.IDEAS.Utilities.Math.Functions.regNonZeroPower

Information

• y(0) is not equal to zero.
• dy/dx is bounded and continuous everywhere.

This function replaces y=|x|ⁿ in the interval -δ...+δ by a 4-th order polynomial that has the same function value and the first and second derivative at x=± δ.

A typical use of this function is to replace the function for the convective heat transfer coefficient for forced or free convection that is of the form h=c |dT|ⁿ for some constant c and exponent 0 ≤ n ≤ 1. By using this function, the original function that has an infinite derivative near zero and that takes on zero at the origin is replaced by a function with a bounded derivative and a non-zero value at the origin. Physically, the region -δ...+δ may be interpreted as the region where heat conduction dominates convection in the boundary layer.

Interface

function regNonZeroPower
  extends Modelica.Icons.Function;
  input Real x "Abscissa value";
  input Real n "Exponent";
  input Real delta = 0.01 "Abscissa value where transition occurs";
  output Real y "Function value";
end regNonZeroPower;

Revisions

• March 30, 2011, by Michael Wetter:
  Added zeroDerivative keyword.
• April 14, 2008, by Michael Wetter:
  First implementation.