A number of binary systems present evidence of enhanced activity around periastron passage, suggesting a connection between tidal interactions and these periastron effects. The aim of this investigation is to study the time-dependent response of a stars surface as it is perturbed by a binary companion. We derive expressions for the rate of dissipation, $dot{E}$, of the kinetic energy by the viscous flows driven by tidal interactions on the surface layer. The method is tested by comparing the results from a grid of model calculations with the analytical predictions of Hut (1981) and the synchronization timescales of Zahn (1977, 2008). Our results for the orbital cycle averaged energy dissipation on orbital separation are consistent with those of Hut for model binaries with orbital separations at periastron >8 stellar radii. The model also reproduces the predicted pseudo-synchronization angular velocity for moderate eccentricities and the same scaling of synchronization timescales for circular orbits with separation as given by Zahn. The computations gives the distribution of $dot{E}$ over the stellar surface, and show that it is generally concentrated at the equatorial latitude, with maxima generally located around four clearly defined longitudes, corresponding to the fastest azimuthal velocity perturbations. Maximum amplitudes occur around periastron passage or slightly thereafter for supersynchronously rotating stars. In very eccentric binaries, the distribution of $dot{E}$ over the surface changes significantly as a function of orbital phase, with small spatial structures appearing after periastron. An exploratory calculation for the highly eccentric binary system delta Sco suggests that the sudden and large amplitude variations in surface properties around periastron may contribute toward the activity observed around this orbital phase.
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