We consider here the problem of a three-dimensional (3D) body subjected to an arbitrarily oriented and remotely applied stationary heat flux. The body includes a non-conductive inhomogeneity (or pore) having the shape of two intersecting spheres with different radii. Using toroidal coordinates, the steady-state temperature field and the heat flux have been expressed in terms of Mehler–Fock transforms. Then, by imposing Neumann BCs at the surface of the spheres, a system of two Fredholm integral equations is obtained and solved based on Gauss–Laguerre quadrature rule. It is shown that the components of the resistivity contribution tensor exhibit a non-monotonic trend with the distance between sphere centers. In particular, if the inhomogeneity has a symmetric dumbbell-shape, then the extrema of the resistivity contribution tensor components occur when the two overlapping spheres have the same size. Differently, when the inhomogeneity has a lenticular shape, then these extrema are attained for a non-symmetric configuration, namely, for different radii of the intersecting spheres.

Resistivity contribution tensor for two non-conductive overlapping spheres having different radii / Lanzoni, Luca; Radi, Enrico; Sevostianov, Igor. - In: MATHEMATICS AND MECHANICS OF SOLIDS. - ISSN 1081-2865. - 27:(2022), pp. 1-15. [10.1177/10812865221108373]

Resistivity contribution tensor for two non-conductive overlapping spheres having different radii

Lanzoni, Luca
;
Radi, Enrico;
2022

Abstract

We consider here the problem of a three-dimensional (3D) body subjected to an arbitrarily oriented and remotely applied stationary heat flux. The body includes a non-conductive inhomogeneity (or pore) having the shape of two intersecting spheres with different radii. Using toroidal coordinates, the steady-state temperature field and the heat flux have been expressed in terms of Mehler–Fock transforms. Then, by imposing Neumann BCs at the surface of the spheres, a system of two Fredholm integral equations is obtained and solved based on Gauss–Laguerre quadrature rule. It is shown that the components of the resistivity contribution tensor exhibit a non-monotonic trend with the distance between sphere centers. In particular, if the inhomogeneity has a symmetric dumbbell-shape, then the extrema of the resistivity contribution tensor components occur when the two overlapping spheres have the same size. Differently, when the inhomogeneity has a lenticular shape, then these extrema are attained for a non-symmetric configuration, namely, for different radii of the intersecting spheres.
13-lug-2022
27
1
15
Resistivity contribution tensor for two non-conductive overlapping spheres having different radii / Lanzoni, Luca; Radi, Enrico; Sevostianov, Igor. - In: MATHEMATICS AND MECHANICS OF SOLIDS. - ISSN 1081-2865. - 27:(2022), pp. 1-15. [10.1177/10812865221108373]
Lanzoni, Luca; Radi, Enrico; Sevostianov, Igor
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/1283440
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