Thermal conductivity is defined as a material’s property to conduct heat. Heat transfer across materials occurs in materials that have lower thermal conductivity and transfers faster in materials with high conductivity. It is important to determine the thermal conductivity of materials since different materials are used for different applications. For instance, materials with high conductivity are more efficient when they are used as heat sinks since they can conduct heat away faster. Those with lower thermal conductivity are often used as insulators (Callister 78).
The classical transfer of energy happens through conduction, radiation, convection or combination of all of the above. Thermal transfer is part of the carriage of the different phases of the substances. In any case, the main force that drives heat transfer is the difference in temperature between two points.
Thermal conductivity data is important when it comes to material science, civil engineering, electronics and many other related fields. The research is important especially in places where there are high variations in temperature. High energy generation in any component requires a material that has high thermal conductivity such as copper. On the other hand, materials that have a low conductivity ratio are used in building materials where insulation is important such as in furnaces so as to slow the heat loss down (Halliday, Resnick and Walker 98).
The thermal conductivity of a material depends on the temperature. Thermal conductivity is a tensor, which means that it is possible to have different values for in different directions. The SI units of thermal conductivity are watts per metre Kelvin (W/(m.k)). The dimensions are M1L1T-3θ-1. Where M represents the mass, L is the length, T is the time and θ-1 represents the temperature. There are influential factors that affect the thermal conductivity of materials. They include temperature, chemical phases, thermal anisotropy, magnetic field, electrical conductivity and convection (Callister 79).
There are different ways to measure thermal conductivity. Each of the methods is efficient only for a limited number of materials. The measurement also depends on the temperature and the thermal properties. The techniques of measurements include steady state and transient methods. Transient methods are useful when the temperature of the environment or the material remains constant with change in time. In this method, the signal analysis is straight forward.
Heat conduction
Heat conduction is more efficient in solids since atoms in solids are closer to each other. Metals are the best thermal energy conductors due to the bonding of the atoms which are the metallic bonds. They have free moving electrons and also have a crystalline structure, which aids in the conduction of heat. As the density decrease, so does the conduction. To quantify the means in which a particular material can conduct heat, thermal conductivity is used. It is also known as the thermal coefficient or the conductivity constant. Thermal conductivity is defined as the infinitesimal quantity of thermal energy that is transmitted during an infinitesimal time interval through a material of a particular thickness in a direction normal to the area due to the difference in temperature. The definition is represented as follows in the equation (Callen 90):
dQdt=qx,t=-kA dt (x,t)dx
Thermal conductivity is considered as a material property. Its values id dependent on the density, temperature and the molecular bonding. The equation is only valid when the medium being used is a homogenous material. When the thermal conductivity occurs in an inhomogeneous material, the thermal conductivity changes with length. In cases where the thermal conductivity k has sharp discontinuities at the interfaces between the different environments, the heat across the inter faces follow Newton’s cooling law. The following equation is the representation:
q(t)= -ήA ΔT
Where ΔT= T1-T2 is the temperature jump across the inter-surface when the heat flows from the first region to the second. The ή is the heat transfer coefficient. It is a characteristic of every thermal interface (Hill 89).
Experimental setup
The rod is attached vertically with the upper side tight with the other metallic clump where water is kept at boiling point by immersing an immersion heater. It is important to keep the receptacle clear so as to avoid drops of hot water humping from the water. .
In the experiment, the rod is in full contact with the air. The air’s temperature can be measured with a thermocouple next to the rod. Another thermocouple can be used to measure local temperature by placing in the special cavities of the rod. The thermocouple should be greased with social thermo-conductive paste. The temperature can be read in Celsius (Hill 102.
The position of the cavities can be as follows with respect to the lower end of the rod: 0 cm (which is at the lower end), 7,0 cm; 10.0 cm; 14.0 cm; 17.5 cm; 21.0 cm; 24.0 cm; 28.0 cm; 31.0 cm; 35,0 cm; 38.5 cm. L = 38.55 cm.
The procedure
A constant flux of energy can be injected into the metallic rod, which is aluminium. The temperature of the rod can be measured at the specific points. Therefore, a steady-state temperature distribution is obtained and recorded.
Another method is through using a guarded heat plate method. The sample aluminium is sandwiched between a hot and cold plate, which allows the heat flow from the hotter side to the cooler side. This kind of set up assumes that the metal rod is isentropic and there is no heat lost in radiation. The measurements of the rod should be taken, which include the length and the surface area. The thermal conductivity can be determined using the following equation (1):
= Q ∙ LA ∙ ΔT
Where Q is the heath load of the sample, L is the length of the sample, which is in metres. A is the cross-sectional area of the material on which the heat is applied. ΔT is the change in temperature or the temperature difference between the top and bottom of the surface (3) (Halliday, Resnick and Walker 99).
The above are two ways in determining the thermal conductivity of a material. One of them is in the transient state while the other is in a homogenous environment. The methods can be used to determine the heat conductivity of different material. The experiments deal with the problem of thermal conduction in a metallic rod or cylinder. The ends of the cylinder sit on different ends with the temperatures T1 and T2. The experiments are meant to determine the value k of Aluminium metal. The plot of a graph is important since the one will be able to observe how the temperature changes with time. The plot will also help in determining the value of k.
Work Cited
Callen, Herbert B. Thermodynamics & an Intro. to Thermostatistics. New York: John Wiley & Sons, 2006. Print
Callister, William. Materials Science and Engineering - An Introduction. New Jersey: John Wiley & Sons, 2003.
Halliday, David, Robert Resnick and Jearl Walker. Fundamentals of Physics (5th ed.). , New York: John Wiley and Sons, 1997. Print.
Hill, Terrell. An introduction to statistical thermodynamics. New York: Courier Corporation, 2012.
