HEATR is a coupled 2.5D electrothermal simulation platform I built to rapidly explore the RFAM process design space. In RFAM, heating is driven by electro-quasi-static (EQS) coupling between the applied RF field and a carbon black doped nylon susceptor. Part geometry directly determines how energy couples into the material, which drives everything downstream: heating, melting, and densification. Understanding and compensating for this geometry-dependent coupling is essential to making good parts. HEATR provides a way to do that quickly, sweeping geometry types, compensation strategies, and exposure parameters in minutes rather than the hours-to-days required by general-purpose FEA tools like COMSOL.
17+
Primitive geometries
Minutes
Per simulation run
7+
Simulation modes
The Geometry-Coupling Problem
In a parallel-plate RF field, energy coupling is not uniform. Corners and edges perpendicular to the applied field concentrate the E-field dramatically, while surfaces parallel to the field couple weakly. This means every different geometry produces a different heating pattern, and for non-symmetric shapes the results can be severe: one region of a part can be fully sintered while another barely reaches melt temperature. This is not a bug you can engineer away at the system level. It is an inherent feature of EQS heating. The only path forward is to understand the coupling for each geometry and develop compensation strategies that work around it. That requires a simulation tool fast enough to explore the space systematically.
Circle: Voltage, E-field & RF Heating
Square: Voltage, E-field & RF Heating
Why Build a Custom Solver?
General-purpose FEA tools like COMSOL can solve the coupled EQS + thermal + phase-change problem, but the overhead of model setup, meshing, and multi-physics coupling makes it impractical to iterate quickly. Changing a geometry, testing a new compensation method, or sweeping an exposure parameter each requires substantial manual effort. HEATR eliminates that overhead with a purpose-built solver tuned specifically for RF-heated powder bed geometries. A simulation that might take an afternoon to set up and run in COMSOL completes in minutes in HEATR, enabling batch sweeps and automated optimization across the full primitive geometry library.
Simulation Modes
HEATR supports multiple modes designed for systematic process exploration:
- Single Exposure: Full coupled electrothermal simulation for any geometry with detailed field, thermal, melt fraction, and densification outputs.
- Parameter Sweeps: Automated batch runs varying exposure time, part size, orientation, and material properties across the primitive geometry library.
- Exposure Optimizer: Bayesian optimization of process parameters to meet target temperature, uniformity, or densification objectives.
- Orientation Optimizer: Pareto optimization of part orientation to maximize sintering uniformity within a static field.
- Turntable Scheduling: Simulates rotational exposure averaging with configurable rotation increments and timing.
Circle: RF Simulation Summary
Square: RF Simulation Summary
Orientation Optimization
The ideal compensation strategy for non-axisymmetric parts would be a turntable that rotates the part through the field during exposure, averaging out the anisotropic coupling. In practice, this is extremely difficult to implement: the susceptor materials are high-impedance, and the electrode walls must maintain continuous contact with the powder medium throughout the process. Physically rotating a part while maintaining that contact is a significant mechanical challenge.
The next best approach is to keep the field static and optimize the orientation of the part within it. HEATR's orientation optimizer searches for the rotation angle that produces the most uniform sintering for a given geometry. The L-shape below illustrates the difference: in its default upright orientation, the vertical arm overheats while the horizontal arm barely reaches melt temperature. After orientation optimization (rotated ~45°), the coupling distributes much more evenly across both arms, producing uniform melt and densification throughout the part.
L-Shape Default: E-field Coupling
L-Shape Optimized: E-field Coupling
Default: Non-Uniform Sintering
Optimized: Uniform Sintering
Default: Density Evolution
Optimized: Density Evolution
Turntable Compensation
While physically challenging, HEATR also supports turntable simulation for research into rotational exposure averaging. The turntable mode rotates the part through configurable increments during RF exposure, averaging the anisotropic field over multiple orientations. For non-axisymmetric geometries, this produces dramatically more uniform heating than any single static orientation. The results below show a square part under turntable exposure, with the characteristic oscillating temperature profile as the field orientation cycles.
Turntable: Thermal Evolution (Animated)
Turntable: RF Summary & Temp. Profile
Outputs & Validation
Each run produces a comprehensive output package: spatial field maps (voltage, E-field, Joule heating), thermal evolution with melt fraction and relative density contours, time-resolved temperature and densification curves, and a full validation report tracking energy balance residuals, numerical stability, and solver diagnostics. This makes it straightforward to compare results across geometries and compensation strategies.
Circle: Temperature, Melt & Density
Square: Temperature, Melt & Density
Optimizer: Convergence Report
Validation: Energy & Solver Diagnostics
Simulation Platform & GUI
HEATR includes a browser-based GUI for operational control and results exploration. The Operation page provides run configuration (geometry, mode, exposure, turntable parameters), a live job queue with real-time progress tracking, and inline simulation previews. The Results browser offers filterable run history with hero previews, expandable per-run metrics with contextual explanations, and quick access to all output figures. The platform also includes a Files tab for direct output browsing and a Theory tab with integrated physics reference documentation.
GUI: Operation & Job Queue
GUI: Results Browser
Technical Details
- Physics: Electro-quasi-static field solve, volumetric Joule heating, transient thermal transport, DSC-calibrated apparent heat capacity phase-change, viscous-capillary densification with Arrhenius/WLF viscosity
- Discretization: 120×120 finite-difference grid with subpixel fill-fraction boundary treatment (8×8 subsampling), harmonic-mean conductivity at material interfaces
- Solver: Sparse direct solver (SuperLU), Forward Euler time integration with adaptive EQS/thermal subcycling
- Modes: Single exposure, parameter sweep, exposure optimizer, turntable scheduling, orientation Pareto optimization, multi-part placement, shell thickness study
- Stack: Python, NumPy, SciPy (sparse), Matplotlib, browser-based GUI with live job management
Electrothermal Simulation
RF Heating
Rapid Iteration
Python
Finite Difference
Process Optimization
Orientation Optimization
Parameter Sweeps
