A turbine component in the preburner section of a turbopump...

A turbine component in the preburner section of a turbopump for a rocket motor is made from Inconel X-750. A "thermal barrier" coating of $0.3 \mathrm{~mm}$-thick YSZ (yttrium-stabilized zirconia) is plasma-sprayed on the surface. This coating has a high reflectance and can significantly reduce the radiation heat loads on cooled surfaces. Upon start-up, the surfaces are initially at $30^{\circ} \mathrm{C}$ and are suddenly exposed to hot gases at $800^{\circ} \mathrm{C}$, with an estimated effective heat transfer coefficient of $180 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}$. Plot the surface and interface temperature as a function of time for short times. Take $k=5.0 \mathrm{~W} / \mathrm{m} \mathrm{K}$ for $\mathrm{YSZ}$.

Key Concepts

Transient Heat Conduction

This concept deals with how temperature within a material changes over time when it is exposed to a sudden thermal load. In heat transfer problems like this one, the temperature distribution evolves within the body in response to transient energy input at the boundary, and the analysis typically involves solving the heat diffusion equation with appropriate boundary and initial conditions to capture these time-dependent changes.

Convective Heat Transfer

Convective heat transfer is the process by which heat is transferred from a surface to a fluid (or vice versa) moving over the surface, and it is characterized by the heat transfer coefficient. In the context of this problem, the surface of the coating is suddenly exposed to a hot gas stream, and the heat convection effect is modeled by a boundary condition that includes the heat transfer coefficient to determine the rate at which thermal energy is supplied to the material.

Thermal Barrier Coatings

Thermal barrier coatings are specialized layers applied to components to protect them from high thermal loads. They are designed to have low thermal conductivity and high thermal reflectance, thereby reducing the amount of heat that penetrates into the substrate. This concept is crucial in high-temperature applications like rocket motor components, where managing heat exposure is critical to component longevity and performance.

Material Thermal Properties

Key material properties, such as thermal conductivity, play a significant role in determining how quickly and efficiently heat is conducted through a material. In problems involving temperature evolution under transient conditions, parameters like thermal conductivity (and related properties such as thermal diffusivity) are essential for predicting the temperature gradients within the coating and at its interface with the substrate.

Short-Time Transient Analysis

For a sudden change in external conditions, as in the start-up scenario described, short-time transient analysis is used to predict the initial temperature response of the system both at the exposed surface and at interfaces within the material. This analysis often relies on approximations, like the semi-infinite solid assumption, to capture the early-time behavior before the thermal penetration depth becomes comparable to the geometry of the system.

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