Question

For a steel alloy it has been determined that a carburizing heat treatment of 9-h duration will raise the carbon concentration to 0.38 wt% at a point 1.2 mm from the surface. Estimate the time (in h) necessary to achieve the same concentration at a 6.4 mm position for an identical steel and at the same carburizing temperature.

Answer 1

t2 = 256 hours

Step-by-step explanation:

Given data:

Carbon concentration ( C ) at 1.2mm from surface, C = 0.38 wt%

Duration( t ) of heat treatment for 0.38wt% at 1.2mm = 9-hr

Estimate the time (in h) necessary to achieve the same concentration at a 6.4 mm

Assuming same concentration of 0.38wt% we will apply Fick's second law for constant surface concentration

attached below is the remaining part of the solution

x1 = 1.2 mm

x2 = 6.4 mm

t1 = 9-hr

t2 = ?

t2 =
`((6.4)/(1.2) )^(2) * 9` = 256 hours