Thermal Properties of Engineering Materials

By thermal properties of material, we mean those properties or characteristics of materials which are the functions of temperature or heat. We are here concerned with the thermal behaviour of solids i.e., the response of solid material to thermal change, i.e., increase or decrease of heat or temperature.

Thermal properties of engineering materials comprise the following:

1. Specific heat.

2. Thermal conductivity.

3. Thermal expansion.

4. Melting point or heat resistance.

5. Thermal shock.

6. Thermal diffusivity.

7. Thermal effect.

These properties are important in applications like thermodynamics, heat transfer, and melting of metals.

1. Specific Heat (Heat Capacity):

The heat capacity of a material is defined as the amount of heat required to raise its temperature by 1°. The heat capacity per unit mass, of material is defined as its specific heat. Heat capacity per mole is defined as its molar heat capacity.

Mathematically, specific heat of a solid is defined as-

Where, m = Mass,

T = Temperature,

Q = Energy content, and

dQ = Energy (heat) added or subtracted to produce the temperature change dT.

For unit mass per degree change in temperature specific heat c = dQ, the quantity of heat that must be added per unit mass of a solid to raise its temperature by one degree. The specific heat of material is sometimes defined as the ratio of its heat capacity to that of water. Specific heat in this becomes the dimensionless unit (as specific heat of water is unity in MKS units).

For gases there are two specific heats i.e., specific heat at constant volume c_v and specific at constant pressure c_p . c_p is always greater than c_v since any substance expands on heating and extra heat is required to raise the temperature by 1 degree in order to compensate for the energy required for expansion. For solids, difference between c_p and c_v is negligible and only one specific heat is used (c_p = c_v = c). This is due to the fact that in solids and liquids the expansion with heating is very small.

According to classical kinetic theory of heat, heat capacity of an atom in a solid (crystalline element) is constant and is equal to 26 kJ/kg atoms (°C) at room temperature. This is to be divided by molecular weight in order to get mass specific heat of a solid.

Specific heat increases slightly with increase in temperature and varies from metal to metal. An increase of 5 percent for every 100°C temperature rise can be used as a general approximation. The effect of raising temperature of metals and alloys is to raise the amplitude of vibration of each atom and the heat energy so absorbed is the specific heat.

2. Thermal Conductivity:

It is defined as the amount of heat conducted in a unit time through a unit area normal to the direction of heat flow. Heat conduction through isotropic solids is expressed by Fourier’s law:

q = Rate of heat flow/unit area normal to the direction of flow,

T = Temperature,

x = Distance measured in the direction of flow, and

k = Thermal conductivity.

Heat flow through solids is due to elastic vibration of atoms or molecules or due to transfer of energy by the free electrons. Metals have large supply of free electrons which account for their thermal conductivity. Both types of conduction occurs in metals and semiconductors. Insulators have lower conductivities as they depend entirely on the lattice vibration of atoms and molecules. This is a slower process than electronic conduction.

The theory of thermal conductivity through crystalline solids (metals) based on quantum (solid state) theory can be explained by concept of phonons which represent the particles (gas) characteristics of a thermal wave. It is a quantum of energy and vibration of a thermoelastic (acoustic) wave.

In dielectrics (thermal insulators) thermal conductivity is caused alone by the atomic or molecular vibration of the lattice (lattice is a geometrical array of lines or points in which atoms are considered spheres) representing a certain type of crystal (say metal) structure.

The progress of this elastic thermal wave (or phonons) through a crystal is akin to a gas molecule through a gas. At a heated surface the motion is increased so that collision with other phonons occurs at an increased rate and thus heat is transmitted to other parts of the phonon gas. Thermal conductivity in solids is given by a formula similar to that derived from the kinetic theory of gases.

Where, k = Thermal conductivity,

c = Specific heat per unit volume,

ν = Average particles velocity or velocity of the lattice wave (the velocity of sound), and

λ = Mean free path of lattice wave (phonon) of a given frequency.

