Thermal Properties in Materials Engineering

Acknowledgement

Lecture material sourced from:
Materials Science and Engineering: An Introduction by William D. Callister, Jr. and David G. Rethwisch, Wiley.
Specifically the Tenth Edition.

Bimetal Strip

Definition: A bimetal strip is a composite material made from two distinct metals that are bonded together. These metals are chosen specifically for their disparate coefficients of thermal expansion (CTE), which means they expand at different rates when exposed to changes in temperature.

Example: A common example of a bimetal strip consists of copper and iron, wherein the differing thermal expansion properties create mechanical movement when heated.

• Unbonded: When the two metals are not bonded, there is no interaction, resulting in the expansion of each metal independently.

• Bonded: When bonded, the metals engage thermally, leading to bending or deflection due to the differential expansion or contraction during heating and cooling cycles, which is utilized in applications like thermostats and temperature sensors.

Heat Capacity

General Definition: Heat capacity is defined as the capacity of a material to absorb heat from its surroundings, thereby affecting its temperature. This property is crucial for materials used in thermal management applications.

Quantitative Definition: Mathematically, heat capacity is expressed as:
C = \frac{dQ}{dT}
Where:

• dQ is the incremental energy input, and

• dT is the resultant change in temperature.

Types of Heat Capacity:

• C_p: Heat capacity measured at constant pressure, which takes into account work done by the system (expansion work).

• C_v: Heat capacity measured at constant volume, which does not include external work.

• It is important to note that typically Cp > Cv because the system can do work at constant pressure, which involves additional energy.

Energy Storage in Materials

Mechanism: Thermal energy is stored in the material as vibrational modes, referred to as phonons, which are quantized modes of vibration for the atoms within the material.

Phonon Definition: Phonons are the quanta of thermal vibrational energy, functioning similarly to photons in electromagnetic waves and playing a significant role in heat conduction.

Heat Capacity vs Temperature

Behavior: The heat capacity of materials generally increases with temperature as the molecular motions become more energetic, facilitating heat absorption.

• It approaches a limiting value of 3R as temperature rises, where R is the universal gas constant (8.31 J/mol-K).

Atomic View: As temperature increases, the average energy of atomic vibrations correspondingly increases, which contributes to heightened thermal energy storage.

Additional Contributions to Heat Capacity

• Electronic Contribution: At temperatures above absolute zero, the kinetic energy of electrons significantly influences thermal energy capacity; however, this contribution is generally minor in materials such as semiconductors, ceramics, and polymers at high temperatures.

Thermal Expansion

Definition: Thermal expansion refers to the increase in the average distance between atoms as a result of temperature elevation, which has implications in material stability and design.

Measurement: It is quantified by the coefficient of thermal expansion (CTE), denoted as \alpha, and is defined by the equation:
\Delta L = \alpha L_0 \Delta T
Where:

• L_0 is the original length of the material, and

• \Delta T denotes the change in temperature.

Effects of Crystallography: The thermal expansion behavior can exhibit anisotropy, meaning it varies with direction, depending on the material structure (crystalline or amorphous). This plays a critical role in selecting materials for various engineering applications.

Thermal Conductivity

Definition: Thermal conductivity represents the ability of a material to conduct heat and is pivotal in applications where heat management is essential.

• Fourier’s Law: The relationship between heat flux q, thermal conductivity k, and temperature gradient is described by Fourier’s law:
  q = -k \frac{dT}{dx}.

Mechanisms of Transfer: Heat transfer in solids typically occurs through lattice vibrations (phonons) and free electrons, making the balance of these mechanisms crucial for efficiency in thermal management systems.

Thermal Stress

Definition: Thermal stress is the internal stress induced by temperature changes within a material, which may lead to mechanical failure, such as cracking or permanent deformation.

Dependents: It is reliant on the material's elastic modulus, linear coefficient of thermal expansion, as well as the magnitude of temperature change experienced by the material.

Applications of Thermal Expansion and Conductivity

• Bimetal strips are extensively used in thermostats and switches due to their predictable mechanical movement from thermal expansion, critical for temperature control in various systems.

• In aerospace applications, materials exhibit high thermal stability and conductivity are used, such as silica tiles in space shuttles, which require effective heat management to protect from extreme temperature fluctuations during re-entry.

Summary of Thermal Properties

• Heat Capacity: Typically, polymers exhibit the highest heat capacities among various materials.

• Coefficient of Thermal Expansion: Polymers also tend to showcase the highest thermal expansion rates, which must be considered in design.

• Thermal Conductivity: Metals demonstrate the greatest conductive capabilities, essential for applications requiring efficient heat dissipation.

• Thermal Shock Resistance: This refers to a material's ability to endure rapid changes in temperature without fracturing.

• Key parameters: Measurement of thermal shock resistance is characterized by parameters such as tensile strength \sigma_f and the ratio \frac{k}{E \alpha}, which are pivotal for maximizing resistance to thermal shock and ensuring longevity and reliability of materials used in fluctuating thermal environments.