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 l_i  (i = 1, k) – temperature is T₁^∗ (T₁^∗ > T₀^∗). The temperature distribution in such a plate is nonaxisymmetric. It is assumed that the radial λ_r and tangential λ_θ heat conduction coefficients are linearly dependent on the temperature T(r, θ): λ_r(T) = λ⁽⁰⁾_r(1 - γT(r, θ)), λ_θ(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 2^nd kind in partial derivatives when a new function Z(r, θ) = [T(r, θ) - γ/2T²(r, θ)] is introduced in consideration.