Experimental tests using air as the working fluid are conducted on a portion of the turbine blade shown in the sketch. The heat flux to the blade at a particular point $(x^{**})$ on the surface is measured to be $q^{\text{'}\text{'}}=95,000\frac{W}{m}2.$

To maintain a steady$-$state surface temperature of $800C,$ heat transferred to the blade is removed by circulating a coolant inside the blade.

Determine the heat flux to the blade at $x^{**}$ if its temperature is reduced to $700C$

Case $1$