In an ideal crystal, the atomic or molecular waves of vibration are harmonic, hence, X is very large and it should have infinite thermal conductivity. In actual crystals mutual scattering and lattice wave (phonons) may occur, due to inharmonicity of the vibration and internal crystal imperfection. Phonons scattering and thus thermal conductivity depends, on crystalline structure of metals and alloys.

A comparison of thermal and electrical conductivities is given below:

Some typical thermal conductivities are shown as follows:

The thermal conductivity of pure metals increases as temperature is lowered often to a considerable degree. Copper has thermal conductivity about 35 times greater at – 269°C than at 20°C.

Alloys, however, do not show this pronounced increase of thermal conductivity at lower temperatures and only small percentages of alloying are required to suppress this change in thermal characteristics.

At normal and elevated temperatures, pure metals and their alloys possess very low temperature co-efficient of thermal conductivity and thus for all design purposes these effects of higher temperature on thermal conductivity are usually ignored.

The thermal conductivity of amorphous solids such as glasses, and plastics increases with a rise in temperature. They generally possess, low thermal conductivity at room temperature. This is due to the fact that amorphous solids have excessive .scattering of phonons by their disordered structure at lower temperatures.

The thermal conductivity of refractories (more complex solids) depends on their chemical composition and crystalline structures. This is due to the presence of impurities and comparatively smaller grain size and porosity which result in lower values of thermal conductivity.

If structure is simple as in case of silicon carbide, thermal conductivity has higher value. Fire clay bricks and fuel fused silica also show an increase in thermal conductivity with increasing temperature. On the other hand in case of magnesite and alumina which are more crystalline in nature, the thermal conductivity decreases with rising temperature.

3. Thermal Expansion:

Thermal expansion arises from the addition of heat energy in the atoms and their subsequent movement away from their equilibrium positions as the temperature rises in solid. This expansion or contraction resulting from increase or decrease in temperature is three dimensional but in practice linear thermal expansion is used for simplicity instead of volume expansion.

The increase in length per unit length per degree rise in temperature is called coefficient of linear expansion. Thermal expansion does not necessarily vary uniformly with temperature but it is sufficiently linear over narrow ranges of temperature.

If the bonds between the atoms are strong and highly directional as in ionic and covalent solids, the thermal expansion will be relatively small. If on the other hand the atoms are more loosely bound as in metals, a greater degree of expansion is there. In molecular solid, where bonding least resists the movement of the molecules, the thermal expansion will be the greatest.

The thermal expansion of solid is related to other thermal properties such as specific heat and melting point as all these properties have their origin in lattice vibrations which increase with the temperature. The atoms or molecules as earlier explained oscillate (vibrate) with a certain amplitude about their equilibrium positions.

The amplitude of this vibration increases as the temperature rises resulting in moving further away of atoms and molecules from their equilibrium position causing an increase in volume (or linear expansion) of solid. In this way magnitude of the coefficient of thermal expansion of solids will depend on their interatomic and intermolecular forms and also on their structural arrangement.

It has been observed that between absolute zero temperature and the melting point, total volume range of elements is approximately constant. This can be interpreted that materials with lower softening (melting) points will have higher expansion coefficients. This also means that thermal expansion will approach zero at the absolute zero temperature.

Organic polymers such as plastics and rubber have many times higher expansion coefficients than metals because of their relatively lower softening point. This may be reduced by addition of filler materials (such as glass fibre, asbestos, alumina etc.) possessing lower thermal expansion coefficients. Alloying of metals have a minor effect on this property.

4. Melting Point:

Melting point or softening point is a significant temperature level as it represents transition point between solid and liquid phases having different structural arrangement of the atoms within the material. As heat is added to a solid, its thermal energy increases until the atoms or molecules on the surface begin to break away from their equilibrium positions.

There is a link between interatomic spacing at which the bonding force is maximum and the amplitude of thermal vibration at which this breaking away occurs as if the atoms can be separated at this point, no further increase in force is needed to separate them further. After melting commences, any further heat is all used up in activating more particles of solids which in turn collide with neighbouring particles transmitting their energy to them.

