Answer:
3.26 secs
Explanation:
Diameter of sphere ( D )= 10 mm
T1 = 75°C
P = 1 atm
T∞ = 23°C
T2 = 35°c
Velocity = 10 m/s
<u>Determine how long it will take to cool the sphere to 35°C</u>
<em>Using the properties of copper and air given in the question</em>
Nu = 2 + (Re)^0.8 (Pr)^0.33
hd / k = 2 + ( vd/v )^0.8 (Pr)^0.33
∴ h ≈ 2594.7 W/m^2k
Given that :
(T2 - T∞) / ( T1 - T∞ ) = exp [ ( -hA / pv CP ) t ]
( 35 - 23 ) / ( 75 - 23 ) = exp [ - 2594.7 * 6 * t / 8933 * 387 * 10 * 10^-3 ]
= ln ( 12/52 ) = -1.466337069 = - 0.45032919 * t
∴ t ≈ 3.26 secs ( -1.466337069 / -0.45032919 )
