Thermal Conductivity and Specific Heat Capacity

There is a niche market for thermoplastics with very high thermal conductivity. These are marketed for CPU cooling in laptop compnters and other high performance applications. An interesting point to note is that thermal and electrical conductivity actually benefit from poor filler dispersion. Agglomeration and network formation (percolation) allows better heat conduction due to the network of particle - particle contacts. 

---

The FDS5 pyrolysis model is used here to qualitatively illustrate the complexity associated with material property estimation. Each condensed-phase species (i.e., virgin wood, char, ash, etc.) must be characterized in terms of its bulk density, thermal properties (thermal conductivity and specific heat capacity, both of which are usually temperature-dependent), emissivity, and in-depth radiation absorption coefficient. Similarly, each condensed-phase reaction must be quantified through specification of its kinetic triplet (preexponential factor, activation energy, reaction order), heat of reaction, and the reactant/product species. For a simple charring material with temperature-invariant thermal properties that degrades by a single-step first order reaction, this amounts to -11 parameters that must be specified (two kinetic parameters, one heat of reaction, two thermal conductivities, two specific heat capacities, two emissivities, and two in-depth radiation absorption coefficients). 

An important method for finding heat transfer coefficients was and still is the experiment. By measuring the heat flow or flux, as well as the wall and fluid temperatures the local or mean heat transfer coefficient can be found using (1.25) and (1.33). To completely solve the heat transfer problem all the quantities which influence the heat transfer must be varied when these measurements are taken. These quantities include the geometric dimensions (e.g. tube length and diameter), the characteristic flow velocity and the properties of the fluid, namely density, viscosity, thermal conductivity and specific heat capacity. 

Figure 24.2. Thermal conductivity and specific heat capacity of dry silty sand versus temperature (U.S. EPA, 2002a).

As described in the previous sections, the changes in the effective thermophysical properties (density, thermal conductivity, and specific heat capacity) are mainly determined by the decomposition process. This process, being kinetic, is not just an univariate function of temperature, but also on time. Therefore, and in contrast to true material properties, effective properties are dependent not only on temperature, but also on time. In order to model the time-dependent physical properties, related kinetic processes must be taken into account, as described by the kinetic equations in Chapter 2. 

Models for the effective thermophysical properties - including mass (density), thermal conductivity, and specific heat capacity - have been developed in Chapter 4. Those material property models are implemented into the heat transfer governing equation in the following. 

A one-dimensional thermal response model was developed to predict the temperature of FRP structural members subjected to fire. Complex boundary conditions can be considered in this model, including prescribed temperature or heat flow, as well as heat convection and/or radiation. The progressive changes of thermophysical properties including decomposition degree, density, thermal conductivity, and specific heat capacity can be obtained in space and time domains using this model. Complex processes such as endothermic decomposition, mass loss, and delatnina-tion effects can be described on the basis of an effective material properties over the whole fire duration. 

Here, K and Cp are, respectively, the thermal conductivity and specific heat capacity of the fluid. The viscous dissipation

strain rate tensor, e = i(V + (Vm) ). The second term of equation (7.59) is the ohmic heating due to the passage of the current. 

Nieto de Castro CA, Murshed SMS, LourenQo MJV, Santos FJV, Lopes MLM, Franca IMP (2012) Enhanced thermal conductivity and specific heat capacity of carbon nanotubes ionanofluids. Int J Therm Sci 62 34—39... 

The following symbols are used in the definitions of the dimensionless quantities mass (m), time (t), volume (V area (A density (p), speed (u), length (/), viscosity (rj), pressure (p), acceleration of free fall (p), cubic expansion coefficient (a), temperature (T surface tension (y), speed of sound (c), mean free path (X), frequency (/), thermal diffusivity (a), coefficient of heat transfer (/i), thermal conductivity (/c), specific heat capacity at constant pressure (cp), diffusion coefficient (D), mole fraction (x), mass transfer coefficient (fcd), permeability (p), electric conductivity (k and magnetic flux density ( B) ... 

