A certain insulation has a thermal conductivity of 0.2 W/m °C What thickness is necessary to effect a temperature drop of 400°C for a heat flux of 200 W/m2?

It is necessary 1 meter of thickness.

Explanation:

You need to know the equation (P/A) = (k*T) / (L), where P/A is the heat flux, k is the thermal conductivity, T the temperature drop, and L the unknown thickness. So if rearrange the variables you will have that L = (k*T) / (P/A), and substituting the terms L = (0.2*400) / (200) = 1 meter