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Heat Transfer in Anisotropic Micropolar Solids

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Abstract

The paper is devoted to the theory of an anisotropic micropolar thermoelastic solid. The requisite equations and notions from pseudotensors algebra and multidimensional geometry are revisited. From the beginning we treat translational displacements as an absolute covariant fields whereas spinor displacements as a contravariant pseudovector. The Helmholtz free energy is employed as a thermodynamic state potential of the following functional arguments: absolute temperature, symmetric parts and accompanying vectors of the linear asymmetric strain tensor and the wryness pseudotensor. The constitutive equations for a general anisotropic micropolar thermoelastic solid including gyrotropic one are derived. That means heat flux vector can be treated as a pseudovector of weight \( + 1\) (or \( - 1\)) algebraically consistent to spinor displacements pseudovector. Nonlinear heat conduction equation and its linearized form are obtained.

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Funding

The present study was financially supported by the Russian Science Foundation (project no. 23-21-00262).

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  1. Ishlinsky Institute for Problems in Mechanics RAS, 119526, Moscow, Russia

    E. V. Murashkin & Yu. N. Radayev

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  1. E. V. Murashkin
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Correspondence to E. V. Murashkin or Yu. N. Radayev.

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Murashkin, E.V., Radayev, Y.N. Heat Transfer in Anisotropic Micropolar Solids. Mech. Solids 58, 3111–3119 (2023). https://doi.org/10.3103/S0025654423700255

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