How to Calculate and Solve for Heat Diffusivity | Solidification of Metals

Last Updated on May 11, 2024

The image above represents heat diffusivity. To calculate heat diffusivity, three essential parameters are needed, and these parameters are Thermal Conductivity (K), Density (ρ) and Heat Capacity at Constant Pressure (c_p).

The formula to Calculate Heat Diffusivity:

α = Kρc_p

Where:

α = Heat Diffusivity
K = Thermal Conductivity
ρ = Density
c_p = Heat Capacity at Constant Pressure

Let’s solve an example;
Find the heat diffusivity when the thermal conductivity is 10, the density is 12 and the heat capacity at constant pressure is 18.

This implies that;

K = Thermal Conductivity = 10
ρ = Density = 12
c_p = Heat Capacity at Constant Pressure = 18

α = Kρc_p
That is, α = (10)(12)(18)
α = 2160

Therefore, the heat diffusivity is 2160 m²/s.

Calculating the Thermal Conductivity when the Heat Diffusivity, the Density and the Heat Capacity at Constant Pressure are Given

K = ^α / _ρcp

Where:

K = Thermal Conductivity
α = Heat Diffusivity
ρ = Density
c_p = Heat Capacity at Constant Pressure

Let’s solve an example;
Find the thermal conductivity when the heat diffusivity is 15, the density is 10 and the heat capacity at constant pressure is 14.

This implies that;

α = Heat diffusivity = 15
ρ = Density = 10
c_p = Heat Capacity at Constant Pressure = 14

K = ^α / _ρcp
Then, K = ¹⁵ / _{10 (14)}
K = ¹⁵ / ₁₄₀
K = 0.107

Therefore, the thermal conductivity is 0.107.

Read more: How to Calculate and Solve for Rate at Which Latent Heat is Evolved | Solidification of Metals

Calculating the Density when the Heat Diffusivity, the Thermal Conductivity and the Heat Capacity at Constant Pressure are Given

ρ = ^α / _{K x cp}

Where:

ρ = Density
α = Heat Diffusivity
K = Thermal Conductivity
c_p = Heat Capacity at Constant Pressure

Let’s solve an example;
Find the density when the heat diffusivity is 18, the thermal conductivity is 12 and the heat capacity at constant pressure is 4.

This implies that;

α = Heat Diffusivity = 18
K = Thermal Conductivity = 12
c_p = Heat Capacity at Constant Pressure = 4

ρ = ^α / _{K x cp}
ρ = ¹⁸ / _{12 x 4}
So, ρ = ¹⁸ / ₄₈
ρ = 0.375

Therefore, the density is 0.375.

Calculating the Heat Capacity at Constant Pressure when the Heat Diffusivity, the Thermal Conductivity and the Density are Given

c_p = ^α / _{K x ρ}

Where:

c_p = Heat Capacity at Constant Pressure
α = Heat Diffusivity
K = Thermal Conductivity
ρ = Density

Let’s solve an example;
Find the heat capacity at constant pressure when the heat diffusivity is 10, the thermal conductivity is 20 and the density is 6.

This implies that;

α = Heat Diffusivity = 10
K = Thermal Conductivity = 20
ρ = Density = 6

c_p = ^α / _{K x ρ}
That is, c_p = ¹⁰ / _{20 x 6}
c_p = ¹⁰ / ₁₂₀
c_p = 0.083

Therefore, the heat capacity at constant pressure is 0.083.

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

How to Calculate Heat Diffusivity With Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the heat diffusivity.

Now, Click on Solidification of Metal under Materials and Metallurgical

Now, Click on Heat Diffusivity under Solidification of Metal

The screenshot below displays the page or activity to enter your values, to get the answer for the heat diffusivity according to the respective parameter which is the Thermal Conductivity (K), Density (ρ) and Heat Capacity at Constant Pressure (c_p).

Now, enter the values appropriately and accordingly for the parameters as required by the Thermal Conductivity (K) is 10, Density (ρ) is 12 and Heat Capacity at Constant Pressure (c_p) is 18.

Finally, Click on Calculate

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