A steady-state heat conduction problem of a nonhomogeneous conical body

Abstract

Numerous studies and textbooks deal with the steady-state thermal conduction of radially nonhomogeneous circular cylinder. In contrast, there are relatively few studies on the thermal conduction problems of conical solid bodies. This study is intended as a modest contribution to the solution of thermal conductance problems of nonhomogeneous conical bodies. A one-dimensional steady-state heat conduction in nonhomogeneous conical body is considered. The thermal conductivity of the hollow conical body in a suitable chosen spherical coordinate system depends on the polar angle but is independent of the radial coordinate and azimuthal angle coordinate. A functionally graded type of material inhomogeneity is considered. All results of the paper are based on Fourier’s theory of heat conduction in solid bodies.