A Minimum Entropy Production Approach to Optimization of Tubular Chemical Reactors with Nature-Inspired Design

The problem of the shape optimization of tubular-type plug-flow chemical reactors equipped with a fluid flow-based cooling system is considered in this work. The hydraulic radius R h ( z ) = 2A ( z ) /P ( z ) and an equivalent surface area-based radius R s = P ( z ) / ( 2π ) were computed from the cross-sectional area A ( z ) and perimeter P ( z ) measured along the nasal duct of Northern reindeer and used for shape optimization as nature-inspired design. The laminar flow in the cooling system was modeled using the Navier–Stokes equations for an incompressible liquid. In the central tube, a set of chemical reactions with temperature-dependent rates was considered. The temperature and flow velocity fields, pumping pressure, mass flow rate, and total heat flux J th were obtained by numerical methods. Comparative analyses of the efficiency of different geometries were conducted on Pareto frontiers for hydraulic resistivity Z h , thermal resistivity Z th , thermal inlet length L th , and entropy production S irr as a sum of contributions from chemical reactions, thermal, and viscous dissipation. It was shown that the tube with R s ( z ) as an interface between the reactor and cooler has the best Pareto efficiency using the ( Z h , Z th , L th ) objective functions. Surprisingly, this design also exhibits the lowest S irr and a more uniform distribution S irr ( z ) (i.e., equipartition) among other designs. This geometry is suggested for densely packed tubular reactors.