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Heat conduction in anisotropic medium with perfectly conductive thread-like inclusions

Sulym Heorhiy, Ilchuk Nataliia, Pasternak Iaroslav

Acta Mechanica et Automatica

2019

Vol. 13, no. 4

251--254

The paper presents a novel approach for the analysis of steady-state heat conduction of solids containing perfectly conductive thread-like inhomogeneities. Modelling of a thread-like heat conductive inhomogeneity is reduced to determination of density of heat distributed along a spatial curve, which replaces the inclusion. Corresponding boundary integral equations are obtained for anisotropic solids with thread-like inclusions. Non-integral terms are computed in a closed form. It is shown that, nevertheless the singularity of the equation is 1/r, it is hypersingular, since the kernel is symmetric. Boundary element approach is adopted for solution of the obtained equations. Numerical example is presented for a rectilinear conductive thread, which verifies derived boundary integral equations.

Thermal modelling along the Kavali-Udipi profile in Southern Indian Shield

Ramana D. V., Thiagarajan S., Singh R. N.

Acta Geophysica Polonica

1999

Vol. 47, nr 4

423-433

The temperature-depth distribution has been calculated down to a depth of 42 km along the 600 km long deep seismic sounding profile across the Kavali-Udipi in the Southern Indian Shield using the two-dimensional solution of the steady-state heat conduction in an inhomogeneous medium. The available geological and geophysical data of this region are used to assign the values for the thermal parameters such as radiogenic heat sources and thermal conductivity. The vertical distribution of the heat sources in the deeper part of the model was estimated from the observed seismic velocities. The range of the mantle heat flow values generally assumed in this region is from 17 to 32 mW/m2. The surface heat flow has also been computed along the profile. The numerical results show that the values of maximum temperature at the Moho range from 340 to 580 C and the values of maximum and minimum surface heat flow range from 37 to 52 mW/m2 and 25 to 39 mW/m2, respectively. These results are useful in understanding the thermo-mechanical evolution of the Indian Shield.