New Galerkin-vector theory and efficient numerical method for analyzing steady-state heat conduction in inhomogeneous bodies subjected to a surface heat flux

This paper reports a unified analogy-based computation methodology, together with a concept of multifield, multifunctional sensing, from elasticity to electromagnetic-chemical-thermal fields, via utilizing the similarities of mechanical-electromagnetic-chemical-thermal (MEMCT) field variables, governing equations, and the material properties pertaining to each individual field. Two equivalences are systemized, which are the field-formulation equivalence and surface-value equivalence. Due to similarity, a number of thermal, electromagnetic, or chemical solutions can be obtained from the direct degeneration of existing mechanical solutions by making specified equivalences of 2G↔k0↔ϖ0↔μ0↔β0 with G for shear modulus, k0 for heat conductivity, ϖ0 for dielectric permittivity, μ0 for magnetic permeability, and β0 for chemical diffusivity, as well as by setting Poisson’s ratio ν → 0.5. These specified equivalences enable quick solutions to other fields directly from mechanics formulations, such as those in the forms of the Galerkin vectors and Papkovich-Neuber potentials, and field coupling, by means of analogy. Several examples are given, one is used to demonstrate that the field solutions of a layered half-space with imperfect thermal, electromagnetic, or chemical interfaces can be readily obtained from the elastic solutions involving interfacial imperfections via the obtained formulation equivalence. A set of simple equations are derived to relate surface behaviors of different fields via the obtained surface-value equivalence, on which a concept of multifield sensing is proposed.

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“…from Refs. [55,64] Two Galerkin vectors are in different formats, and direct result simplification not applicable due to the involvement of g c ,…”

Section: This Workmentioning

confidence: 99%

A Unified Analogy-Based Computation Methodology From Elasticity to Electromagnetic-Chemical-Thermal Fields and a Concept of Multifield Sensing

Zhang

Wang

2022

ASME Open Journal of Engineering

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Semi-analytical study on elastic field of two joined dissimilar materials with interfacial cracks under prescribed loading

Yang,

Zhou,

Wang

et al. 2024

Applied Mathematical Modelling

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Semi-analytical solution for temperature rise in a heterogeneous half plane containing arbitrarily shaped inhomogeneities subjected to surface heating

Yang

Xiong

Zhou

et al. 2021

Journal of Thermal Stresses

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New Galerkin-vector theory and efficient numerical method for analyzing steady-state heat conduction in inhomogeneous bodies subjected to a surface heat flux

Cited by 4 publications

References 40 publications

A Unified Analogy-Based Computation Methodology From Elasticity to Electromagnetic-Chemical-Thermal Fields and a Concept of Multifield Sensing

A Unified Analogy-Based Computation Methodology From Elasticity to Electromagnetic-Chemical-Thermal Fields and a Concept of Multifield Sensing

Semi-analytical study on elastic field of two joined dissimilar materials with interfacial cracks under prescribed loading

Semi-analytical solution for temperature rise in a heterogeneous half plane containing arbitrarily shaped inhomogeneities subjected to surface heating

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