Hyperbolic heat conduction and thermoelastic solution of functionally graded CNT reinforced cylindrical panel subjected to heat pulse

Abstract

As a first attempt, the combined application of the differential quadrature method (DQM) and the Newton Raphson method is used to solve the non-Fourier heat conduction equations to obtain temperature, displacements, and stresses in a cylindrical panel made of functionally graded, carbon nanotubes (CNTs) reinforced composite. The heat conduction of a domain made of nanocomposites subjected to heat generation is simulated with a finite heat wave speed. Furthermore, based on the three-dimensional elasticity theory, the thermoelastic analysis of the nanocomposite cylindrical panel subjected to the transient heat conduction is presented. The dynamic Young's modulus of Single-Walled Carbon Nanotubes (SWCNT) can be expressed as a function of loading rate and environmental temperature. All material properties such as heat capacity (Cp), thermal relaxation time (τ), density (ρ) and thermal conductivity (K) are considered as a function of both temperature and CNT volume fraction. The hyperbolic heat conduction is solved to obtain temperature in the spatial and temporal domains. Then by implementing the obtained temperature in thermoelastic equations of the cylindrical panel, the displacements and stresses will be obtained at each time step. The proposed method marches in the time direction block by block. In each block, there are several time levels, and the numerical results at these time levels are obtained simultaneously. Through this way, the numerical solution at the (n + 1)th time level depends on the solutions at its previous levels from the 1st to the nth levels. The final results in the temporal domain are obtained using the Newton–Raphson method. Accuracy of the present solution is confirmed by comparing with some available results in the literature. A detailed numerical study is conducted to examine the effects of heat wave speed and heat flux, CNT volume fraction and the geometrical parameters on the deflection of the cylindrical panel.