  In this article, we have considered a time-dependent two-parameter singularly
perturbed parabolic problem with discontinuous convection coefficient and
source term. The problem contains the parameters $\epsilon$ and $\mu$
multiplying the diffusion and convection coefficients, respectively. A boundary
layer develops on both sides of the boundaries as a result of these parameters.
An interior layer forms near the point of discontinuity due to the
discontinuity in the convection and source term. The width of the interior and
boundary layers depends on the ratio of the perturbation parameters. We discuss
the problem for ratio $\displaystyle\frac{\mu^2}{\epsilon}$. We used an upwind
finite difference approach on a Shishkin-Bakhvalov mesh in the space and the
Crank-Nicolson method in time on uniform mesh. At the point of discontinuity, a
three-point formula was used. This method is uniformly convergent with second
order in time and first order in space. Shishkin-Bakhvalov mesh provides
first-order convergence; unlike the Shishkin mesh, where a logarithmic factor
deteriorates the order of convergence. Some test examples are given to validate
the results presented.
