$8\mathrm{.}17$

In a wind tunnel experiment, an aluminum plate $2\mathrm{.}0$ m in length is electrically heated at a power density of $\backslash (1\backslash$mathrm$\{$~kW$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash )$ and is cooled on one surface by air flowing at $\backslash (10\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The air in the wind tunnel has a temperature of $290$ K and is at $1$ atm pressure, and the Reynolds number at the end of turbulent transition regime is observed to be $400,000.$ Estimate the average temperature of the plate.