Thermal properties of rubber compound : thermal diffusivity

Thermal diffusivity can be conveniently determined by observing temperature change as a function of time for sample geometrical shapes under heating condition. Alternatively of course if k r and Cp are known or separately determine. Thermal diffusivity can be calculated from its definition as thermal diffusivity = k/r*Cp. As specific heat is an additive property, it is generally convenient to calculate specific heats of rubber compound than to measure them. Specific heat of a rubber compound is given by

Cp = w1*C1 + w2*C2 + w3*C3 + …..

where w1, w2 and w3 are weight fractions of the ingredients and C1, C2 and C3 are their specific heat. In general for rubber compound above the grass transition thermal diffusivity tends to decrease slightly with increasing temperature. This is attributed to an increase of specific heat as temperature increase. However some author stated that there is no significant change in thermal diffusivity over the temperature range from room temperature up to 140 *C.

How to increased thermal conductivity of rubber compound.

Thermal conductivity is the basic parameter for defining heat flow in a material. Normally the thermal conductivity of rubber compound is inversely propertional to temperature but in the range of 20-90*C, the value of thermal conductivity of both gum and carbon black filled compound are slightly changed, therefore it can be assumed that the thermal conductivity of rubber is independent of temperature without any significant error. The inclusion of filler has a marked effect on thermal conductivity of the rubber compound which postulated that 10 phr of carbon black may be expected to increase the thermal conductivity by about 17% at room temperature. In the meantime we founded that thermal conductivity was an additive property depending on the volume fraction of the ingredient by an appropriate conductivity and adding these product to the thermal conductivity of gum vulcanisate. A large dependence of conductivity on loading of carbon black was reported that thermal conductivity of rubber compound increased almost linearly with black content in the range of 10-50 phr. An experimental result clearly showed that thermal conductivity increased linearly with carbon black loading and therefore the mathermatical relations between thermal conductivity and carbon black loading were introduce as

k(w) = k(0) + 0.32w

or

k(j) = k(0) + 0.4jf

where w is the weight fraction and j is the volume fraction of crabon black.

Apart from carbon black loading carbon black structure seems to have an influence on the thermal conductivity of rubber as well. Effect of carbon black structure on thermal conductivity of NR compound we found that higher carbon black structure gives higher value of thermal conductivity. However the degree of change in thermal conductivity as a function of carbon black structure is small and is not straight forward.

Thermal Properties : Basic principal of heat transfer

Holman had proposed a difinition of heat transfer as “science which seeks to predict the energy transfer which may take place between material bodies as a result of temperature difference”. The energy transfer is known as heat . There are three mode of heat transfer : conduction, convection, and radiation.

1. Conduction heat transfer : When a single body is subjected to a temperature gradient heat will be transferred from the hight temperature region to the low temperature region. This mode of heat transfer is call “conduction” and from Fourier’s law for steady state condition, the heat transfer rate per unit area is proportional to the normal temperature gradient, as shown in equation 1

when dQ/dt is the heat transfer rate and partial derivative of temperature respective to x is the temperature gradient in the direction of the heat flow. The constant k is called the thermal conductivity of the material which is define as the heat transport in a material per unit temperature gradient per unit area between two isothermal planes. In case of unsteady state (transient) conduction, where the temperature at any point in a body varies with both time and position, the basic Fourier equation becomes a patial differential :

where C and r are specific heat and density, respectively. The expression k/(rC) is called “thermal diffusivity” of the material and is represented by a .A hight value of a could either result from a high value of thermal conductivity (k), which would indicate a rapid energy transfer rate, or from a low value of the thermal heat capacity rC . The low value of heat capacity indicate that less of the energy moving through the material would be absorbed and used to raise the temperature of the material thus more energy would be available for further transfer. Therefore, the larger the value of a , the faster will heat diffuse through the material.