Motor Thermal Management Analysis — Electromagnetic-Thermal Coupling Theory and Practice
Theoretical Foundations of Motor Thermal Management
Why Electromagnetic-Thermal Coupling is Necessary
Professor, is motor temperature analysis done separately from electromagnetic analysis? I thought we could calculate thermal effects independently from electromagnetic effects…
Good question. The answer is that coupled analysis is essential. The reason is that electromagnetic and thermal effects influence each other bidirectionally.
Specifically, motor heat sources fall into three categories — copper loss, iron loss, and mechanical loss. These losses increase temperature. Then what happens is…
- Copper resistivity increases → copper loss increases further (positive feedback)
- Permanent magnet residual flux density $B_r$ decreases → torque drops, current must increase to maintain output, generating more heat
- Iron loss characteristics also change → the B-H curve of silicon steel varies with temperature
This means we need an iterative loop: "Run electromagnetic analysis to get losses → Run thermal analysis to get temperature → Update material properties with new temperature → Re-run electromagnetic analysis." This feedback loop is essential.
So they influence each other that much! I understand copper resistance increases with temperature, but magnets are affected too?
Yes, especially with NdFeB (Neodymium) magnets. The temperature coefficient is about $-0.12\%/°\text{C}$, so a magnet with $B_r = 1.3\,\text{T}$ at room temperature drops to about $1.14\,\text{T}$ at 150°C. Moreover, the risk of irreversible demagnetization increases sharply above 150°C. Once irreversible demagnetization occurs, cooling the magnet won't restore it.
That's scary… Irreversible. Are high-performance EV motors okay during continuous highway driving on steep grades?
That's exactly the biggest design challenge. Accurately predicting magnet temperature at worst-case conditions using electromagnetic-thermal coupled analysis is one of the most critical tasks in motor design.
Loss Classification and Heat Generation Mechanisms
What are the proportions of copper loss, iron loss, and mechanical loss?
Proportions vary by motor type and operating condition. Here's a typical breakdown for EV IPMSMs:
| Loss Type | Location | Proportion of Total Loss (typical) | Temperature Dependence |
|---|---|---|---|
| Copper Loss $P_{cu}$ | Stator Winding | 50–70% | Increases with temperature |
| Iron Loss $P_{fe}$ | Stator Core, Rotor Core | 15–30% | Slightly decreases with temperature |
| Mechanical Loss $P_{mech}$ | Bearings, Air Gap (windage) | 5–15% | Speed dependent |
| Magnet Eddy Current Loss | Permanent Magnet | 1–5% | Harmonic dependent |
Copper loss is over half! What's the formula for copper loss?
The basic formula is $P_{cu} = I^2 R$, but with temperature compensation it becomes:
where $R_0$ is resistance at reference temperature $T_0$ (typically 20°C), and $\alpha_{Cu} \approx 0.00393\,/°\text{C}$ is the temperature coefficient of copper resistivity.
For example, if a motor has 10W of copper loss at 20°C and winding temperature reaches 150°C:
$P_{cu}(150) = 10 \times [1 + 0.00393 \times (150 - 20)] = 10 \times 1.511 \approx 15.1\,\text{W}$
This means copper loss increases by about 50%. Without coupled analysis, this effect is missed.
A 50% increase is significant… How is iron loss calculated?
The Steinmetz equation (developed in the 1890s) has been the standard for iron loss. The Modified Steinmetz Equation (MSE) is dominant in engineering practice.
First term: hysteresis loss ($k_h$ is hysteresis coefficient, $\beta \approx 1.6 \sim 2.0$)
Second term: classical eddy current loss ($k_e$ is eddy current coefficient)
Third term: anomalous eddy current loss ($k_{ex}$ due to domain wall motion)
Three coefficients? Are these determined experimentally?
Yes, they're fitted from manufacturer test data (Epstein test or ring core test results). For example, NIPPON STEEL's 35H300 silicon steel shows iron loss of $3.0\,\text{W/kg}$ at $1.5\,\text{T}$ and 50Hz. Coefficients are determined by curve-fitting such data.
Governing Equations
Now that we know the losses, what equation determines the temperature distribution?
