  This work is aimed at the study and analysis of the heat transport on a metal
bar of length $L$ with a solid-solid interface. The process is assumed to be
developed along one direction, across two homogeneous and isotropic materials.
Analytical and numerical solutions are obtained under continuity conditions at
the interface, that is a perfect assembly. The lateral side is assumed to be
isolated and a constant thermal source is located at the left-boundary while
the right-end stays free allowing the heat to transfer to the surrounding fluid
by a convective process. The differences between the analytic solution and
temperature measurements at any point on the right would indicate the presence
of discontinuities. The greater these differences, the greater the
discontinuity in the interface due to thermal resistances, providing a measure
of its propagation from the interface and they could be modeled as temperature
perturbations. The problem of interest may be described by a parabolic equation
with initial, interface and boundary conditions, where the thermal properties,
the conductivity and diffusivity coefficients, are piecewise constant
functions. The analytic solution is derived by using Fourier methods. Special
attention is given to the Sturm-Liouville problem that arises when deriving the
solution, since a complicated eigenvalue equation must to be solved. Numerical
simulations are conducted by using finite difference schemes where its
convergence and stability properties are discussed along with physical
interpretations of the results.
