Chapter 5, Problem 5.77P

Interpretation Introduction

Interpretation:

Whether the magnesium diffusion or oxygen diffusion will limit the rate needs to be determined, the time required for the ${1500}^{0}C$ temperature needs to be determined.

Concept introduction:

The ceramic part is made from MgO at ${1700}^{0}C$ in 1.5 hr. but the temperature is reduced to ${1500}^{0}C$ reduce thermal stresses. Thus, the time required is calculated by Fick's equation as follows:

$\frac{Cs-Cx}{Cs-Co}=erf(\frac{x}{2\sqrt{Dt}})$

Here,

Cs = Constant concentration

Co = Initial concentration

Cx = concentration at depth x

T = time required

D = diffusion coefficient