Question

A 25 cm stainless steel ball is removed from the oven at a uniform temperature of 300 C. The ball isthen subjected to the flow of air at one atm pressure and 27 C with a velocity of 3 m/sec. Thesurface temperature of the ball eventually drops to 200 C. Determine the convection heat transfercoefficient during this cooling process.

Answer 1

13.8 W/m^2 °C

Step-by-step explanation:

At average surface temperature, the dynamic viscosity of air is

`\mu_s=\mu_(at 25^0C) = 2.76 10^(-5) kg/ms\\\\`

The properties of air at temperature of 27°C and 1 ATM are:

k = 0.02551 W/m · °C

V= 1.562 x 10⁵ m²/s

μ= 1.849 x 10⁵ kg/ms

Pr = 0.7296

Reynolds number⇒

`Re=(VD)/(v) =((3 \ m/s)(0.25 \ m))/(1.562 * 10^5 m^2/s) = 4.802 * 10^4\\`

Nusselt number ⇒

`Nu = (hD)/(k) = 2 + [0.4Re^(1/2)+0.06Re^(2/3)]Pr^(0.4)((\mu_(\infty))/(\mu_s) )\\\\= 2 + [0.4(4.802 * 10^4)^(1/2)+0.06(4.802 * 10^4)^(2/3)](0.7296)^(0.4)((1.849 * 10^(-5))/(2.76 *10^5 ) )\\\\=135`

The convection heat transfer co efficient is

`h=(k * Nu)/(D) =(0.02551*135)/(0.25) \\\\= 13.8 W/m^2 .^oC`