Abstract
In order to solve the transient heat transfer problem of the laminated structure, a semianalytical method based on calculus is adopted. First, the time domain is divided into tiny time segments; the analytical solution of transient heat transfer of laminated structures in the segments is derived by using the method of separation of variables. Then, the semianalytical solution of transient heat transfer in the whole time domain is obtained by circulation. The transient heat transfer of the three-layer structure is analyzed by the semianalytical solution. Three time-varying boundary conditions (a: square wave, b: triangular wave, and c: sinusoidal wave) are applied to the surface of the laminated structure. The influence of some key parameters on the temperature field of the laminated structure is analyzed. It is found that the surface temperature of the laminated structure increases fastest when heated by square wave, and the maximum temperature can reach at 377°C, the temperature rises the most slowly when heated by the triangular wave, and the maximum temperature is 347°C. The novelty of this work is that the analytical method is used to analyze the nonlinear heat transfer problem, which is different from the general numerical method, and this method can be applied to solve the heat transfer problem of general laminated structures.
Highlights
In practical engineering applications, there are many problems of transient heat transfer in laminated structures [1, 2]
Fu and Cheng solved the semianalytical solution of temperature field analysis of the three-dimensional structure of the laminated cylinder by using the fine integration method [14]
In order to solve the transient heat transfer problem of the laminated structure with time-varying boundary conditions, it is necessary to carry out differentiation in the time domain
Summary
There are many problems of transient heat transfer in laminated structures [1, 2]. Liu et al solved the temperature field of the three-layer heat transfer structure using the inverse Fourier transform method [9]. Ramadan solved the transient heat transfer problem of the multilayer structure by the semianalytical method and analyzed the non-Fourier characteristics of the heat transfer process [15]. Li et al studied transient heat transfer in laminated structures by using a backward differential method [16]. Liu and Shi used the lattice Boltzmann method to solve the numerical solution of heat transfer in multilayer structures [17]. Shan et al studied the heat transfer of a multilayer structure using a Mathematical Problems in Engineering modified scale-boundary finite element method [18]. Guo et al simulated the transient heat transfer problem of the three-layer structure by using the improved time-domain discontinuous Galerkin method and improved the numerical fluctuation problem of the traditional method [19]
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