Thermal Conductivity

What is Thermal Conductivity

Thermal conductivity is defined as the ability of a material to transfer heat from one part to another due to temperature difference. In other words, it measures how quickly and efficiently heat can travel through a material or substance. The higher the thermal conductivity value of a material, the faster heat will travel through it. On the other hand, materials with low thermal conductivities are better insulators since they do not allow for much heat transfer.

Diagram showing thermal transfer in a heated rod

The thermal conductivity of a material depends on several factors, such as its composition, density, and structure. Generally speaking, materials with higher densities tend to have higher thermal conductivities than those with lower densities. For example, metals are typically good thermal conductors because they contain densely packed atoms that are able to efficiently transfer heat from one place to another.

Thermal conductivity is an intrinsic property of a material, which means it’s independent of the size and shape of the material.

Thermal Conduction Formula

The rate of heat transfer through conduction can be found as:

\frac{Q}{t} = \frac{k A Δ T}{d}

Where:

$k$ is the thermal conductivity constant
$\frac{Q}{t}$ is the amount of heat energy transferred through the material per second
$d$ is the thickness of the material
$A$ is the cross-sectional area of the material
$Δ T$ is the difference in temperature (T_hot - T_cold)

The SI unit of theraml conductivity is Watts per meter Kelvin (W/m·K).

The imperial unit of thermal conductivity is BTU/(hr·ft⋅°F).

Thermal Conduction Example

What is the rate of heat flow through a glass window that is 2m wide, 3m long, and 1.5cm thick if the outside temperature is 20°C and the inside temperature is 25°C? The thermal conductivity constant (k) for glass is $0.84 \frac{J}{s \cdot m \cdot ℃}$

Solution

Step 1) We write down the given parameters:

W = 2m L = 3m d = 0.015m T_hot = 25°C T_cold = 20°C k = 0.84 J/s⋅m⋅°C

Step 2) We find the cross-sectional area (A):

A = 2 × 3 = 6m²

Step 3) We find the temperature difference (ΔT):

ΔT = 25°C - 20°C = 5°C

Step 3) Now, we can find the rate of heat flow using the thermal conduction formula:

\frac{Q}{t} = \frac{k A Δ T}{d} = \frac{0.84 (6) (5)}{0.015} = 1680 J/s

Factors Affecting Thermal Conductivity

The thermal conductivity of a material is affected by several factors, including:

Atomic and molecular structure: A material’s atomic and molecular structure can have a significant impact on its thermal conductivity. In general, materials with highly ordered structures, such as crystalline solids, have higher thermal conductivities than materials with disordered structures, such as glass or amorphous solids.
Impurities and Defects: The presence of impurities or faults in a material can impact its thermal conductivity. For example, the addition of small amounts of impurities or dopants can increase or decrease the thermal conductivity of some materials. Similarly, the presence of defects such as vacancies or dislocations can reduce thermal conductivity by disrupting the regular lattice structure of the material.
Density: The density of a material influences its thermal conductivity. In general, materials with higher densities have better thermal conductivities because the closer proximity of atoms or molecules enhances the transfer of heat.

Understanding these factors and how they affect thermal conductivity is important for designing materials and devices that require high thermal efficiency or operate in extreme environments. By exploiting these factors, scientists and engineers can develop new materials and systems with improved thermal conductivity for a wide range of applications.

Applications of Thermal Conductivity

Thermal conductivity has a wide range of applications and is used in many fields, from engineering and materials science to physics and chemistry. Some common applications of thermal conductivity include:

Thermal management: Thermal conductivity is crucial for designing and optimizing thermal management systems for electronic devices, such as computers, smartphones, and other electronics. By selecting materials with high thermal conductivity, it is possible to efficiently transfer heat away from sensitive components and dissipate it into the surrounding environment.
Energy conversion: Numerous energy conversion processes, such as the production of thermoelectric power, solar thermal energy systems, and waste heat recovery, depend heavily on thermal conductivity. By optimizing the thermal properties of materials used in these systems, it is possible to improve their overall efficiency and performance.
Materials science: The thermal conductivity of materials can provide important information about their structure, composition, and properties. By measuring thermal conductivity, researchers can gain insights into the thermal behavior of materials under different conditions and use this information to develop new materials with specific thermal properties.
Building and construction: Thermal conductivity is important for designing energy-efficient buildings and structures. By selecting materials with appropriate thermal properties, it is possible to minimize energy consumption for heating and cooling, as well as improve overall comfort and indoor air quality.
Food and agriculture: Thermal conductivity is used in the food and agriculture industries to measure the thermal properties of food products, such as their thermal diffusivity and thermal effusivity. This information is important for designing processing and storage systems that can maintain food quality and safety.

Thermal Conductivity Summary
Definition	The ability of a material or substance to transfer heat.
Symbol	$k$
Formula	$K = \frac{Q}{t} \frac{d}{A Δ T}$
Units	SI Unit (W/m·K)	Imperial Unit (hr·ft⋅°F)

Why is thermal conductivity important?: Thermal conductivity is important because it describes how efficiently a material can transfer heat. This property is crucial for many industrial and scientific applications, such as electronics cooling, energy conversion, and building insulation.

Is thermal conductivity a physical property?: Yes, thermal conductivity is a physical property of materials that describes how efficiently they can transfer heat. It is also an intrinsic property of a material, meaning that it is independent of the sample’s size and shape.

What factors affect thermal conductivity?: Several factors can affect the thermal conductivity of a material, including its composition, Atomic structure, high temperature, Pressure, and density.

Can thermal conductivity be negative?: No, thermal conductivity is always positive, as heat always flows from hot to cold. A negative thermal conductivity value would imply that heat flows in the opposite direction (from cold to hot), which is a violation of the second law of thermodynamics.

How can thermal conductivity be improved in materials?: Thermal conductivity can be improved in materials by increasing their density, reducing impurities, and altering their structure. Adding conductive materials, such as carbon or graphene, can also improve thermal conductivity.