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On the theory of heat for micromorphic bodies
Affiliation:1. Department of Mathematics, Al.I. Cuza University, 6600 Iaşi, Romania;2. Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università di Napoli, Via Monteoliveto 3, 80134, Napoli, Italy;1. Department of Nuclear Engineering and Technology, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;2. State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;1. School of Mathematics, South China University of Technology, Guangzhou, 510641, PR China;2. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, PR China;1. Department of Mechanical Engineering, 126 Spencer Laboratory, University of Delaware, Newark, DE 19716-3140, USA;2. Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, PR China;3. Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen 518055, China;4. State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, PR China;5. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, PR China
Abstract:The paper deals with the problem of heat flow in a micromorphic continua with microtemperatures. The master balance laws of micromorphic continua established by Eringen [Int. J. Eng. Sci. 8 (1970) 819] and the entropy balance postulated by Green and Naghdi [Proc. R. Soc. Lond. A 357 (1977) 253] are used to obtain a new theory of heat for materials with inner structure. The theory permits propagation of heat as thermal waves at finite speed. In the framework of the linear theory a uniqueness result and a solution of Galerkin type are established. The effect of concentrated loads is also studied.
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