The foundation is the 3D transient heat conduction equation. The loss density $q_{loss}$ from electromagnetic analysis becomes the heat source term.
$\rho$: density [kg/m³], $c_p$: specific heat [J/(kg·K)], $k$: thermal conductivity [W/(m·K)], $q_{loss}$: volumetric heat generation rate [W/m³]
The key point is that $q_{loss}$ is a function of temperature $T$. As temperature rises, copper loss increases and iron loss characteristics change. This is why $q_{loss}(\mathbf{x}, T)$ is written that way.
Ah, so heat generation itself depends on temperature. That's why you can't just solve it one way.
Exactly. Additionally, thermal resistances between motor components are very important. These interfaces greatly affect temperature distribution:
| Interface | Thermal Resistance Cause | Typical Value |
|---|---|---|
| Winding-Slot Wall | Impregnating varnish + air gap | $R_{th} \approx 0.01 \sim 0.05\,\text{K·m²/W}$ |
| Core-Frame | Contact resistance from press-fit | $R_{th} \approx 10^{-4} \sim 10^{-3}\,\text{K·m²/W}$ |
| Magnet-Rotor Core | Adhesive layer | $R_{th} \approx 0.005 \sim 0.02\,\text{K·m²/W}$ |
| Air Gap | Low air conductivity + convection | $h \approx 50 \sim 300\,\text{W/(m²·K)}$ |
Permanent Magnet Demagnetization Risk
You mentioned irreversible demagnetization earlier. Can you give more details? What temperature is actually critical?
It depends on the magnet grade. Here are representative values:
| Magnet Grade | $B_r$ (20°C) | Max Operating Temp | $\alpha_{B_r}$ [%/°C] |
|---|---|---|---|
| N52 (High $B_r$, Low Heat Resistance) | 1.43 T | 80°C | -0.12 |
| N42SH (Mid $B_r$, High Heat Resistance) | 1.30 T | 150°C | -0.11 |
| N38UH (Low $B_r$, Ultra-High Heat Resistance) | 1.23 T | 180°C | -0.10 |
| SmCo (Samarium Cobalt) | 1.05 T | 300°C | -0.035 |
Irreversible demagnetization depends not only on temperature but also on the strength of the opposing magnetic field. During flux-weakening operation (high d-axis current), if temperature is also high, the operating point on the B-H curve can drop below the **knee point**, causing irreversible demagnetization. The rule is to verify demagnetization margin at the worst case of "maximum current × maximum temperature."
Flux-weakening operation is the most dangerous. The thought of magnets failing during full-throttle highway driving is terrifying…
Insulation Class and Permissible Temperature
Besides magnets, there are temperature limits for windings too, right?
Exactly. The insulation film on windings has thermal-resistance classes defined by IEC 60085. Exceeding these limits rapidly degrades insulation life.
| Insulation Class | Max Permissible Temp | Representative Insulation Material | Applications |
|---|---|---|---|
| Class B | 130°C | Polyester-based | Industrial General-Purpose Motors |
| Class F | 155°C | Epoxy-based | Typical EV Motors |
| Class H | 180°C | Silicone-based | High-Power EV, Aircraft |
| Class N | 200°C | Polyimide-based | Special High-Temperature |
In practice, "Class F insulation with Class B temperature rise" is common—use 155°C-rated material but keep actual temperature below 130°C. The 25°C margin is a safety factor.
Steinmetz's Empirical Formula — Over 100 Years Still in Use
In the 1890s, Charles Steinmetz compiled vast experimental data into an empirical formula relating iron loss to flux density and frequency. No computers existed then—only hand calculations and endless experiments. Remarkably, the "Steinmetz equation" remains in active use at cutting-edge motor design tools like JMAG, Maxwell, and Motor-CAD over 130 years later. It represents how experimental data-driven approaches can overcome the limits of pure theory—a tribute to the determination of previous engineers.
