Question

Steel balls 10 mm in diameter are annealed by heating to 1150 k and then slowly cooling to 450 k in an air environment for which T, = 325K and h = 25 W/m2-K. Assuming the properties of the steel to be k = 40 W/m-K, rho = 7800 kg/m3, and c = 600 J/kg-K, estimate the time required for the cooling process.

Answer 1

Answer:

The answer is below

Explanation:

Given that:

ρ = 800 kg/m3, c = 600 J/kg-K,  k = 40 W/m-K, Initial temperature = Ti = 1150,

Environment temperature = T = 450 K, Final temperature = T∞ = 325 K

Diameter = 10 mm = 0.01 m, A = 6

The estimated time for cooling process (t) is given as:

$t=\frac{\rho dc}{hA} ln\frac{T_i-T_\infty}{T-T_infty}=\frac{7800*0.01*600}{25*6} ln\frac{1150-325}{450-325}\\ \\t=589\ s\\t=0.1635\ h$

The estimated cooling time is 589 s