A silicon wafer with thickness of $925m$ is being heated with a uniform heat flux at the lower surface. The silicon wafer has a thermal conductivity that varies with temperature and can be expressed as $k(T)=(a+bT+c{T}^2)\frac{W}{m}*K,$ where $a=437,b=-1\mathrm{.}29,$ and $c=0\mathrm{.}00111.$ To avoid warping, the temperature difference across the wafer thickness can not exceed $2C.$ If the upper surface of the silicon wafer is at a uniform temperature of $600K,$ determine the maximum allowable heat flux.