An optimization approach to find the thermodynamic limit on convective mass transfer enhancement for a given viscous dissipation

Entropy generation minimization in a channel flow: Application to different advection-diffusion processes and boundary conditions

“…This velocity field results in a thermal plume shape at the beginning of the heated zone. The presence of a vortex in the velocity field resulting from variational optimization is also observed in other physical situations, such as the improvement of chemical reaction [38] or diffusion [36] processes and the optimization of heat transfer in a turbulent gas flow [35]. Vortex generation is also a subject of numerical simulation [9] and experimental [8] work aimed, for example, at associating and optimizing actuators and riblets to produce vortexes.…”

“…In this set of equations, V is the velocity vector of the fluid, ρ its density, P its pressure, µ its dynamic viscosity and F is a volume force field that will be used in the optimization process described below: F can be considered as a virtual force field allowing the velocity field to be varied in order to examine all possible flow configurations and find the one that minimizes the objective functional (and respects the conservation equations and boundary conditions), without a priori on its pattern. The practical realization of the resulting optimal velocity field can be approached by passive means, such as baffles placed in the fluid path, or by the use of porous materials as described in [36] and [35].…”

“…27) that can be compared with the momentum equation (Eq. 28), which leads [36] to identify ∇P (Eq. 29) and F (Eq.…”

“…The total 45 generated entropy rate can be minimized in order to find this optimal trade-off [32,33,34]. It is also possible to look for a minimum of entropy generation while fixing a constraint on the total viscous dissipation in the flow [35,36], the latter being related to the pressure drop, which is a quantity to be controlled in industrial applications.…”

“…The optimizations carried out 720 in the present work have all been performed at constant physical properties in order to examine in detail the behavior of the method in this first case. This enables to start from initial solutions known in the literature [36] and then to vary the boundary conditions and the opti-725 mization parameters. However, the properties of fluids generally depend on temperature.…”