8.2 Defining Properties Using Temperature-Dependent Functions

Material properties can be defined as functions of temperature. For most properties, you can define a polynomial, piecewise-linear, or piecewise-polynomial function of temperature:

• polynomial:

  
  

  
  

• piecewise-linear:

  
  

  
  

  where $1 \leq n \leq N$ and $N$ is the number of segments

• piecewise-polynomial:

  
  

  $$\mbox{for} \; T_{{\rm min},1} \leq T < T_{{\rm max},1}: \; \phi (T) = A_1 + A_2 T + A_3 T^2 + ...$$

  $$\mbox{for} \; T_{{\rm min},2} \leq T < T_{{\rm max},2}: \; \phi (T) = B_1 + B_2 T + B_3 T^2 + ...$$ (8.2-3)

  
  

In the equations above, $\phi$ is the property.

If you define a polynomial or piecewise-polynomial function of temperature, the temperature in the function is always in units of Kelvin or Rankine. If you use Celsius or Kelvin as the temperature unit, then polynomial coefficient values must be entered in terms of Kelvin. If you use Fahrenheit or Rankine as the temperature unit, enter the values in terms of Rankine.

Some properties have additional functions available and for some only a subset of these three functions can be used. See the section on the property in question to determine which temperature-dependent functions you can use.