Non-classical heat equation with singular memory term

In this paper, we consider the non-classical heat equation with singular memory term. This equation has many applications in various fields, for example liquids mechanics, solid mechanics, and heat conduction theory first, we prove that the solution exists locally in time. Then we investigate the converegence of the mild solution of non-classical heat equation, and the mild solution of classical heat equation.

The application of Taiji thought in packaging design

This article starts with the thought of Taiji, and analyzes the related contents of Taiji elements. The visual guidance sequence in packaging design was analyzed through the analysis of the human eye’s visual guidance mode. This paper probes into the symbolic elements of the shape and composition of Taiji graphics, and obtains the concrete practice way of Taiji thought and visual guidance in packaging design, by combining the traditional Chinese Taiji thought with the modern visual conduction theory, a new way of modern packaging design is obtained.

Size Dependent Thermo-Piezoelectricity for In-Plane Cracks

The finite element method (FEM) is developed to analyse the size effect (flexoeletricity) for 2-D crack problems in thermo-piezoelectricity. Flexoelectricity is observed in micro/nanoelectronic structures, where large strain gradients destroy the symmetric structure of atoms in crystals and thereby causing polarization, even in dielectric materials. In contrast to using classical Fourier heat conduction theory, a finite speed of the thermal wave is considered in the higher order transport equation. The variational principle is applied to derive the FEM equations and C1-continuous elements are employed in the implementation of the FEM. An example is presented to demonstrate the effect of the characteristic time parameter on the crack opening displacement and temperature distribution.

Thermoelastic Response of a Rectangular Plate under Hyperbolic Heat Conduction Model in Differential Transform Domain

In the present work, a semi-analytical solution is presented for the thermoelastic response of a finite plate of rectangular geometry considering hyperbolic heat conduction model. The solution of thermoelastic displacement, thermal stresses and temperature are obtained using differential transform method under hyperbolic, non-Fourier heat conduction theory. For special case, thermal stresses and displacement functions are determined numerically and plotted graphically to analyze the effect of the thermal relaxation time.