Question

Turbine blades mounted to rotating disc in a gas turbine engine are exposed to a gas stream that is at $T_{\infty }={1200}^{\circ }C$ and maintains 3 convection coefficient of $h=250W/m^{2}K$ over the blade. Thermal conductivity of blade is $20W/rnK$ and blade have a length of 50 mm. Blade profile has a constant cross-sectional area of $6\times {10}^{-4}{m}^2$ and perimeter of 110 mm. For cooling purpose base of blade is maintand at ${300}^{\circ }C$ . The rate of heat transfer from each blade is equal to;

• A. $700W$
• B. $508W$
• C. $908W$
• D. $221W$

Answer 1

The correct option is B $508W$

$\frac{T_L-T_{\infty }}{T_0-T_{\infty }}=\frac{1}{\cos hmL}$

$m=\sqrt{\frac{hP}{kA}}=\sqrt{\frac{250\times 0.11}{20\times 6\times {10}^{-4}}}$

$m=47.87\text{per meter}$

$mL=47.87\times 0.05=2.39$

$Q=\sqrt{hPkA}{\theta }_0\tan hmL$

$=\sqrt{250\times 0.11\times 20\times {610}^{-4}}\times [1200-300]\times \tan h\left(2.39\right)$

$Q=517\times 0.983$

$Q=508W$