Numerical Calculation Methods for Motor Thermal Management
LPTN (Lumped Parameter Thermal Network)
Are there methods other than FEM for calculating motor temperature? FEM seems to take a long time…
Good observation. Motor thermal analysis has two main approaches:
- LPTN (Lumped Parameter Thermal Network) — thermal circuit network with concentrated parameters
- FEM (Finite Element Method) — 3D distributed parameter model
For design exploration with many parametric studies, use LPTN. For detailed design verification on the final few candidates, use FEM. A two-stage approach like this is the industry standard.
LPTN is like an electrical circuit?
Exactly! We solve thermal problems using electrical circuit analogy:
| Electrical Circuit | Thermal Circuit | Unit |
|---|---|---|
| Voltage $V$ | Temperature $T$ | °C or K |
| Current $I$ | Heat Flow $\dot{Q}$ | W |
| Resistance $R$ | Thermal Resistance $R_{th}$ | K/W |
| Capacitance $C$ | Thermal Capacitance $C_{th}$ | J/K |
| Current Source | Heat Source (Loss) | W |
Each motor component (winding, teeth, yoke, magnet, shaft, frame) becomes a node, connected by thermal resistances. A typical motor has 20–50 nodes.
$[C_{th}]$: thermal capacitance matrix, $[G_{th}]$: thermal conductance matrix ($G = 1/R_{th}$), $\{P_{loss}\}$: heat source vector at each node
How fast is it?
LPTN solves in milliseconds per operating point. Running the entire efficiency map (e.g., 100×100 = 10,000 points) takes tens of seconds. FEM would take days for the same task. That's why Motor-CAD uses LPTN.
FEM Coupled Analysis
How does FEM coupled analysis actually work in practice?
FEM electromagnetic-thermal coupling typically follows this flow:
- Electromagnetic FEM: Run transient analysis for one rotation (or several electrical cycles) → calculate time-averaged loss density for each element
- Map loss density to thermal FEM source term
- Solve thermal FEM to get temperature distribution
- Update material properties (copper resistivity, magnet $B_r$, iron loss coefficients) from temperature
- Re-run electromagnetic FEM with updated properties
- Repeat steps 2–5 until temperature converges (typically 3–5 iterations)
Do you use different meshes for electromagnetic and thermal?
Good question. Electromagnetic and thermal meshes have different requirements:
- Electromagnetic mesh: Very fine elements in air gap needed (accurate flux density calculation). Thousands of elements in 2D cross-section.
- Thermal mesh: Air gap treated as convection boundary condition, only solid regions meshed. Hundreds of thousands to millions of elements in 3D.
They're typically separate. Loss data is "mapped" between them. JMAG and Maxwell have built-in mapping functions.
Coolant Circuit Modeling
How do we model cooling systems? Water jackets, oil cooling, etc.?
Coolant circuit modeling has three levels:
Level 1: Fixed Heat Transfer Coefficient
Set a constant $h$ on the cooling surface. Simplest but least accurate.
For water jacket, $h \approx 3000 \sim 5000\,\text{W/(m²·K)}$ is typical.
Level 2: 1D Coolant Flow Path Model
Calculate coolant temperature change along the flow path. Compute $h$ dynamically from Nusselt number correlations.
Here $P_{wet}$ is wetted perimeter, $\dot{m}$ is mass flow rate. Motor-CAD uses this approach.
Level 3: 3D CFD Coupling
Full 3D mesh and flow analysis in Fluent/Star-CCM+. Highest accuracy but maximum cost. Used for jacket geometry optimization or oil-spray pattern design.
Which level is used most in practice?
Level 2 dominates in design phases. Level 3 is reserved for final verification once cooling system geometry is finalized. By the way, EV thermal management increasingly uses **ATF (Automatic Transmission Fluid) oil cooling** with direct spray on coil ends, which is difficult to model with Level 2 alone—CFD becomes necessary there.
Coupling Strategy: Weak vs. Strong Coupling
What's the difference between weak and strong coupling?
| Aspect | Weak Coupling (One-way / Sequential) | Strong Coupling (Two-way / Fully Coupled) |
|---|---|---|
| Data Exchange | Electromagnetic to thermal, or several iterations | Bidirectional exchange at every time step |
| Computational Cost | Low (each solver runs 1–5 times) | High (convergence iterations every step) |
| Accuracy | Sufficient for steady-state or gradual transient | Needed for rapid transients |
| Tool Example | JMAG→Fluent, Maxwell→Icepak | COMSOL (built-in coupling) |
| Use Case | Steady-state rated, efficiency maps | Motor lock, transient overload |
90%+ of practical cases use weak coupling. Strong coupling is only truly needed in extreme cases like rotor lock where temperature changes by hundreds of degrees in seconds.
