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Thermal Conductivity Calculator

Calculate thermal conductivity, thermal resistance, heat flux, and heat transfer rates for different materials.

Parameters

ⓘ
Select what you want to calculate
ⓘ
Select the material (updates thermal conductivity)
W/m·Kⓘ
Thermal conductivity of the material
°Cⓘ
Temperature difference across the material
mⓘ
Thickness of the material
m²ⓘ
Cross-sectional area for heat transfer
Show Trail

Controls

xⓘ

Calculated Values

Heat Flux
60.00;W/m260.00;W/m²
Heat Transfer Rate
60.00;W60.00;W
Thermal Resistance
0.83;K/W0.83;K/W

Examples

Heat Flux Through a Wall

Calculate the heat flux through a 0.2 m thick brick wall with thermal conductivity 0.6 W/m·K when the temperature difference is 30°C.

  • Heat Flux: 90.0090.00
  • Heat Transfer Rate: 90.0090.00
  • Thermal Resistance: 0.330.33

Finding Thermal Conductivity

A material with thickness 0.1 m has a heat flux of 200 W/m² when the temperature difference is 40°C. Calculate its thermal conductivity.

  • Thermal Conductivity: 0.500.50
  • Heat Transfer Rate: 200.00200.00
  • Thermal Resistance: 0.200.20

Thermal Resistance Calculation

Calculate the thermal resistance of a 0.05 m thick aluminum plate with area 2 m². The thermal conductivity of aluminum is 237 W/m·K.

  • Thermal Resistance: 0.000.00
  • Temperature Difference: 0.110.11
  • Heat Flux: 500.00500.00

Visualization

Thermal Conductivity and Heat Transfer

Thermal conductivity (k) is a material property that measures how well a material conducts heat. It represents the amount of heat energy that flows through a unit area of material per unit time per unit temperature gradient.

The heat flux (q) through a material is given by Fourier's law: q = k(ΔT/L), where k is the thermal conductivity, ΔT is the temperature difference across the material, and L is the thickness of the material.

Thermal resistance (R) is a measure of how much a material resists heat flow. It is given by: R = L/(kA), where A is the cross-sectional area. Higher thermal resistance means less heat transfer for the same temperature difference.

The heat transfer rate (Q) through a material can be calculated using: Q = qA = kA(ΔT/L) = ΔT/R. This equation shows the relationship between heat transfer rate, temperature difference, and thermal resistance.

Different materials have vastly different thermal conductivities. Metals like copper (401 W/m·K) and aluminum (237 W/m·K) have high thermal conductivity, while insulating materials like fiberglass (0.04 W/m·K) have low thermal conductivity.

Thermal conductivity depends on the material's molecular structure, density, and temperature. Generally, materials with free electrons (metals) conduct heat better than materials with bound electrons (insulators).

In engineering applications, thermal conductivity is crucial for designing heat exchangers, insulation systems, electronic cooling, and building materials. Understanding thermal conductivity helps optimize energy efficiency.

Composite materials and layered structures can have effective thermal conductivities that differ from their individual components. This is important in designing thermal barriers and heat management systems.

Explore Further

More thermodynamics tools

Physics Equations

Heat Flux
q=kΔTLq = k\frac{\Delta T}{L}
Thermal Conductivity
k=qLΔTk = q\frac{L}{\Delta T}
Thermal Resistance
R=LkAR = \frac{L}{kA}
Heat Transfer Rate
Q=ΔTRQ = \frac{\Delta T}{R}

Step-by-Step Solution

See how the main results are calculated.

1

Identify Variables

List the known values

Result:

ThermalConductivity(k)=0.12W/m⋅KTemperatureChange(ΔT)=50°CThickness(L)=0.1mArea(A)=1m2Thermal Conductivity (k) = 0.12 W/m·K Temperature Change (ΔT) = 50°C Thickness (L) = 0.1 m Area (A) = 1 m²

Explanation:

We have the thermal conductivity, temperature change, thickness, and area values.

2

Apply Heat Flux Formula

Use q = k(ΔT/L) to find heat flux

Equation:

q=kΔTLq = k\frac{\Delta T}{L}

Calculation:

q=0.12W/m⋅K×50°C0.1mq = 0.12 W/m·K × \frac{50°C}{0.1 m}
q=60.00W/m2q = 60.00 W/m²

Result:

q=60.00W/m2q = 60.00 W/m²

Explanation:

The heat flux formula relates thermal conductivity, temperature gradient, and heat flow per unit area.

3

Calculate Heat Transfer Rate

Find the total heat transfer rate

Equation:

Q=qAQ = qA

Calculation:

Q=60.00W/m2×1m2Q = 60.00 W/m² × 1 m²
Q=60.00WQ = 60.00 W

Result:

Q=60.00WQ = 60.00 W

Explanation:

The heat transfer rate is calculated by multiplying heat flux by the cross-sectional area.

4

Calculate Thermal Resistance

Find the thermal resistance of the material

Equation:

R=LkAR = \frac{L}{kA}

Calculation:

R=0.1m0.12W/m⋅K×1m2R = \frac{0.1 m}{0.12 W/m·K × 1 m²}
R=0.833333K/WR = 0.833333 K/W

Result:

R=0.833333K/WR = 0.833333 K/W

Explanation:

Thermal resistance is a measure of how much a material resists heat flow.

Frequently Asked Questions (FAQ)

What is thermal conductivity?

Thermal conductivity is a material property that measures how well a material conducts heat. It represents the amount of heat energy that flows through a unit area per unit time per unit temperature gradient.

What is the difference between heat flux and heat transfer rate?

Heat flux (q) is heat transfer per unit area (W/m²), while heat transfer rate (Q) is the total heat transfer (W). They are related by Q = qA, where A is the area.

What is thermal resistance?

Thermal resistance is a measure of how much a material resists heat flow. It is given by R = L/(kA) and is measured in K/W. Higher resistance means less heat transfer.

Why do metals have high thermal conductivity?

Metals have high thermal conductivity because they have free electrons that can carry heat energy efficiently. These electrons can move freely and transfer energy quickly through the material.

What are the units of thermal conductivity?

Thermal conductivity is measured in watts per meter per kelvin (W/m·K) or watts per meter per degree Celsius (W/m·°C). Both units are equivalent.

How does thickness affect heat transfer?

Thicker materials have higher thermal resistance and therefore lower heat transfer rates for the same temperature difference. Heat transfer is inversely proportional to thickness.

What is Fourier's law?

Fourier's law states that heat flux is proportional to the temperature gradient: q = -k(dT/dx). For a uniform material, this becomes q = k(ΔT/L).

How is thermal conductivity used in engineering?

Thermal conductivity is used to design heat exchangers, insulation systems, electronic cooling, building materials, and thermal management systems. It helps optimize energy efficiency and thermal performance.

Practice MCQs

  1. What is the formula for heat flux?
  2. What are the units of thermal conductivity?
  3. Which material has the highest thermal conductivity?
  4. What is the relationship between thermal resistance and heat transfer?
  5. What is the formula for thermal resistance?
  6. How does thickness affect thermal resistance?
  7. What is the relationship between heat flux and area?
  8. Which material would be best for insulation?

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