  The shearing motion of tidal flows that are excited in non-equilibrium binary
stars transform kinetic energy into heat via a process referred to as tidal
heating. In this paper we aim to explore the way tidal heating affects the
stellar structure. We used the TIDES code, which solves the equations of motion
of the three-dimensional (3D) grid of volume elements that conform multiple
layers of a rotating binary star to obtain an instantaneous value for the
angular velocity, $\omega''$, as a function of position in the presence of
gravitational, centrifugal, Coriolis, gas pressure, and viscous forces. The
released energy, $\dot{E,}$ was computed using a prescription for turbulent
viscosity that depends on the instantaneous velocity gradients. The $\dot{E}$
values for each radius were injected into a MESA stellar structure calculation.
The method is illustrated for a 1.0+0.8 M$_\odot$ binary system, with an
orbital period of $P$=1.44d and departures from synchronous rotation of 5% and
10%. We find that heated models have a larger radius and surface luminosity, a
smaller surface convection zone, and lower nuclear reaction rates than the
equivalent standard stellar models, and their evolutionary tracks extend to
higher temperatures. The magnitude of these effects depends on the amount of
injected energy, which, for a fixed set of stellar, rotation and orbital
parameters, depends on the perturbed star's density structure and turbulent
viscosity. Tidal heating offers a possible alternative for describing phenomena
such as bloated or overluminous binary components, age discrepancies, and
aspherical mass ejection, as well as the extended main sequence turnoff in
clusters. However, establishing its actual role requires 3D stellar structure
models commensurate with the nonspherically symmetric properties of tidal
perturbations.
