In this paper, an innovative constitutive model of modified Fourier's heat conduction law (Fick's diffusion law), which takes the effects of relaxation time, Philip n-diffusion flux on heat transfer (diffusion) and thermal diffusivity parameters into account, the n-diffusion Cattaneo telegraph equation is firstly proposed. The approximate analytical solutions are obtained by employing the Adomian decomposition method which coincide with exact solution in good agreement. Moreover, the involved parameters have strong effects on the temperature distribution which are presented graphically and discussed. The mathematical method and techniques employed in this paper also have the significance for some other problems in science and engineering. The results showed that the temperature oscillates and decreases with increasing and decreasing of thermal diffusivity and relaxation time parameters, without and with reaction term respectively, but the oscillations of temperature decay rapidly until reaching zero with decreasing of Philip n-diffusion parameter for spatial evolution with and without reaction term. The temperature decreases with increasing parameter of relaxation time, Philip n-diffusion or thermal diffusivity for temporal evolution. (C) 2017 Elsevier Ltd. All rights reserved.