A transient regime for transforming thermal convection: Cloaking, concentrating, and rotating creeping flow and heat flux

By treating a set of equations governing transient heat and mass transfer simultaneously, here we develop the transformation theory for thermal convection with unsteady creeping flow in porous media, whose steady counterpart has been previously studied. We find that the transformation theory can still be valid when the temperature, density, and velocity of fluids vary with time. As applications, we design thermal cloaks, concentrators, and rotators at transient states examined by finite-element simulations, which can be used to control the magnitude or direction of heat flux in convection. Also, we discuss both the effects of natural or mixed convection and the differences between steady and unsteady states. This work develops a theory for dynamically controlling the flow of heat associated with thermal convection.