Transfer function methods are more efficient for solving long-time transient heat transfer problems than Euler, Crank-Nicolson, or other classical techniques. Transfer functions relate the output of a linear, time-invariant system to a time series of current and past inputs, and past outputs. Inputs are modeled by a continuous, piecewise linear curve. The computational effort required to perform a simulation with transfer functions can be significantly decreased by using the Pade´ approximation and bilinear transformation to determine transfer functions with fewer coefficients. This paper presents a new model reduction method for reducing the number of coefficients in transfer functions that are used to solve heat transfer problems. There are two advantages of this method over the Pade´ approximation and bilinear transformation. First, if the original transfer function is stable, then the reduced transfer function will also be stable. Second, reduced multiple-input single-output transfer functions can be determined by this method.
On the expansion of the transfer function for the model reduction of stage systems.