions are consistent with the physics happening at the porous surface and therefore accurately predict spatial temperature and moisture contents during thermal processes of food. The most significant conclusion of the study is that heat and mass transfer coefficients vary with bulk flow velocity of liquid water and vapor at the surface and should not be ignored.