  We study the dynamics of charge and energy currents in a Coulomb-coupled
double quantum dot system, when only one of the two dots is adiabatically
driven by a time-periodic gate that modulates its energy level. Although the
Coulomb coupling does not allow for electron transfer between the dots, it
enables an exchange of energy between them which induces a time variation of
charge in the undriven dot. We describe the effect of electron interactions at
low temperature using a time-dependent slave-spin 1 formulation within
mean-field that efficiently captures the main effects of the strong
correlations as well as the dynamical nature of the driving. We find that the
currents induced in the undriven dot due to the mutual friction between
inter-dot electrons are same order than those generated in the adiabatically
driven dot. Interestingly, up to 43$\%$ percent of the energy injected by the
ac sources can be transferred from the driven dot to the undriven one. We
complete our analysis by studying the impact of the Coulomb interaction on the
resistance of the quantum dot that is driven by the gate.
