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`

Step-by-step 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* 0.5=0.1 m^2`

drag force is given by

`F_d=c_f\cdot A\rho (v^2)/(2)`

`c_f=(2F_d)/(\rho Av^2)`

`c_f=(2* 0.3)/(0.9458* 0.1* 100^2)`

`c_f=(0.6)/(945.8)`

`c_f=0.000634`

we know average heat transfer coefficient is

`h=(c_f)/(2)* \frac{\rho vc_p}{P_r^{(2)/(3)}}`

`h=(0.000634)/(2)* \frac{0.9458* 100* 1009}{(0.711)^{(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=(6100)/(37.92)+20=180.86^(\circ)C`