DUAL-PHASE-LAG HEAT CONDUCTION IN AN FG HOLLOW SPHERE: EFFECT OF THERMAL PULSE TYPE AND LOCATION OF A HEAT SOURCE

The purpose of this paper is to introduce a new mathematical model to solve the heat conduction equation based on the Dual-Phase-lag (DPI.) theory for investigation of temperature field affected by thermal pulse and heat source location on an FG hollow sphere. This new model, named augmented state space method, based on the laminate approximation theory in the Laplace domain, can obtain a transient solution, and then the results obtained are converted into the time domain by applying the numerical Laplace transform inversion with consideration of Gibb's phenomenon. Numerical analyses show the effects of thermal pulse and heat source location and phase lags ratio as boundary conditions on the distribution of temperature on an FG sphere. It is clear that the thermal pulse functions and location of a heat source have different effects on the temperature distribution. In addition, by changing the phase lags ratios, the temperature distribution on a radius and in time history are obtained. Eventually, the results obtained by this method are verified by using some problems available in the literature.