Question

For a steel alloy it has been determined that a carburizing heat treatment of 14 h duration at 809°C will raise the carbon concentration to 0.54 wt% at a point 3.6 mm from the surface. Estimate the time necessary to achieve the same concentration at a 6.0 mm position for an identical steel and at a carburizing temperature of 1100°C. Assume that D0 is 2.5 × 10-5 m2/s and Qd is 120 kJ/mol.

Answer 1

Answer:

$t_2 = 27.7 hr$

Explanation:

Given data:

carbon concentration  =  0.54%

from the relation given below calculate the time required to achieve concentration at 6.00 mm from surface

$\frac{x^2}{Dt} = constant$

D considered constant

$\frac{x^2}{t} =  constant$

here, x POSITION FROM SURFACE, t is time required to achieve concentration

$\frac{x_1^2}{t_1} = \frac{x_2^2}{t_2}$

$\frac{3.6^2}{14} = \frac{6^2}{t_2}$

$t_2 = 27.7 hr$