Application of Hybrid Differential Transform/Control-Volume Method to Hyperbolic Heat Conduction Problems

This article presents a hybrid differential transform/control-volume method to solve hyperbolic heat conduction problems. First, the governing equations are transformed using the differential transform technique. Second, the temperature spectra, given by predefined shape functions are calculated through a recursive formula after applying the control-volume method to each individual subinterval. Finally, the inverse differential transform technique is adopted to determine the temperature by a finite-term power series. Numerical oscillation can be effectively suppressed by choosing suitable values of the powers of shape functions, and the simulation results match well with the analytic solutions.