Lyapunov-based temperature regulation by flow reorientation

Transport of scalars, in the form of heat or chemicals, by fluid flow is a key feature for the effective operation of applications that range from chemical
species mixing to subsurface resource extraction. Therefore, enhancing transport of these scalars by improving their dispersion will prove beneficial to
a large variety of industries. Systems that involve scalar transfer from the boundary and have a substantial influence of diffusion and/or chemical reactions
on heat/chemical transport are of particular interest. The system considered in this work intends to rapidly homogenize a scalar field by reorienting a laminar base flow. In conventional heating/mixing approaches a periodic reorientation
scheme is designed towards effective fluid mixing and thus lacks robustness to perturbations required for widespread application. In this work we present two novel methods that accomplishes transport acceleration by adjusting the fluid flow reorientation. Rationale behind these methods is that influencing
transport rates by fluid flow is analogous to influencing the decay rate of a Lyapunov function. This reasoning leads to the design of a bang-bang regulator
and a general nonlinear regulator. We numerically investigate the performance of these regulators on a representative thermal flow problem: boundary heating of an initially cold fluid by reorientation of a 2D flow fields. Results show that the proposed regulators improve heating rates by up to 80 % compared to mere diffusive heating.