Question

air at 1 atm and 20 c is flowing over the top surface of a .2x.5 m thin metal foil. the air stream velocity is 100 m/s and the metal foil is heated electrically with a uniform heat fluz 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

The surface temperature of the metal foil is 453.645 K

Step-by-step explanation:

The properties of the air at 100°C and 1 atm are the follows:

ρ = density = 0.9458 kg/m³

Cp = specific heat = 1009 J/kg K

Pr = 0.7111

The surface area of the plate is equal to:

`A=WL`

Where

W = width of the plate = 0.2 m

L = length of the plate = 0.5 m

`A=0.2*0.5=0.1m^(2)`

The average friction coefficient is equal to:

`C_(f) =(F)/((A\rho V^(2) )/(2) )`

Where

F = drag force = 0.3 N

V = velocity of air flow = 100 m/s

`C_(f) =(0.3)/((0.1*0.9458*100^(2) )/(2) ) =0.000634`

The average heat transfer coefficient is equal to:

`h=(C_(f)\rho VC_(p) )/(2Pr^(2/3) ) =(0.000634*0.9458*100*1009)/(2*(0.7111x^(2/3)) ) =37.972W/m^(2) K`

The surface temperature is:

`T_(s) =(q)/(h) +T\alpha`

Where

q = heat flux = 6100 W/m²

Tα = temperature of the air = 20°C = 293 K

`T_(s) =(6100)/(37.972) +293=453.645K`