An elliptical inhomogeneity under nonuniform heat flux

We use complex variable techniques to study the decoupled two-dimensional steady-state heat conduction and thermoelastic problems associated with an elliptical elastic inhomogeneity perfectly bonded to an infinite matrix subjected to a nonuniform heat flux at infinity. Specifically, the nonuniform remote heat flux takes the form of a linear distribution. It is found that the internal temperature and thermal stresses inside the elliptical inhomogeneity are quadratic functions of the two in-plane coordinates. Explicit closed-form expressions of the analytic functions characterizing the temperature and thermoelastic field in the matrix are derived.

Automated summary

In this study, complex variable techniques were used to investigate the decoupled two-dimensional steady-state heat conduction and thermoelastic problems between an elliptical elastic inhomogeneity and an infinite matrix. It was found that the internal temperature and thermal stresses inside the elliptical inhomogeneity are quadratic functions of the two in-plane coordinates. Explicit closed-form expressions for the analytic functions characterizing the temperature and thermoelastic field in the matrix were derived.