The thermal conductivity of composites W-Ag, Mo-Ag, Fe-Ag
Marcin Madej, Jan Leżański, Tadeusz Telejko Akademia Górniczo-Hutnicza, Wydział Inżynierii Metali i Informatyki Przemysłowej, al. Mickiewicza 30, 30-059 Kraków, Poland
Quarterly No. 2, 2008 pages 172-178
DOI:
keywords: powder, sintered material, infiltration, composites, thermal conductivity
abstract To solve the heat conduction equation we need to know geometry of the conducting body, its thermo-physical properties, the distribution of internal heat sources or sinks (if existing) as well as the initial and boundary conditions. The accuracy of the determination of those unknown quantities strongly which influence the result of final temperature field calculations. The heat conduction equation should also take into consideration the heat effect of the phase transformation if the heating or cooling of steel is analyzed. Therefore, the determination of latent heat of phase transformation and thermal properties of the material are of great importance. Thermal conductivity can be measured in any apparatus which supplies the specified boundary condition to a particular solution of heat conduction equation in Cartesian, cylindrical or spherical coordinates. The thermal diffusivity can be therefore evaluated from this method if the temperature measurements inside the body are provided. Next, the thermal conductivity λ can be calculated when the density ρ and the heat capacity cp are known. Since the temperature in the body can vary with time, the methods based on this method belong to the non-stationary ones. Some of those methods have been described in literature. The presented methods of thermal conductivity determination have been based on the solutions, which assume that the thermo-physical parameters do not depend on temperature. It is impossible to obtain a closed form solution to the heat conduction equation if the thermal diffusivity varies with temperature, even for the one-dimensional case. Those methods are therefore limited to narrow temperature intervals, approaching zero. Thus, many experimental tests must be carried out for evaluation of the influence of temperature on the thermal diffusivity or conductivity. The development of numerical methods and computational techniques has stimulated the applications of inverse methods to problems which can be governed by differential equations, including heat conduction. If the boundary conditions for the direct solution of heat conduction problem are unknown, the measurements of temperatures in a sample renders it possible to evaluate the heat conduction by using an inverse technique. The method proposed in the paper allows simultaneous determination of the thermal conductivity. To present the base of the method the following conduction problem is considered that the cylindrical steel sample is uniformly heated at the front surface. The inverse procedure can be performed in the following steps: accomplishment of the temperature measurements in the selected points of the sample during heating or cooling, determination of the thermal conductivity λ(t) and the heat generation qv. The circumferential surface of the sample can be thermally insulated. The method involves some experimental tests and several steps of calculations. In the first test, the sample is heated at the front surface to the temperature above the phase transformation and temperatures in selected points inside the body are measured. The test bench should be designed in the way which gives one-dimensional heat conduction in the body. As a result of an experimental test the temperature field in the sample is obtained. The same experiment must be performed during cooling process of the sample. The heated up cylindrical sample is suddenly cooled at the front surface to the temperature below the phase transformations. Data form these tests are necessary to solve the inverse problem with the use of some additional information including specific heat, density, thermocouple location, etc. Attempts have been made to describe the influence additions powders: tungsten, molybdenum and iron on the thermal conductivity of silver infiltrated composites. The physical and mechanical properties of the investigated composites the thermal conductivities of composites W+40%Ag, Mo+40%Ag and Fe+40%Ag are presented and from the analysis of the obtained results it may be concluded that the thermal conductivity is mainly affected by the used powders (tungsten, molybdenum, iron) and volume of silver and the porosity level