  Let $(T^k,h_k)=(S_{r_1}^1\times S_{r_2}^1 \times ... \times S_{r_k}^1,
dt_1^2+dt_2^2+...+dt_k^2)$ be flat tori, $r_k\geq ...\geq r_2\geq r_1>0$ and
$(\mathbb R^n,g_E)$ the Euclidean space with the flat metric. We compute the
isoperimetric profile of $(T^2\times \mathbb R^n, h_2+g_E)$, $2\leq n\leq 5$,
for small and big values of the volume. These computations give explicit lower
bounds for the isoperimetric profile of $T^2\times\mathbb R^n$. We also note
that similar estimates for $(T^k\times \mathbb R^n, h_k+g_E)$, $2\leq k\leq5$,
$2\leq n\leq 7-k$, may be computed, provided estimates for $(T^{k-1}\times
\mathbb R^{n+1}, h_{k-1}+g_E)$ exist. We compute this explicitly for $k=3$. We
use symmetrization techniques for product manifolds, based on work of A. Ros
and F. Morgan.