Oil Cooling vs. Water Cooling — A Design Inflection Point
The choice between oil cooling (ATF spray) and water cooling (jacket) is a recurring debate in EV thermal design. Water cooling has smaller thermal resistance and is easier to control, but cannot directly reach coil ends. Oil cooling can spray directly on coil ends for powerful local cooling, but oil churning increases parasitic loss. In continuous operation, water cooling often wins; in peak power, oil cooling excels. Recent premium EVs use **hybrid cooling**—both simultaneously. Coupled analysis reveals which approach truly dominates for a specific design.
Practical Application of Motor Thermal Management
Analysis Workflow
Professor, where do I start if I want to do motor electromagnetic-thermal coupled analysis?
Here's the typical workflow:
- Motor Specification Summary: Rated/peak current, speed range, cooling method, insulation class
- Electromagnetic FEM (2D Transient): Representative operating points (rated/peak torque/max speed) → calculate losses
- LPTN or 3D Thermal FEM: Map losses → get temperature distribution
- Temperature-Corrected Material Properties: Update copper resistivity, magnet $B_r$ → re-run electromagnetic FEM
- Convergence Confirmation: Iterate until temperature change is <1°C
- Demagnetization Check: Verify magnet operating point stays above knee point at max temperature
- Drive Cycle Transient Analysis: Run through WLTP or US06 driving patterns to confirm thermal behavior
Mesh Generation Guidelines
Any special considerations for motor thermal analysis meshing?
Motor-specific mesh considerations:
- Winding Modeling: Meshing individual copper wires (thousands) is impractical. Model as equivalent cross-section with equivalent properties reflecting packing fraction.
- Silicon Steel Lamination: Impossible to mesh each lamina separately. Use a homogeneous material with anisotropic thermal conductivity (higher in-plane, lower through-thickness).
- Coil End: Absent in 2D electromagnetic analysis but accounts for 20–30% of copper loss. **Must be modeled in 3D thermal analysis.**
- Air Gap: In electromagnetic mesh it's ultra-fine (<0.1mm elements), but in thermal analysis it's replaced by convection boundary condition.
- Thermal Contact Resistance Interfaces: Core-frame, magnet-rotor interfaces need TCR (Thermal Contact Resistance) definition.
If you forget coil ends, temperature is underestimated by 20–30%?
Exactly. Coil end is thermally worst-positioned. Slot-embedded winding has the core nearby for heat dissipation, but coil ends stick out into the end space with only air (natural convection) to cool them. **Maximum temperature occurs at coil end ~100% of the time.** Overlooking it breaks your design.
Boundary Conditions and Heat Transfer Coefficient Settings
How do we decide the heat transfer coefficient $h$ value? Are there standard values?
Representative values exist, but they strongly depend on flow speed, temperature, and geometry. The correct approach is to calculate from Nusselt number correlations.
| Cooling Surface | $h$ Range [W/(m²·K)] | Notes |
|---|---|---|
| Natural Convection (Outer Surface) | 5–25 | Sealed motor outer surface |
| Forced Air (Fan-Cooled) | 30–100 | Totally Enclosed Fan Cooled (TEFC) |
| Water Jacket (Laminar) | 500–2,000 | Low flow rate |
| Water Jacket (Turbulent) | 3,000–8,000 | Proper flow rate |
| ATF Oil Spray | 500–3,000 | Spray velocity and angle dependent |
| Air Gap (Rotor Surface) | 50–300 | Speed dependent, Taylor-Couette flow |
Air gap heat transfer is a frequent stumbling point. The rotating flow between rotor and stator (Taylor-Couette flow) undergoes a transition determined by Taylor number $Ta$:
$\omega$: angular velocity, $r_m$: mean radius, $\delta$: gap height, $\nu$: kinematic viscosity. When $Ta > 1700$, Taylor vortices appear and heat transfer jumps.
