Consider Couette flow between two plates a distance of 2 millimeters apart whose top plate moves with a velocity of \(1 \mathrm{~m} / \mathrm{s}\) and the bottom plate is held fixed. The temperature of both plates are held fixed at zero degrees Celsius. The thermal conductivity is \(0.6 \frac{\mathrm{W}}{\mathrm{mK}}\) and the dynamic viscosity is \(10^{-3} \mathrm{~Pa} \cdot \mathrm{s}\). Find a value for the non-dimensional temperature in the middle in the flow. Unscale the result and obtain a value for the temperature in the middle of the flow in Celsius.