Unsteady anisotropic heat conduction in heterogeneous composite conical shells with temperature-dependent thermal conductivities: an analytical study

The present study proposes an exact analysis for unsteady anisotropic conduction heat transfer in heterogeneous composite conical shells. The fibers in the composite conical shell are wound in arbitrary directions so that a defined fiber angle changes between 0 degrees and 90 degrees. The cone's base is considered to have a general linear boundary condition, while the effects of internal heat generation, thermal convection, and external radiation heat flux on the temperature distribution are investigated. The heterogeneity of the heat transfer problem is caused by a linear dependence of conduction coefficients on the temperature. To solve the governing equations, first, the Kirchhoff transformation followed by an appropriate finite integral transform is applied. The resulting nonhomogeneous equation is then separated into two equations, i.e., steady equation and unsteady equation. The solution of the steady case is derived using Green's function, while the separation of variables method is utilized to solve the unsteady part. Eventually, the temperature distribution is achieved by applying the inverse transforms on the subsequent solutions. The verification of this solution is based on the comparison between the present analytical results and numerical computations with a second-order finite difference code. Applicability of the present solution is evaluated for resolving an industrial case problem.