BuildSysPro.IBPSA.Utilities.Math.RegNonZeroPower

# .BuildSysPro.IBPSA.Utilities.Math.RegNonZeroPower

Power function, regularized near zero, but nonzero value for x=0

## Information

Block that approximates y=|x|n where 0 < n < 2 so that

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

This block 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 block 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 block, 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.

See the package `Examples` for the graph.

## Revisions

- November 2, 2022, by Michael Wetter:
  Set minimum and maximum attribute on `n`, improved assertion and documentation.
  This is for Buildings, #3135.
- November 29, 2013 by Marcus Fuchs:
  Implementation based on IBPSA.Utilities.Math.Functions.regNonZeroPower.

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