The structure is therefore transformed from a solid having definite equilibrium positions to a liquid having only short range order. During melting no further rise in temperature occurs and solid and liquid phases exist at the same temperature. Melting temperature depends upon the amount of thermal energy required.

This in turn depends on the nature of interatomic and intermolecular bonds. Therefore higher melting point is exhibited by those materials possessing stronger bonds. Covalent, ionic, metallic and molecular types of solids have decreasing order of bonding strength and thus the melting points.

Crystalline solids have a sharp melting point at which there is sudden transformation from solids to liquid states. Amorphous solids such as glasses, plastics and rubbers and also clays do not have definite melting points but soften gradually over a certain temperature range.

Relation between Thermal Expansion and Melting Point:

Both depend upon the bonds between atoms (or molecules) of the solid and so are related. For each class of materials

α T_m = constant, …(10.4)

Where, α = Coefficient of thermal expansion, and

T_m = Melting temperature.

Therefore, any two materials of a given class possessing same coefficient of expansion will therefore have approximately same melting point.

The value of this constant is as under:

There is an interesting conclusion that for a material to be coated to another material, coating will have to be of different class than the base material if both must have same thermal expansion.

Heat Resistance:

Melting point determines the heat resistance of a material as any material for high temperature application should have its melting point above the service temperature. Ceramic materials are known to have high melting points and good chemical stability but they are difficult to fabricate and cannot take thermal or mechanical shock.

Following is the list of some materials possessing resistance to high temperatures:

5. Thermal Shock:

Thermal shock is the effect of a sudden change of temperature on a material whereas thermal shock resistance can be defined as the ability of material to withstand thermal stresses due to sudden and severe changes in the temperature at the surface of a solid body.

If a solid structure is prevented so that it cannot expand or contract freely on heating or cooling, excessive thermal stresses may result culminating in thermal shock and causing failure of the body. Thermal shock resulting from cooling which results in tensile stresses at the surface is much more dangerous than that from heating.

Thermal shock resistance of a solid is sometimes given by the equation:

Where, k = Thermal conductivity,

σ_t = Tensile strength,

E = Young’s modulus, and

α = Linear co-efficient of thermal expansion.

For maximum shock resistance:

(i) Thermal-conductivity should be high.

(ii) Thermal expansion should be low.

(iii) Material should have low elastic modulus and high tensile strength.

c. Brittle materials such as glass and ceramics are particularly prone to thermal shock because they readily experience brittle failure instead of plastic yield.

6. Thermal Diffusivity:

Thermal diffusivity (h) is defined as:

c_p ρ represent heat requirement per unit volume. A material having high heat requirement per unit volume possesses a low thermal diffusivity because more heat must be added to or removed from the material for affecting a temperature change. Thermal diffusivity is therefore associated with the diffusion of thermal energy and may be taken to represent an energy flux arising from the motion of phonons through a relatively stationary atomic array. As phonons are in the nature of waveform, the atoms vibrate in unison but are not physically transported.

7. Thermal Stresses:

When expansion or contraction of a body due to temperature change is wholly or partially prevented, thermal stress will be developed in body. Thermal stress may arise from external bodies connected to one under stress as for example, welded structure, railway line shrink fit components. Or, it may be due to non-uniform expansion of the body itself, for example bimetallic strips used in thermostatic controls. The value of thermal stress, expansion or contraction can be calculated by applying simple stress calculation theory.

8. Thermo-Elastic Effect:

When a solid is subjected to a load, work is done on it and it changes in volume. If this work is done at constant temperature, an adiabatic temperature rise (without transfer of heat to or from the surroundings) occurs. This will appear in the form of rise of temperature of solid when it is in stretched condition. Similarly when the solid is rapidly relaxed, -it will feel. cool. This warming or cooling phenomenon is called thermoelastic effect.