This article presents the formulation and solution of a linear non-stationary heat conduction problem with an axisymmetric hypersonic flow around a hemispherical blunting of the aircraft head. The material of the heat-shielding layer of blunting has anisotropy of thermal conductivity, characterized by the ratio of thermal conductivity coefficients along and across the layer. The temperature over the thickness of the power metal shell of the head part is assumed uniform. A quantitative analysis of the temperature state of the head part in the laminar flow regime and during the transition to the turbulent regime was carried out.

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