Coefficient of Thermal Expansion


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Paraffins such as those found in Opticool Fluid may be used as heat transfer mediums in electrical cooling and thermal systems, in liquid phase cooling of electronic components, in thermal energy storage and a host of similar applications 1,2,. Although air and water have long been employed as cost-effective heat transfer agents, paraffins have the advantage of being good electrical insulators which is important in applications where removal of heat by convection – that is to have the fluid directly in contact with heated electronic components – is desired.

Paraffins have better thermal insulating capability than air-cooled systems. Their other notable properties that make paraffins useful for cooling applications include thermal and chemical stability, non-toxicity, biodegradability, and low cost.

One particular property found within paraffins involves a low coefficient of thermal expansion. Coefficient of thermal expansion is defined as the change in volume of a material per one degree Celsius change in temperature. This is an intensive property and is unique for each substance.

For applications requiring fluid to be contained in pipes or containers, this property is important to consider in choosing the fluid suited for each application. As the fluid is exposed to varying temperatures, its volume also changes and the container or pipes should be designed to accommodate this volume changes to ensure proper functioning. This helps to avoid build-up of hydraulic pressure and spills during equipment servicing as well. Because the coefficient of thermal expansion for paraffins are much lower than that of air, their use as coolants offer many advantages to modern systems designers in the unending pursuit of technological miniaturization.

The coefficient of thermal expansion of a particular substance is precisely determined via experimental methods such as dilatometric and pycnometric procedures. The first method measures the changes in volume of the object using a length sensitive device and requires that the objects are highly elastic, mostly solids or solid-like material such as pastes. The second method relies on the fact that changes in volume can be indirectly obtained from the densities of materials as temperatures change 3. Both methodologies are extremely laborious to perform 3, however, if the fluid is well-researched and their densities are known for a certain temperature of interest, the coefficient of thermal expansion of the fluid can be estimated. Thus, volume changes can be calculated as well in the following manner.

To obtain the equation for the Coefficient of Thermal Expansion, we begin with the Ideal Gas Law:


From the above equation, we have the Volumetric Coefficient of Thermal expansion, beta, as: Fig1a2 This is the coefficient of Thermal expansion, changing with Temperature.

For a finite change of Temperature, we can get the approximate value of the Thermal expansion coefficient as:


It should be noted here that for Fluids, beta or Coefficient of Volumetric Thermal expansion is used; while for Solids alpha or Coefficient of Linear Thermal expansion is commonly used. With that, we will have the following formula for the fluid as:


And for a solid as:


For an application that uses a Solid as a container for the Fluid, we will be dealing with Volume of the Solid. Thus, obtaining the relationship of alpha and beta as applied to solid will be useful, and the approximate relationship will be as follows:


With the relevant equations outlined, we can now apply these to a practical application. We will start by calculating the required size of a container needed to accommodate a volume of a particular liquid (Paraffin) over a known temperature range. We will use the graph shown here to indicate the temperature range of operation (given that the density at said points are known):



For further analysis, we will calculate the Void space (volume) of the Container when the liquid completely cools down. This is the state #3 in the above graph. It should be noted that the locations of the said temperature points are arbitrary as long as density at that point is known.  For this analysis, we assume that T1 = T3 (that applies to the full temperature range of the Fluid).


Specific Example

For the case of Paraffin (C16-C28), we have the Following:



Mineral oils are a mixture of hydrocarbons constituting saturated straight chain and cyclic hydrocarbons as well as aromatic hydrocarbons. Paraffins are purified portions of mineral oils and consist primarily of “paraffinic” or saturated straight chain hydrocarbons. Paraffins are also further classified to many fractions having specific flash/fire points, depending upon the number of carbons in the backbone of the constituent hydrocarbon for a certain fraction. In real-world cooling applications, densities of a specific paraffin fraction at a certain temperature should be accurately identified in order to accurately estimate the coefficient of thermal expansion and volume changes using the equations above. While some values may be obtained via textbooks and information found on the Internet, more reliable data may be obtained from suppliers or manufacturers for each fluid under evaluation.

  1. N. Ukrainczyk, S. Kurajica, and J. Sipusie. “Thermophysical Comparison of Five Commercial Paraffin WSaes as Latent Heat Storage Materials.” Chem. Biochem. Eng. . 24 (2) 129-1377 (2010).
  1. B. Zalba, J. Marin, L. Cabea and H. Mehling. “Review on thermal energy storage with phase change: materials, heat transfer analysis and application.”Applied Thermal Engineering 23 (2003) 251-283.
  1. M. Schimmelpfenning, K. Weber, F. Kalb, K.-H. Feller, T. Butz and M. Matthai. “Volume expansions of paraffins from dip tube measurements.”