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A $0.2 \:m$ thick infinite black plate having a thermal conductivity of $3.96 \: W/m-K$ is exposed to two infinite black surfaces at $300 \: K$ and $400 \: K$ as shown in the figure. At steady state, the surface temperature of the plate facing the cold side is $350\:K$. The value of Stefan-Boltzmann constant, $\sigma$, is $5.67 \times 10^{-8} \: W/m^2 \: K^4$. Assuming $1-D$ heat conduction, the magnitude of the heat flux through the place (in $W/m^2$) is ___________ (correct to two decimal places)

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