Condition for the existence of the optimal wall thickness dividing two different environments with local heat exposure

The sufficient conditions for the existence of an optimal thickness of an orthotropic dividing wall are determined with the zero-order Hankel integral transform. Both wall surfaces participate in a heat transfer with external media with constant temperatures, and one of them is also affected by a stationary axisymmetric heat flux with a Gaussian-type intensity. The need to minimize the temperature of the most heated point of the object of study is used as an optimality criterion. A sufficient condition is obtained in the form of an inequality that establishes a connection between the thermophysical characteristics of the orthotropic material of the wall and the parameters of the external thermal effects. The accuracy of the obtained condition was established by a computational experiment.