Validation and Verification
How do we verify that analysis results are correct?
Motor thermal analysis validation has three stages:
- Energy Balance Check: Sum of input losses = heat rejected by cooling system + stored heat (transient). Mismatch signals model error.
- Sensitivity Analysis: Vary uncertain parameters (contact resistance, winding equivalent conductivity) by ±30% and check temperature sensitivity.
- Experimental Correlation: Compare with thermocouple/Pt100 winding temperature, IR camera frame surface, coolant inlet-outlet temperature difference (calorimetry). Target is ±10°C agreement.
±10°C is pretty tight. Do you actually achieve that?
With experimental calibration of contact resistance and winding equivalent properties, ±5°C is achievable. Conversely, using "textbook values" as-is often produces ±20–30°C error. Experimental calibration is the key to analysis accuracy.
Motor Thermal Management: Software & Solver Comparison for Motor Thermal Management
Major Tool Comparison
What software options exist for motor electromagnetic-thermal coupling?
There are "specialty tools" and "general-purpose multiphysics tools."
| Tool | Developer | Thermal Method | EM Coupling | Strengths |
|---|---|---|---|---|
| Motor-CAD | Ansys (formerly MDL) | LPTN + CFD | Maxwell integration | Fast parametric exploration |
| JMAG-Designer | JSOL | 3D FEM thermal | Built-in coupling | Unified EM-thermal-structural |
| Maxwell + Icepak | Ansys | 3D FEM/CFD | Workbench link | Detailed 3D CFD cooling |
| COMSOL | COMSOL AB | 3D FEM | Full internal coupling | Flexible physics combination |
| Flux + Portunus | Altair | LPTN + FEM | System coupling | Control system integration |
| FEMM + Custom | OSS + proprietary | External link | Manual | Low cost |
Motor-CAD uses LPTN, not FEM. Is accuracy okay?
Motor-CAD's LPTN is backed by 50+ years of academic research and proper calibration achieves ±5°C steady-state accuracy. However, local temperature non-uniformity (e.g., within-slot variations) is invisible—FEM is needed for that. Practical split-use:
- Design exploration (100+ candidates) → Motor-CAD (LPTN)
- Detailed verification (final 2–3 candidates) → JMAG / Maxwell+Icepak (FEM)
- Cooling optimization → Star-CCM+ / Fluent (3D CFD)
Selection Guidelines
On a budget, what's the best choice?
Build incrementally based on budget and scope:
- Budget = Zero: FEMM (2D EM, free) + Python/Excel manual LPTN. Sufficient for academic research.
- ~1–3M JPY/year: Motor-CAD alone. Covers design exploration well.
- ~5–10M JPY/year: JMAG + 3D thermal. Japanese motor manufacturers' standard setup.
- ≥10M JPY/year: Full Ansys suite (Maxwell + Motor-CAD + Fluent + Icepak). Large OEM integrated environment.
The "Seamless Electromagnetic-Thermal Coupling" Revolution
Motor-CAD (Motor Design Ltd., acquired by Ansys in 2022) became dominant in automotive/aerospace because it was the first tool to couple electromagnetic and thermal analysis **within the same environment**. Previously, users exported loss distributions from EM FEA, imported them into separate thermal software—introducing data conversion errors and model inconsistencies. Motor-CAD automated this link, cutting iteration cycles drastically. However, its LPTN foundation (≈50 nodes) cannot represent complex fluid cooling in detail—that's why high-end designs still rely on CFD for coolant optimization.
Motor Thermal Management: Common Issues & Debugging for Motor Thermal Management
Common Errors and Solutions
Have you ever had "analysis doesn't match experiment" nightmares?
