Журнал Белорусского государственного университета: Математика, информатика (May 2018)
The solution of the nonaxisymmetric stationary problem of heat conduction for the polar-orthotropic annular plate of variable thickness with thermal insulated bases
Abstract
In the work is given the solution of nonaxisymmetric stationary heat conduction problem for profiled polar-orthotropic annular plates with thermally insulated bases. The dependence of the thermophysical characteristics of the plate material of the temperature is taken into account. Temperature values are set on the contours of the annular plate: temperature T0∗ is constant on the internal contour, and on the outer contour on several arcs with length li (i = 1, k) – temperature is T1∗ (T1∗ > T0∗). The temperature distribution in such a plate is nonaxisymmetric. It is assumed that the radial λr and tangential λθ heat conduction coefficients are linearly dependent on the temperature T(r, θ): λr(T) = λ(0)r(1 - γT(r, θ)), λθ(T) = λ(0)θ(1 - γT(r, θ)) here the parameter γ > 1; the constants λ(0)r, λ(0)θ are determined experimentally at the primary temperature T0. The primary nonlinear differential heat equation is reduced to a linear differential equation of the 2nd kind in partial derivatives when a new function Z(r, θ) = [T(r, θ) - γ/2T2(r, θ)] is introduced in consideration.
