## How to Calculate and Solve for the Total Volume Shrinkage | Solidification of Metals The image above represents total volume shrinkage.

To compute for total volume shrinkage, three essential parameters are needed and these parameters are Liquid Shrinkage of Metal or Alloy (εv.l), Freezing Shrinkage (εv.f) and Solid Shrinkage (εv.s).

The formula for calculating the total volume shrinkage:

εv.t = εv.l + εv.f + εv.s

Where:

εv.t = Total Volume Shrinkage
εv.l = Liquid Shrinkage of Metal or Alloy
εv.f = Freezing Shrinkage
εv.s = Solid Shrinkage

Let’s solve an example;
Find the total volume shrinkage when the liquid shrinkage of metal or alloy is 14, the freezing shrinkage is 7 and the solid shrinkage is 2.

This implies that;

εv.l = Liquid Shrinkage of Metal or Alloy = 14
εv.f = Freezing Shrinkage = 7
εv.s = Solid Shrinkage = 2

εv.t = εv.l + εv.f + εv.s
εv.t = 14 + 7 + 4
εv.t = 25

Therefore, the total volume shrinkage is 25.

Calculating the Liquid Shrinkage of Metal or Alloy when the Total Volume Shrinkage, the Freezing Shrinkage and the Solid Shrinkage is Given.

εv.l = εv.t – εv.f – εv.s

Where:

εv.l = Liquid Shrinkage of Metal or Alloy
εv.t = Total Volume Shrinkage
εv.f = Freezing Shrinkage
εv.s = Solid Shrinkage

Let’s solve an example;
Find the liquid shrinkage of metal or alloy when the total volume shrinkage is 44, the freezing shrinkage is 12 and the solid shrinkage is 6.

This implies that;

εv.t = Total Volume Shrinkage = 44
εv.f = Freezing Shrinkage = 12
εv.s = Solid Shrinkage = 6

εv.l = εv.t – εv.f – εv.s
εv.l = 44 – 12 – 6
εv.l = 26

Therefore, the liquid shrinkage of metal or alloy is 26.

## How to Calculate and Solve for Volume Shrinkage | Solidification of Metals The image above represents volume shrinkage.

To compute for volume shrinkage, two essential parameters are needed and these parameters are Mould Volume (Vm) and Volume of Casting at 20°C (Vo).

The formula for calculating the volume shrinkage:

εv= Vm – Vo / Vo x 100%

Where:

εv = Volume Shrinkage
Vm = Mould Volume
Vo = Volume of Casting at 20°C

Let’s solve an example;
Find the volume shrinkage where the mould volume is 30 and the volume of casting at 20°C.

This implies that;

Vm = Mould Volume = 30
Vo = Volume of Casting at 20°C = 3

εv= Vm – Vo / Vo x 100%
εv = 30 – 3 / 3 x 100%
εv = 27 / 3 x 100%
εv = 9 x 100%
εv = 900%

Therefore, the volume shrinkage is 900%.

## How to Calculate and Solve for Linear Shrinkage | Solidification of Metals The image above represents linear shrinkage.

To compute for linear shrinkage, two essential parameters are needed and these parameters are Linear Dimension of the Mould (lm) and Size of the Casting at 20°C (lo).

The formula for calculating linear shrinkage:

εL = lm – lo / lo x 100%

Where:

εL = Linear Shrinkage
lm = Linear Dimension of the Mould
lo = Size of Casting at 20°C

Let’s solve an example;
Find the Linear shrinkage where the linear dimension of the mould is 20 and the size of casting is 10.

This implies that;

lm = Linear Dimension of the Mould = 20
lo = Size of Casting at 20°C = 10

εL = lm – lo / lo x 100%
εL = 20 – 10 / 10 x 100%
εL = 10 / 10 x 100%
εL = 1 x 100%
εL = 100%

Therefore, the linear shrinkage is 100%.

## How to Calculate and Solve for Heat Extraction by Radiation | Solidification of Metals The image above represents heat extraction by radiation.

To compute for heat extraction by radiation, four essential parameters are needed and these parameters are Emissivity (ε), Stefan-Boltzmann Constant (σ), Surface Temperature of Metal (Tsurf) and Ambient Temperature (Tamb).

The formula for calculating heat extraction by radiation:

qx = εσ(Tsurf4 – Tamb4)

Where:

qx = Heat Extraction by Radiation
ε = Emissivity
σ = Stefan-Boltzmann Constant
Tsurf = Surface Temperature of Metal
Tamb = Ambient Temperature

Let’s solve an example;
Find the heat extraction by radiation where the emissivity is 20, the stefan-boltzmann constant is 5.67E-8, the surface temperature of metal is 14 and the ambient temperature is 12.

