The models used to examine the processes of the solid-state fermentation bioreactors can be improved using the heat and mass transfer models compared to empirical models. This study examines the oxygen balance equations, water balance and energy balance equations for solid-state fermentation bioreactors. For the precise study of these important transport problems some advanced ingredients of applied mathematics such as sobolev spaces, weak solutions, Galerkin method, Gronwall's inequality and Harnack's inequality has been used. Based upon these concepts, the solutions of the balance equations for bioreactors is presented. By the proposed method, the uniqueness of the solutions of the balance equations has been proved. This procedure leads to a general methodology for reducing these initial/boundary partial differential equations to a system of ordinary differential equations which easily can be solved. It is also shown in this structure that the solution is the best answer since it supports the infinite diffusion speed of disturbances.

heat and mass transfer model, solid state fermentation bioreactor, balance-transport models, parabolic boundary value problem, weak solution