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

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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.

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How to Calculate and Solve for Diffusion Flux | Diffusion in Alloying

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The image above represents diffusion flux.

To compute for diffusion flux, three essential parameters are needed and these parameters are Mass Transfer (M), Cross-sectional Area (A) and Time (t).

The formula for calculating diffusion flux:

J = M/At

Where:

J = Diffusion Flux
M = Mass Transfer
A = Cross-sectional Area
t = Time

Given an example;
Find the diffusion flux when the mass transfer is 8, the cross-sectional area is 2 and the time is 6.

This implies that;

M = Mass Transfer = 8
A = Cross-sectional Area = 2
t = Time = 6

J = M/At
J = 8/(2)(6)
J = 8/12
J = 0.66

Therefore, the diffusion flux is 0.66 mol m-2 s-1.

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How to Calculate and Solve for Initial Grain Diameter | Deformation

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The image above represents initial grain diameter.

To compute for initial grain diameter, four essential parameters are needed and these parameters are Average Grain Size Diameter (d), Time (t), Time Independent Constant (k) and Time Independent Constant (n).

The formula for calculating initial grain diameter:

do = (dn – kt)(1/n)

Where:

d = Average Grain Size Diameter
k, n = Time Independent Constants
t = Time

Given an example;
Find the initial grain diameter when the average grain size diameter is 2, the time is 3, the time independent constant is 6 and the time independent constant is 9.

This implies that;

d = Average Grain Size Diameter = 2
k = Time Independent Constant = 6
n = Time Independent Constant = 9
t = Time = 3

do = (dn – kt)(1/n)
do = (29 – (6)(3))(1/9)
do = (512 – (18))(1.992)
do = (494)(1.992)
do = 1.99

Therefore, the initial grain diameter is 1.99 mm.

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How to Calculate and Solve for Avrami Equation | Phase Transformation

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The image above represents avrami equation.

To compute for avrami equation, three essential parameters are needed and these parameters are Time (t), Time Independent Constant for the Reaction (K) and Time Independent Constant for the Reaction (n).

The formula for calculating avrami equation:

y = 1 – exp(-Ktn)

Where:

y = Avrami Equation
K = Time Independent Constants for the Reaction
n = Time Independent Constants for the Reaction
t = Time

Let’s solve an example;
Find the avrami equation when the time independent constant for the reaction is 18, the time independent constant for the reaction is 10 and the time is 12.

This implies that;

K = Time Independent Constants for the Reaction = 18
n = Time Independent Constants for the Reaction = 10
t = Time = 12

y = 1 – exp(-Ktn)
y = 1 – exp(-(18)(12)10)
y = 1 – exp((-18)(61917364224))
y = 1 – exp(-1114512556032)
y = 1 – 0
y = 1

Therefore, the avrami equation is 1.

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