Heat Shield Thermal Analysis.

How does heat move through an insulating tile and into the metal structure beneath it—and how does that structure’s temperature change with time?

My interest in thermal protection grew out of Rowan Rocketry and curiosity about reentry physics in Kerbal Space Program. For this Heat Transfer midterm project, I explored a reusable, non-ablative tile concept inspired by Starship.

I developed the annotated drawing, set up the material and boundary assumptions, formulated an energy balance, and compared analytical calculations with a Simulink / Simscape thermal model.

The SolidWorks drawing shows the tile’s hexagonal outline, side view, and annotated section. Its purpose is to define the modeled layers and identify convection, radiation, conduction, and thermal storage.

The report combines sourced properties with assumed temperatures and dimensions. Keeping those inputs explicit makes it easier to understand which choices drive the predicted temperature.

The model follows heat through the coating and insulation to the steel. On the interior side, the steel exchanges heat with a 300 K environment through convection and radiation.

Two layers in series

The insulation contributes about 4.006 K/W and the coating about 0.0513 K/W. The difference shows why the low-conductivity insulation dominates the modeled resistance.

The steel energy balance

The calculation includes interior heat loss. Although a handwritten note uses the word “adiabatic” for the inside air, the equations and Simscape diagram use a fixed 300 K interior boundary with convection and radiation. This page follows the implemented heat-exchange model.

The Blockpad calculation assumes a 500 K hot-side interface and an initial steel temperature of 300 K. It balances conduction through the two insulating layers against interior convection and radiation.

Checking the lumped-temperature assumption

Using an interior convection coefficient of 10 W/(m²·K), a 3 mm characteristic length, and steel conductivity of 15 W/(m·K), the report calculates Bi = 0.002. This is below the usual 0.1 screening criterion for a lumped-capacitance approximation.

That calculation supports a uniform-temperature treatment under the selected interior convection conditions. It is a simplified check, rather than a complete assessment of every thermal boundary acting on the steel.

The Simscape model starts with a 2,000 K external thermal source. It includes external convection and radiation, conduction through the TUFI and AETB layers and steel, thermal masses for insulation and steel, and interior heat exchange with a 300 K boundary.

Temperature and heat-flow sensors record the steel’s response. Compared with the fixed-interface analytical calculation, the numerical model represents additional thermal storage and the path by which heat reaches the structure.

The temperature scope approaches approximately 671.2 K over the displayed simulation interval of about 2,000 seconds. This is the response to the project’s fixed conditions; it is not a flight-specific reentry trajectory or measured hardware temperature.

The comparison is most useful as a lesson in model definition. The two calculations do not expose the steel to the same thermal boundary, so their temperature difference does not establish the accuracy of either model.

The report gives a relative temperature difference of about 44.6%, using the Simscape temperature as the denominator. This describes disagreement between the models, rather than error against an experimentally established answer.

Interpreting the heating-rate comparison

The analytical initial rate is 0.158 K/s. The report also labels the Simscape value of 0.0002308 K/s as an initial rate. That value appears in the model screenshot alongside the final temperature; the supplied record does not establish when it was sampled. An initial-rate comparison would require matching both models’ starting conditions and reading the simulation rate at time zero.

What I would carry into the next analysis

• Match the boundaries before comparing models: a fixed interface and a full external heat path answer different questions.
• Separate assumed and sourced inputs: thermal properties, convection coefficients, and temperatures all affect the result.
• Keep the time history: equilibrium temperature alone does not describe the response during a finite heating event.
• Verify against a common case: align model inputs first, then compare with analytical benchmarks or physical measurements.

The complete 10-page report includes the project motivation, annotated drawing, input table, thermal network, calculations, Simscape model, temperature response, discussion, and references.

Eight report visuals are included below. Vector drawings and handwritten pages have been rendered as images, and the simulation plots retain their original visible annotations. Select any image to open it at full size.