A New Approach to Direct Solution of 2D Heat Transfer Problem with Non-Linear Source Terms in Frequency Domain

摘要

Frequency response is a convenient form to describe the dynamic characteristics of a linear system to facilitate the control system design and analysis. For a non-linear dynamic system, if the amplitude of the input signal around the steady-state operating point is small enough, the system can be approximated as a linear system. Based on this assumption, a new approach is proposed to directly obtain the frequency response of a heat transfer system with non-linear source terms when the inputs are subject to low amplitude sinusoidal signals. In this approach, the governing partial differential equation for heat transfer in time domain can be transferred into a time independent partial differential equation in frequency domain, non-linear source terms can be linearized, and boundary conditions can be transferred into frequency domain representation. The frequency response obtained from the equation in frequency domain can be used to construct the transfer function of the system. To verify the proposed method, the dynamic characteristic of the system based on the transfer function is compared with that calculated by solving the governing heat transfer equation in time domain.