The Optimum Thickness is Locally Heated Thermal Barrier Coating with a Temperature-Dependent Thermal Conductivity

Abstract

Applying a thermal barrier coating can ensure effective protection of structures from localized intense heat exposure. When applying a coating layer to the surface structure the thermal contact on this surface, generally, differs from the ideal value and corresponds to some value of a coefficient of contact heat transfer. With high density of the localized heat flux a temperature at the hottest point of the coating outer surface can substantially exceed the temperature of the protected structure, which makes it necessary to take into account the dependence of the thermal conductivity of the coating material on the temperature.For a quantitative analysis of the impact of the above features of thermal interaction between the coating and the protected cover design it is advisable to use the mathematical modeling methods, allowing to build an adequate mathematical model of heat transfer process in a layer of thermal barrier coating. This model should enable us to determine a thermal state of the coating at its specified thickness and also to find an optimal ratio of defining parameters, ensuring the lowest possible temperature at the hottest point of the outer surface of the coating. One of these parameters may be the thickness of the coating layer, which should be regarded as optimal.The paper offers a mathematical model that describes a process of the stationary thermal conductivity with the locally heated outer surface of the thermal barrier coating on a cooled flat wall. The coefficient of thermal conductivity of the coating material depends on the temperature, and the thermal contact between the coating and the wall is accepted as non-ideal. A quantitative analysis of the mathematical model is reduced to the solution of the boundary value problem for the Laplace equation in the cylindrical coordinate system. A solution to the problem obtained in the analytical form allows us to find the area of defining parameters where the minimum possible value of the temperature at the hottest point of the surface can be ensured by changing a thickness of the coating with temperature-dependent thermal conductivity. It is found that in case of an ideal thermal contact between the coating and the structure to be protected the temperature at the heattest point of outer coating surface monotonically increases with its thickness, i.e. there is no possibility to select the optimal thickness of the locally heated thermal barrier coating.

Keywords

• thermal barrier coating
• local heating
• the optimum thickness of the coating