High thermal conductivity, high specific heat capacity and high evaporation enthalpy... 

In this section, heat and temperature related or dependent properties of polytetrafluoroethylene resins are discussed. These include thermal stability, thermal expansion, thermal conductivity, and specific heat (heat capacity). These characteristics are important to both design and use of PTFE parts. 

High thermal conductivity, high specific heat capacity, and high evaporation enthalpy of water predestine it as a heat removal fluid see Section 2.4. 

B. Weidenfeller, M. Hofer, F.R. Schilling, Thermal conductivity, thermal diflusivity, and specific heat capacity of particle filled polypropylene. Compos. Part A Appl. Sci. Manuf. 35, 423-29 (2004)... 

The thermal properties of ZnO doped with A1 and Mg were also studied by a number of groups [149-153] for the evaluation of the thermoelectric performance. Tsubota et al. [152] investigated the thermal conductivity of sintered (Zni yMgy)i xAlj 0 (x O-Q. , y = 0-0.1) samples determined from thermal diffusivity and specific heat capacity measured by the laser flash technique and differential scanning calorimetry (DSC), respectively. The temperature dependences of the thermal conductivities of (Zni yMgy)o.9gAlo.o20 (y = 0.0-02,0.1) are shown in Figure 1.29 in comparison with that of ZnO. The reduction of k from... 

Here, Q is the heat energy input per area p and Cp are the density and specific heat capacity, respectively and indices g, d, and s refer to the gas, metal, and liquid sample layers, respectively. With Eq. (106), the thermal conductivity of the sample liquid is obtained from the measured temperature response of the metal without knowing the thermal conductivity of the metal disk and the thickness of the sample liquid. There is no constant characteristic of the apparatus used. Thus, absolute measurement of thermal conductivity is possible, and the thermal conductivities of molten sodium and potassium nitrates have been measured. ... 

The velocity held is determined by the characteristic length L0, and velocity w0 e.g. the entry velocity in a tube or the undisturbed velocity of a fluid flowing around a body, along with the density g and viscosity rj of the fluid. While density already plays a role in frictionless flow, the viscosity is the fluid property which is characteristic in friction flow and in the development of the boundary layer. The two material properties, thermal conductivity A and specific heat capacity c, of the fluid are important for the determination of the temperature held in conjunction with the characteristic temperature difference Ai 0. The specihc heat capacity links the enthalpy of the fluid to its temperature. 

Although, the transient grating measurements yield values for thermal diffusivity for each IL directly, the thermal conductivity must be found from a knowledge of the density and specific heat capacity through the relation a = Only a few values of density and heat capacity have... 

The specific heat of a material (kJ kg °K ) is the energy required to raise the temperature of a unit mass by one degree (Fig. 24.2). The product of the specific heat and density is referred to as the heat capacity (kJ m °K ) and provides a measure of the material s ability to store heat. The heat capacity of soils and fluids change with temperature however, the range of variation for heat capacity of different soils is generally small compared with the variability of other parameters such as permeability. Similar to thermal conductivity, the bulk heat capacity of a soil is the combined heat capacity of the soil particles and the fluid in the pore space. 

Most polymer products approximate to series of flat or curved plate-like elements joined together. This simplifies the analysis of heat flow by reducing it to a one-dimensional problem—see Figure 7.16. The wall of the component is of half-thickness L and is cooled by an environment ai temperature T. Within a polymer of thermal conductivity k, density p, and specific heat capacity c, the variation of temperature T is then governed by the equation of one-dimensional heat conduction ... 

Standard techniques of vector analysis allow to equate the heat flow into the volume V to the heat flow across its surface. This operation leads to the linear and homogeneous Fourier differential equation of heat flow, given as Eq. (3). The letter k represents the thermal diffusivity in m s, which is equal to the thermal conductivity k divided by the density and specific heat capacity. The Laplacian operator is + d dy + d ld-z, where x, y, and z are the space coordinates. 

---