How to Calculate and Solve for Effective Heat of Fusion | Solidification of Metals

The image above represents effective heat of fusion.

To compute for effective heat of fusion, three essential parameters are needed and these parameters are Latent Heat of Fusion (Hf), Heat Capacity at Constant Pressure (cp) and Change in Temperature (ΔT).

The formula for calculating effective heat of fusion:

H = Hf + cpΔT

Where:

H = Effective Heat of Fusion
Hf = Latent Heat of Fusion
cp = Heat Capacity at Constant Pressure
ΔT = Change in Temperature

Let’s solve an example;
Find the effective heat of fusion when the latent heat of fusion is 12, the heat capacity at constant pressure is 14 and the change in temperature is 10.

This implies that;

Hf = Latent Heat of Fusion = 12
cp = Heat Capacity at Constant Pressure = 14
ΔT = Change in Temperature = 10

H = Hf + cpΔT
H = 12 + 14(10)
H = 12 + 140
H = 152

Therefore, the effective heat of fusion is 152 J/Kg.

Calculating the Latent Heat of Fusion when the Effective Heat of Fusion, the Heat Capacity at Constant Pressure and the Change in Temperature is Given.

Hf = H – cpΔT

Where:

Hf = Latent Heat of Fusion
H = Effective Heat of Fusion
cp = Heat Capacity at Constant Pressure
ΔT = Change in Temperature

Let’s solve an example;
Find the latent heat of fusion when the effective heat of fusion is 42, the heat capacity at constant pressure is 10 and the change in temperature is 2.

This implies that;

H = Effective Heat of Fusion = 42
cp = Heat Capacity at Constant Pressure = 10
ΔT = Change in Temperature = 2

Hf = H – cpΔT
Hf = 42 – (10)(2)
Hf = 42 – 20
Hf = 22

Therefore, the latent heat of fusion is 22.

Continue reading How to Calculate and Solve for Effective Heat of Fusion | Solidification of Metals

How to Calculate and Solve for Total Latent Heat | Solidification of Metals

The image above represents total latent heat.

To compute for total latent heat, three essential parameters are needed and these parameters are Density of Solidifying Metal (ρ’), Volume of Casting (V) and Latent Heat of Fusion (Hf).

The formula for calculating the total latent heat:

Q = ρ’VHf

Where:

Q = Total Latent Heat
ρ = Density of Solidifying Metal
V = Volume of Casting
Hf = Latent Heat of Fusion

Let’s solve an example;
Find the total latent heat when the density of solidifying metal is 12, the volume of casting is 14 and the latent heat of fusion is 10.

This implies that;

ρ = Density of Solidifying Metal = 12
V = Volume of Casting = 14
Hf = Latent Heat of Fusion = 10

Q = ρ’VHf
Q = (12)(14)(10)
Q = 1680

Therefore, the total latent heat is 1680 J/Kg.

Calculating the Density of Solidifying Metal when the Total Latent Heat, the Volume of Casting and the Latent Heat of Fusion is Given.

ρ = Q / VHf

Where;

ρ = Density of Solidifying Metal
Q = Total Latent Heat
V = Volume of Casting
Hf = Latent Heat of Fusion

Let’s solve an example;
Find the density of solidifying metal when the total latent heat is 20, the volume of casting is 4 and the latent heat of fusion is 2.

This implies that;

Q = Total Latent Heat = 20
V = Volume of Casting = 4
Hf = Latent Heat of Fusion = 2

ρ = Q / VHf
ρ = 20 / (4)(2)
ρ = 20 / 8
ρ = 2.5

Therefore, the density of solidifying metal is 2.5

Continue reading How to Calculate and Solve for Total Latent Heat | Solidification of Metals

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.

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