How to Calculate and Solve for Steady State Diffusion | Diffusion in Alloying

Last Updated on January 12, 2023

The image above represents steady state diffusion.

To compute for steady state diffusion, three essential parameters are needed and these parameters are Diffusion Gradient (dC/dx), Cross-sectional Area (A) and Time (t).

The formula for calculating steady state diffusion:

J = ^dC/dx/_At

Where:

J = Steady State Diffusion
dC/dx = Diffusion Gradient
A = Cross-sectional Area
t = Time

Given an example;
Find the steady state diffusion when the diffusion coefficient is 12, the cross-sectional area is 4 and time is 2.

This implies that;

dC/dx = Diffusion Gradient = 12
A = Cross-sectional Area = 4
t = Time = 2

J = ^dC/dx/_At
J = ¹²/₍₄₎₍₂₎
J = ¹²/₈
J = 1.5

Therefore, the steady state diffusion is 1.5mol m^-2 s^-1.

Calculating the Diffusion Coefficient when the Steady State Diffusion, the Cross-sectional Area and the Time is Given.

dC/dx = J x At

Where:

dC/dx = Diffusion Gradient
J = Steady State Diffusion
A = Cross-sectional Area
t = Time

Given an example;
Find the diffusion coefficient when the steady state diffusion is 3, the cross-sectional area is 4 and the time is 9.

This implies that;

J = Steady State Diffusion = 3
A = Cross-sectional Area = 4
t = Time = 9

dC/dx = J x At
dC/dx = 3 x (4)(9)
dC/dx = 3 x 36
dC/dx = 108

Therefore, the diffusion coefficient is 108.

Calculating the Cross-sectional Area when the Steady State Diffusion, the Diffusion Coefficient and the Time is Given.

A = ^dC/dx / _{J x t}

Where:

A = Cross-sectional Area
J = Steady State Diffusion
dC/dx = Diffusion Gradient
t = Time

Let’s solve an example;
Given that, the steady state diffusion is 12, the diffusion coefficient is 72 and the time is 6.

This implies that;

J = Steady State Diffusion = 12
dC/dx = Diffusion Gradient = 72
t = Time = 6

A = ^dC/dx / _{J x t}
A = ⁷² / _{12 x 6}
A = ⁷² / ₇₂
A = 1

Therefore, the cross-sectional area is 1.

Calculating the Time when the Steady State Diffusion, the Diffusion Coefficient and the Cross-sectional Area is Given.

t = ^dC/dx / _{J x A}

Where:

t = Time
J = Steady State Diffusion
dC/dx = Diffusion Gradient
A = Cross-sectional Area

Let’s solve an example;
Find the time when the steady state diffusion is 8, the diffusion coefficient is 40 and the cross-sectional area is 3.

This implies that;

J = Steady State Diffusion = 8
dC/dx = Diffusion Gradient = 40
A = Cross-sectional Area = 3

t = ^dC/dx / _{J x A}
t = ⁴⁰ / _{8 x 3}
t = ⁴⁰ / ₂₄
t = 1.67

Therefore, the time is 1.67s.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the steady state diffusion

Now, Click on Diffusion In Alloying under Materials and Metallurgical

Now, Click on Steady State Diffusion under Diffusion In Alloying

The screenshot below displays the page or activity to enter your values, to get the answer for the steady state diffusion according to the respective parameter which is the Diffusion Gradient (dC/dx), Cross-sectional Area (A) and Time (t).

Now, enter the values appropriately and accordingly for the parameters as required by the Diffusion Gradient (dC/dx) is 12, Cross-sectional Area (A) is 4 and Time (t) is 2.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the steady state diffusion and presents the formula, workings and steps too.