A Fast Fourier Transform Solution for 1D Unsteady Heat Transfer Model Bounded by Varying Temperature

Using the Fourier transform to solve a one-dimensional heat conduction model with temperature f(t) as the boundary requires complex integral transformation operations. According to the property of the Fourier transform, f(t) is regarded as a symbol in the process operation, and the universal theory resolution of such a problem is established without directly solving the f(t) transformation. f(t) is then substituted into the theoretical solution to obtain the solution of the actual model. Using the theo-retical solution, the solutions of 3 types of common functions are given. Combined with the characteristics of the model, precautions during the solving process are proposed. The example application demonstrates the establishment and application process of inversing model parameters based on the inflection point of temperature variation over time.