How to Calculate and Solve for Thickness of Solidifying Metals | Solidification of Metals

The image above represents thickness of solidifying metals.

To compute for thickness of solidifying metals, six essential parameters are needed and these parameters are Melting Temperature of Metal (Tm), Initial Mould Temperature (To), Heat Diffusivity (α), Time (t), Density (ρ’) and Latent Heat of Fusion (Hf).

The formula for calculating thickness of solidifying metals:

M = 2(Tm – To)√(α)√(t) / √(π)ρ’Hf

Where:

M = Thickness of Solidifying Metal
Tm = Melting Temperature of Metal
To = Initial Mould Temperature
α = Heat Diffusivity
t = Time
ρ = Density
Hf = Latent Heat of Fusion

Let’s solve an example;
Find the thickness of solidifying metal when the melting temperature of metal is 4, the initial mould temperature is 8, the heat diffusivity is 2, the time is 6, the density is 3 and the latent heat of fusion is 7.

This implies that;

Tm = Melting Temperature of Metal = 4
To = Initial Mould Temperature = 8
α = Heat Diffusivity = 2
t = Time = 6
ρ = Density = 3
Hf = Latent Heat of Fusion = 7

M = 2(Tm – To)√(α)√(t) / √(π)ρ’Hf
M = 2(4 – 8)√(2)√(6) / √(π)(3)(7)
M = 2(-4)(1.414)(2.449) / (1.772)(3)(7)
M = -27.712 / 37.22
M = -0.744

Therefore, the thickness of solidifying metal is -0.744 m.

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How to Calculate and Solve for Temperature of Solidifying Metals | Solidification of Metals

The image above represents temperature of solidifying metals.

To compute for temperature of solidifying metals, three essential parameters are needed and these parameters are Surface Temperature (T), Melting Temperature of Metal (Tm) and Initial Temperature of Environment or Mould (To).

The formula for calculating temperature of solidifying metals:

Tsm = T – Tm / To – Tm

Where:

Tsm = Temperature of Solidifying Metals
T = Surface Temperature
Tm = Melting Temperature of Metal
To = Initial Temperature of Environment or Mould

Let’s solve an example;
Find the temperature of solidifying metals when the surface temperature is 12, the melting temperature of metal is 9 and the initial temperature of environment or mould is 10.

This implies that;

T = Surface Temperature = 12
Tm = Melting Temperature of Metal = 9
To = Initial Temperature of Environment or Mould = 10

Tsm = T – Tm / To – Tm
Tsm = 12 – 9 / 10 – 9
Tsm = 3 / 1
Tsm = 3

Therefore, the temperature of solidifying metals is 3 K.

Calculating for Surface Temperature when the Temperature of Solidifying Metals, the Melting Temperature of Metal and the Initial Temperature of Environment or Mould is Given.

T = Tsm (To – Tm) + Tm

Where;

T = Surface Temperature
Tsm = Temperature of Solidifying Metals
Tm = Melting Temperature of Metal
To = Initial Temperature of Environment or Mould

Let’s solve an example;
Find the surface temperature when the temperature of solidifying metals is 10, the melting temperature of metal is 8 and the initial temperature of environment or mould is 14.

This implies that;

Tsm = Temperature of Solidifying Metals = 10
Tm = Melting Temperature of Metal = 8
To = Initial Temperature of Environment or Mould = 14

T = Tsm (To – Tm) + Tm
T = 10 (14 – 8) + 8
T = 10 (6) + 8
T = 68

Therefore, the surface temperature is 68 K.

Continue reading How to Calculate and Solve for Temperature of Solidifying Metals | Solidification of Metals