Mathematical description of recuperative heat transfer in a bioreactor during the filling of an apparatus

Abstract

Despite the observed trend of a ubiquitous transition to continuously operating apparatuses, the specificity of the production technology of many microbiological products retains the advisability of using batch apparatuses. As an example, we mention the cooled bioreactors and yeast concentrate collectors used in the production of baker’s yeast. The work considers the problem of the mathematical description of unsteady recuperative heat transfer in a batch capacitive apparatus (bioreactor) with a product distributor on a heat transfer surface during countercurrent movement of coolants with a filling level of the apparatus changing during the process. The problem is formulated by partial differential equations (in coordinate and time) with a moving boundary between sections with different heat transfer conditions. When formulating the problem, simplifying assumptions and boundary conditions were adopted. The mathematical problem posed is solved using the Laplace transforms. The mathematical description of recuperative heat transfer in bioreactors during the filling of the apparatus showed that with countercurrent movement of heat transfer liquids and coolants, the apparatus has an advantage in terms of the main indicator - heat transfer capacity and has a higher energy efficiency. The performed calculations make it possible to choose the apparatus design correctly and determine the rational thermal regime of its operation regarding related technological operations.