已知数列\(\{a_{n}\}\)的前\(n\)项和\(S_{n}\)满足\(2S_{n}-na_{n}=n\)，\(n\in N^{+}\)，且\(a_{2}=3.\)
\((1)\)求数列\(\{a_{n}\}\)的通项公式；
\((2)\)设\(b_{n}=\dfrac{1}{a_{n}\sqrt{a_{n+1}}+a_{n+1}\sqrt{a_{n}}}\)，\(T_{n}\)为数列\(\{b_{n}\}\)的前\(n\)项和，求使\(T_{n}>\dfrac{9}{20}\)成立的最小正整数\(n\)的值．