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

Answer:

13.8 W/m^2 °C

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⇒

$Re=\frac{VD}{v} =\frac{(3 \ m/s)(0.25 \ m)}{1.562 \times 10^5 m^2/s} = 4.802 \times 10^4$

Nusselt number ⇒

$Nu = \frac{hD}{k} = 2 + [0.4Re^{1/2}+0.06Re^{2/3}]Pr^{0.4}(\frac{\mu_{\infty}}{\mu_s} )\\\\= 2 + [0.4(4.802 \times 10^4)^{1/2}+0.06(4.802 \times 10^4)^{2/3}](0.7296)^{0.4}(\frac{1.849 \times 10^{-5}}{2.76 \times10^5 } )\\\\=135$

The convection heat transfer co efficient is

$h=\frac{k \times Nu}{D} =\frac{0.02551\times135}{0.25} \\\\= 13.8 W/m^2 .^oC$