Write the expression as an algebraic (nontrigonometric) expression in $u$, for $u>0$.
$$\csc \left(\mathrm{arccot}\frac{\sqrt{4-u^2}}{u}\right)$$
$$\csc \left(\mathrm{arccot}\frac{\sqrt{4-u^2}}{u}\right)=$$

Step 1 ：Write the expression as an algebraic (nontrigonometric) expression in $u$, for $u>0$.

Step 2 ：$$\csc \left(\mathrm{arccot}\frac{\sqrt{4-u^2}}{u}\right)$$

Step 3 ：The given expression is in terms of trigonometric and inverse trigonometric functions. To convert it into an algebraic expression, we need to use the properties and identities of these functions.

Step 4 ：The first step is to simplify the argument of the cosecant function, which is the arccotangent of a ratio. The arccotangent of a number is the angle whose cotangent is that number. The cotangent of an angle in a right triangle is the ratio of the adjacent side to the opposite side.

Step 5 ：We can consider a right triangle where the adjacent side is $\sqrt{4-u^2}$ and the opposite side is $u$. The hypotenuse of this triangle, by the Pythagorean theorem, is $\sqrt{(\sqrt{4-u^2}{)}^2+u^2}=\sqrt{4}=2$.

Step 6 ：The cotangent of the angle is then $\frac{\sqrt{4-u^2}}{u}$, so the angle is indeed $\mathrm{arccot}\frac{\sqrt{4-u^2}}{u}$.

Step 7 ：The cosecant of an angle in a right triangle is the ratio of the hypotenuse to the opposite side. So, the cosecant of this angle is $\frac{2}{u}$.

Step 8 ：Therefore, the given expression simplifies to $\frac{2}{u}$.

Step 9 ：Final Answer: The algebraic expression equivalent to the given trigonometric expression is $$\boxed{{\displaystyle \frac{2}{u}}}$$