An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition

Abstract

In a flexible electronic heater (FEH), periodic metal wires are often encapsulated into the soft elastic substrate as heat sources. It is of great significance to develop analytic models on transient heat conduction of such an FEH in order to provide a rapid analysis and preliminary designs based on a rapid parameter analysis. In this study, an analytic model of transient heat conduction for bi-layered FEHs is proposed, which is solved by a novel symplectic superposition method (SSM). In the Laplace transform domain, the Hamiltonian system-based governing equation for transient heat conduction is introduced, and the mathematical techniques incorporating the separation of variables and symplectic eigen expansion are manipulated to yield the temperature solutions of two subproblems, which is followed by superposition for the temperature solution of the general problem. The Laplace inversion gives the eventual temperature solution in the time domain. Comprehensive time-dependent temperatures by the SSM are presented in tables and figures for benchmark use, which agree well with their counterparts by the finite element method. A parameter analysis on the influence of the thermal conductivity ratio is also studied. The exceptional merit of the SSM is on a direct rigorous derivation without any assumption/predetermination of solution forms, and thus, the method may be extended to more heat conduction problems of FEHs with more complex structures.

Investigation of the Performance of Battery Thermal Management Based on Direct Refrigerant Cooling: Simulation, Validation of Results, and Parametric Studies

“…In this study, the constant rate of heat generation is set based on the constant heat flux during the simulation and experiment as supported by previous studies, including Wang et al [33], Ikramov et al [34], and Xu et al [35]. This generated heat flux will transfer…”

“…In this study, the constant rate of heat generation is set based on the constant heat flux during the simulation and experiment as supported by previous studies, including Wang et al [33], Ikramov et al [34], and Xu et al [35]. This generated heat flux will transfer to the module using the conduction heat transfer mechanism at the contact area between the battery surface and the module housing.…”

“…Thus, the simulated results (solution) can later be proven to be independent of the number of grid elements (grid independence test). The trigonal bipyramid is selected for this work, which is consistent with the physical problem as supported by [33][34][35].…”

Editorial for the Special Issue on Structural Analyses and Designs for Flexible/Stretchable Electronics

“…Twelve articles are by authors from China and one paper each was contributed by authors from Germany, Italy, Poland, and Russia. A comprehensive range of aspects related to the structural analyses, designs, and fabrication of flexible/stretchable devices and smart materials are covered, including mechanical analyses of flexible/stretchable devices [ 1 , 2 , 3 , 4 ], thermal analyses of flexible heaters [ 5 , 6 , 7 , 8 , 9 ], mechanical–conductive analyses of island-type structures in flexible/stretchable devices [ 10 ], thermo-mechanical analyses and designs of morphing aircraft structures [ 11 ], adhesive bonding technology for flexible substrates [ 12 ], electrohydrodynamic jet printing technology for flexible substrates [ 13 ], process parameters’ influence on the resistance of 3D-printed electrically conductive structures [ 14 ], and recent advances in flexible radio frequency microelectromechanical systems (RE MEMS) [ 15 ] and triboelectric nanogenerators (TENGs) [ 16 ].…”

“…Li et al [ 8 ] conducted systematic thermal and mechanical analyses of a kind of flexible microheater with two different wire structures and provided structural design guidelines to obtain high-efficiency flexible microheaters for different applications. Xu et al [ 9 ] proposed an analytic model of transient heat conduction for bi-layered flexible electronic heaters via symplectic superposition and Laplace transformation and further analyzed the thermal conductivity ratios’ effect on the conduction process. Slepchenkov et al [ 10 ] studied the mechanical and conductive behaviors of graphene–carbon nanotube hybrid films with an island topology under axial deformation using the self-consistent charge density functional tight-binding method.…”