RESEARCH ARTICLE Nonlinear Analysis of a One-Dimensional Non-Fourier Heat Conduction Problem Seyfolah Saedodin 1 • Mohammad Javad Noroozi 1 • Davood Domiri Ganji 2 Received: 30 May 2015 / Accepted: 3 May 2017 Ó The National Academy of Sciences, India 2017 Abstract In this paper, the problem of Non-Fourier heat conduction in a one-dimensional finite body was studied. Non-Fourier heat conduction model of thermal wave was used for thermal analysis of the problem. Temperature- dependent heat conductivity was assumed and a nonlinear equation was obtained. To solve the equations, semi-ana- lytical methods of Reduced Differential Transform Method (RDTM) and Homotopy Perturbation Method (HPM) were applied. It was concluded that nonlinear analysis of Non- Fourier heat conduction problems is highly important and higher accuracy of RDTM with respect to HPM was specified. Keywords Non-Fourier  C–V model  RDTM  HPM  Nonlinear model List of symbols c p Specific heat (J kg -1 K -1 ) FO Fourier number k Thermal conductivity (W m -1 K -1 ) k 0 Reference thermal conductivity (W m -1 K -1 ) L Characteristic length (m) q Heat flux (W m -2 ) T Temperature (K) T 0 Reference temperature (K) ~ T Dimensionless temperature t Time (s) ~ t Dimensionless time t total Total time x Space direction (m) ~ x Dimensionless space direction Greek symbols a 0 Reference thermal diffusivity (m 2 s) b Dimensionless relaxation time c Dimensionless coefficient for taking into account of temperature-dependent conductivity q Density (kg m -3 ) s Relaxation time (s) 1 Introduction Heat conduction is a mechanism of heat transfer during which thermal energy is transferred from an area with higher temperature to an area with lower temperature. A fundamental equation which can describe the mentioned mechanism well was first introduced in 1822 by a French physicist called Joseph Fourier in a thesis entitled ‘‘ana- lytical theory of heat’’ [1]. Parabolic classic equation of Fourier heat conduction was used until 1950 in all analyses at that time. While all scientists were accepted that hypothesis of this equation based on infinite motion speed of thermal energy inside matter was a non-physical hypothesis. Of course, this hypothesis is valid in many conventional applications but Fourier law isn’t able to predict correctly thermal behavior of the matter in some cases such as heat transfer at very low temperatures [2], heat transfer in very small sizes [3] or heat transfer with very high rate in short times [4]. In the half of 20th century, some scientists like Morse and Feshbach [5], Cattaneo [6] and Vernotte [7] in & Mohammad Javad Noroozi Mo.j.noroozi@gmail.com 1 Faculty of Mechanical Engineering, Semnan University, P.O.B. 35131-19111, Semnan, Iran 2 Department of Mechanical Engineering, Babol University of Technology, P.O.B. 484, Babol, Iran 123 Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. DOI 10.1007/s40010-017-0379-0