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In this paper, we present the hydrodynamic limit of a multiscale systemdescribing the dynamics of two populations of agents with alignmentinteractions and the effect of an internal variable. It consists of a kineticequation coupled with an Euler-type equation inspired by the thermomechanicalCucker--Smale (TCS) model. We propose a novel drag force for the fluid-particleinteraction reminiscent of Stokes' law. Whilst the macroscopic species isregarded as a self-organized background fluid that affects the kinetic species,the latter is assumed sparse and does not affect the macroscopic dynamics. Wepropose two hyperbolic scalings, in terms of a strong and weak relaxationregime of the internal variable towards the background population. Under eachregime, we prove the rigorous hydrodynamic limit towards a coupled systemcomposed of two Euler-type equations. Inertial effects of momentum and internalvariable in the kinetic species disappear for strong relaxation, whereas anontrivial dynamics for the internal variable appears for weak relaxation. Ouranalysis covers both the case of Lipschitz and weakly singular influencefunctions

Hydrodynamic limit of a coupled Cucker-Smale system with strong and weak internal variable relaxation