Question

Air at 1 atm and 20°C is flowing over the top surface of a 0.2 m 3 0.5 m-thin metal foil. The air stream velocity is 100 m/s and the metal foil is heated electrically with a uniform heat flux of 6100 W/m2. If the friction force on the metal foil surface is 0.3 N, determine the surface temperature of the metal foil. Evaluate the fluid properties at 100°C.

Answer 1

Answer:$180.86^{\circ}C$

Explanation:

Properties of Fluid at $100^{\circ}C$

$P_r=0.711$

$\rho =0.9458 kg/m^3$

$c_p=1009 J/kg/k$

$Flux =6100 W/m^2$

Drag force $F_d=0.3 N$

$A=0.2\times 0.5=0.1 m^2$

drag force is given by

$F_d=c_f\cdot A\rho \frac{v^2}{2}$

$c_f=\frac{2F_d}{\rho Av^2}$

$c_f=\frac{2\times 0.3}{0.9458\times 0.1\times 100^2}$

$c_f=\frac{0.6}{945.8}$

$c_f=0.000634$

we know average heat transfer coefficient is

$h=\frac{c_f}{2}\times \frac{\rho vc_p}{P_r^{\frac{2}{3}}}$

$h=\frac{0.000634}{2}\times \frac{0.9458\times 100\times 1009}{(0.711)^{\frac{2}{3}}}$

$h=37.92 W/m^2-K$

Surface Temperature of metal Foil

$\dot{q}=h(T_s-T{\infty })$

$T_s=\frac{\dot{q}}{h}$

$T_s$ is the surface temperature and T_{\infty }[/tex] is ambient temperature

$T_s=\frac{6100}{37.92}+20=180.86^{\circ}C$