Double asymptotic expansion in the problem of radiation heat exchange of annular fins of trapezoidal shape

We propose a method of double asymptotic expansion of an approximate analytic solution of the problem on thermal irradiation of annular radiator fins with a trapezoidal cross-section, which is reduced to a nonlinear differential equation of the second order with variable coefficients. The method is based on using the Poincaré small parameter method and method of phase integrals.