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8.2.3 Inputs for Piecewise-Polynomial Functions

To define a piecewise-polynomial function of temperature for a material property, follow these steps:

1.   In the Materials panel, choose piecewise-polynomial in the drop-down list to the right of the property name (e.g., Cp). The Piecewise-Polynomial Profile panel (Figure  8.2.4) will open automatically. Since this is a modal panel, first perform the following steps.

Figure 8.2.4: The Piecewise-Polynomial Profile Panel
figure

2.   Specify the number of Ranges. For the example of Equation  8.2-5, two ranges of temperatures are defined:


 c_p (T) = \left\{ \begin{array}{ll} {\rm for} \; 300 \leq T ... ... 10^{-8} T^3 - 3.153 \times 10^{-12} T^4 & \end{array} \right. (8.2-5)

You may define up to three ranges. The ranges must be supplied in the order of increasing value of temperature. The solver will not sort them for you.

3.   For the first range ( Range = 1), specify the Minimum and Maximum temperatures, and the number of Coefficients. (Up to eight coefficients are available.) The number of coefficients defines the order of the polynomial. The default of 1 defines a polynomial of order 0. The property will be constant and equal to the single coefficient $A_1$. An input of 2 defines a polynomial of order 1. The property will vary linearly with temperature and so on.

4.   Define the coefficients. Coefficients 1, 2, 3,... correspond to $A_1$, $A_2$, $A_3$,... in Equation  8.2-3. The panel in Figure  8.2.4 shows the inputs for the first range of Equation  8.2-5.

5.   Increase the value of Range and enter the Minimum and Maximum temperatures, number of Coefficients, and the Coefficients ( $B_1$, $B_2$, $B_3$,...) for the next range. Repeat if there is a third range.


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