  We report on the Andreev spectroscopy and specific heat of high-quality
single crystals BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$. The intrinsic multiple Andreev
reflection spectroscopy reveals two anisotropic superconducting gaps $\Delta_L
\approx 3.2 \textendash 4.5$\,meV, $\Delta_S \approx 1.2 \textendash 1.6$\,meV
(the ranges correspond to the minimum and maximum value of the coupling energy
in the $k_xk_y$-plane). The $25 \textendash 30 \%$ anisotropy shows the absence
of nodes in the superconducting gaps. Using a two-band model with s-wave-like
gaps $\Delta_L \approx 3.2$\,meV and $\Delta_S \approx 1.6$\,meV, the
temperature dependence of the electronic specific heat can be well described. A
linear magnetic field dependence of the low-temperature specific heat offers a
further support of s-wave type of the order parameter. We find that a d-wave or
single-gap BCS theory under the weak-coupling approach cannot describe our
experiments.