This implies that;

ε = Emissivity = 20
σ = Stefan-Boltzmann Constant = 5.67E-8
Tsurf = Surface Temperature of Metal = 14
Tamb = Ambient Temperature = 12

qx = εσ(Tsurf4 – Tamb4)
qx = 20(5.67e-8)(144 – 124)
qx = 20(5.67e-8)(38416 – 20736)
qx = 20(5.67e-8)(17680)
qx = 0.02004912

Therefore, the heat extraction by radiation is 0.02004912 W.

## How to Calculate and Solve for Heat Flux | Solidification of Metals The image above represents heat flux.

To compute for heat flux, three essential parameters are needed and these parameters are Heat Emission (h), Surface Temperature (Ts) and Initial Temperature (To).

The formula for calculating heat flux:

qx = h(Ts – To)

Where:

qx = Heat Flux (T)
h = Heat Emission
Ts = Surface Temperature
To = Initial Temperature

Let’s solve an example;
Find the heat flux when the heat emission is 21, the surface temperature is 12 and the initial temperature is 10.

This implies that;

h = Heat Emission = 21
Ts = Surface Temperature = 12
To = Initial Temperature = 10

qx = h(Ts – To)
qx = 21(12 – 10)
qx = 21(2)
qx = 42

Therefore, the heat flux is 42 W.

Calculating the Heat Emission when the Heat Flux, the Surface Temperature and the Initial Temperature is Given.

h = qx / Ts – To

Where:

h = Heat Emission
qx = Heat Flux (T)
Ts = Surface Temperature
To = Initial Temperature

Let’s solve an example;
Find the heat emission when the heat flux is 40, the surface temperature is 20 and the initial temperature is 10.

This implies that;

qx = Heat Flux (T) = 40
Ts = Surface Temperature = 20
To = Initial Temperature = 10

h = qx / Ts – To
h = 40 / 20 – 10
h = 40 / 10
h = 4

Therefore, the heat emission is 4.

## How to Calculate and Solve for Freezing Time | Solidification of Metals The image above represents freezing time.

To compute for freezing time, three essential parameters are needed and these parameters are Thickness of Solidified Metal (M), Constant (β) and Heat Diffusivity (α).

The formula for calculating freezing time:

t = / 4β²α

Where:

t = Freezing Time
M = Thickness of Solidified Metal
β = Constant
α = Heat Diffusivity

Let’s solve an example;
Find the freezing time when the thickness of solidified metal is 8, the constant is 10 and the heat diffusivity is 2.

This implies that;

M = Thickness of Solidified Metal = 8
β = Constant = 10
α = Heat Diffusivity = 2

t = / 4β²α
t = / 4(10)²(2)
t = 64 / 4(100)(2)
t = 64 / 800
t = 0.08

Therefore, the freezing time is 0.08 s.

Calculating the Thickness of Solidified Metal when the Freezing Time, the Constant and the Heat Diffusivity is Given.

M = t x 4β²α

Where:

M = Thickness of Solidified Metal
t = Freezing Time
β = Constant
α = Heat Diffusivity

Let’s solve an example;
Find the thickness of solidified metal when the freezing time is 21, the constant is 9 and the heat diffusivity is 2.

This implies that;

t = Freezing Time = 21
β = Constant = 9
α = Heat Diffusivity = 2

M = t x 4β²α
M = 21 x 4(9²)(2)
M = 21 x 4(81)(2)
M = 21 x 4(162)
M = 21 x 648
M = 13668

Therefore, the thickness of solidified metal is 13668.

## 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.

## How to Calculate and Solve for Solidification Time | Solidification of Metals The image above represents solidification time.

To compute for solidification time, three essential parameters are needed and these parameters are Chvorinov’s Constant (C), Volume (V) and Surface Area (A).

The formula for calculating solidification time:

t = C(V / A)

Where:

t = Solidification Time
C = Chvorinov’s Constant
V = Volume
A = Surface Area

Let’s solve an example;
Find the solidification time when the chvorinov’s constant is 15, the volume is 12 and the surface area is 8.

This implies that;

C = Chvorinov’s Constant = 15
V = Volume = 12
A = Surface Area = 8

t = C(V / A)
t = 15(12 / 8)
t = 15(1.5)
t = 22.5

Therefore, the solidification time is 22.5s.

Calculating the Chvorinov’s Constant when the Solidification Time, the Volume and the Surface Area is Given.

C = tA / V

Where:

C = Chvorinov’s Constant
t = Solidification Time
V = Volume
A = Surface Area

Let’s solve an example;
Find the Chvorinov’s Constant when the solidification time is 20, the volume is 12 and the surface area is 8.

This implies that;

t = Solidification Time = 20
V = Volume = 12
A = Surface Area = 8

C = tA / V
C = (20)(8) / 12
C = 160 / 12
C = 13.3

Therefore, the chvorinov’s constant is 13.3

## 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

## 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.