Thermal Conductivity of Materials
Thermal conductivity is basically an indicator of rate of flow of heat through a material. A higher value of thermal conductivity means that material is a good conductor of heat whereas a lower value means that material is a bad conductor of heat and will act as an insulator.
Physical structure and density determine the value of thermal conductivity of a material. It is denoted by ‘k’ and is defined as rate of heat transfer through a unit thickness of the material per unit area and per unit temperature difference.
Solids
Solids generally consist of free electrons and atoms bound in periodic arrangement called lattice. Thermal conductivity in solids is attributed to migration of free electrons and lattice vibrations. Therefore, thermal conductivity of a solid is the sum of electronic component and lattice vibration component. Thermal conductivity of pure metals is high and contribution of electronic component is significant as compared to that of lattice vibration component as shown in Figure below. Thermal conductivity of an alloy of two metals is considerably lower that that of either of two metals. For example values of thermal conductivity of copper and Nickel are 401 W/(m- oK) and 91 W/(m- oK) respectively where as thermal conductivity of constantan ( 55% copper and 45% Nickel) is only 23 W/(m- oK). Arrangement of molecules in a material strongly affects the lattice component of thermal conductivity. Crystalline solid such as diamond has the highest value of thermal conductivity at room temperature. Thermal conductivity of solids generally decreases with increase in temperature.
Fluids
Solids generally have the highest value of thermal conductivity followed by liquids and gases on account of intermolecular spacing between the molecules. In solids molecules are closely packed, in liquids loosely packer and in gases very loosely packed. Thermal conductivity of gases increases with increase in temperature while that of liquids decreases with increase in temperature with glycerin and water being exceptions. Table 3 gives the values of thermal conductivity of different materials.
Thermal Conductivity of Materials at Room Temperature
S. No. Material Conductivity, k ,W/(m-K)
1. Diamond 2300
2. Silver 429
3. Copper 401
4. Gold 317
5. Aluminum 237
6. Iron 80.2
7. Glass 0.78
8. Water 0.607
9. Wood 0.17
10. Air 0.026
Objectives of conduction analysis
The basic objective of conduction analysis is to determine the variation of temperature with respect to location and time throughout a body.
The knowledge of temperature distribution with in a body is required to determine heat transfer rate. Location of a point with in a body, at which temperature is to be determined, is specified by choosing a suitable coordinate system amongst Cartesian coordinates, cylindrical coordinates or spherical coordinates. Temperature at a point is expressed as
- T (x, y, z, t) in rectangular or Cartesian coordinates for parallelepiped bodies
- T (r, φ, z, t) in cylindrical coordinates for cylindrical bodies
- T (r, φ, θ, t) in spherical coordinates for spherical bodies.
For any irregular shaped body, generally rectangular or Cartesian coordinates are used for conduction analysis.
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