Many times (laughs). Common issues organized by symptom:
| Symptom | Root Cause | Solution |
|---|---|---|
| Winding temp 50°C higher than measured | Winding equivalent conductivity too low (insufficient impregnation assumed) | Recalculate equivalent properties from actual packing/impregnation fraction |
| Magnet temp much lower than measured | Magnet eddy current loss ignored | Add eddy current loss calculation with segmentation and conductivity |
| Coupling iteration oscillates (won't converge) | Copper loss temperature dependence too strong, positive feedback diverges | Use relaxation factor ($\alpha = 0.3–0.7$) to limit update magnitude |
| Coolant outlet temp doesn't match | Coolant flow setting differs from actual / bypass leakage | Use measured flow data; confirm no bypass leakage |
| Frame surface temp too high | Natural convection $h$ on outer surface too low | Model cooling fins correctly; use correlation formula for $h$ |
| Steady-state shows unrealistic high temp | Heat has no escape path (boundary condition error) | Verify energy balance: input power = loss = heat rejection |
What's a relaxation factor?
When updating temperature in coupled iteration, take a weighted average of new and old values:
$\alpha = 1$ uses calculated value directly (oscillation-prone). $\alpha = 0.5$ takes the midpoint (stable but slow). Typically $\alpha = 0.5–0.7$ balances stability and speed.
Debug Checklist
When analysis "doesn't work," what's a systematic approach?
Follow this checklist top-to-bottom:
- Energy Balance: Total loss [W] ≈ Coolant heat absorption $(\dot{m} c_p \Delta T_{coolant})$ + outer surface rejection? Mismatch signals setup error.
- Loss Plausibility: EM FEM losses match overall efficiency? If efficiency is 90% at 10kW input, total loss should be ~1kW.
- Material Anisotropy: Is silicon steel through-lamination conductivity set to 1/10–1/20 of in-plane value? (Common mistake: using equal values.)
- Contact Resistance: Is core-frame interface $R_{th}$ defined? Zero (perfect contact) is unrealistic and over-predicts cooling.
- Coil End: Is it modeled in 3D? Omitting it misses the maximum temperature location.
- Coolant Temperature Gradient: Is temperature treated as spatially constant? Reality shows inlet-to-outlet rise; use 1D flow model.
- Unit Consistency: EM loss [W/m³] → thermal input [W]. Check unit conversion, especially across software boundaries.
This checklist is invaluable! I'm saving it. Motor thermal management is challenging because it needs electromagnetic + thermal + fluid knowledge simultaneously. But that's exactly what makes it rewarding.
Exactly. Multiphysics is hard but engineers who master it are in demand during the EV era. Keep at it!
Related Topics
Numerical Calculation Methods for Motor Thermal Management
Detailed Numerical Methods
How are motor thermal management equations actually solved numerically?
Motor thermal analysis relies on two main frameworks—LPTN for fast parametric studies and FEM for detailed spatial resolution. Let me walk through the discretization.
FEM Discretization
Using shape functions $N_i$, we approximate the unknown field:
This Galerkin approximation transforms the PDE into a discrete system:
Element assembly integrates local contributions:
where $w_g$ are Gauss quadrature weights, $\xi_g$ integration points, and $|J|$ Jacobian determinant.
Time Integration for Transients
For transient thermal analysis:
Implicit (Backward Euler): Unconditionally stable, larger time steps permitted.
Explicit (Forward Euler): Requires CFL stability: $\Delta t \leq \frac{\rho c_p \Delta x^2}{2k}$. Faster per step but many steps needed.
Element Types for Motor Analysis
Common element choices:
| Element Type | Order | Nodes (3D) | Accuracy | Cost |
|---|---|---|---|---|
| Tetrahedral Linear | Linear | 4 | Low (shear-locking) | Low |
| Tetrahedral Quadratic | Quadratic | 10 | High | Medium |
| Hexahedral Linear | Linear | 8 | Medium | Medium |
| Hexahedral Quadratic | Quadratic | 20 | Very High | High |
| Prism | Linear/Quad | 6/15 | Medium-High | Medium |
Solver Methods and Preconditioning
Large sparse systems are solved iteratively with preconditioning:
| Preconditioner | Characteristic | Cost | Robustness |
|---|---|---|---|
| ILU(0) | Incomplete LU, zero fill-in | Low | Medium |
| ILU(k) | Incomplete LU, k fill-in | Medium | High |
| AMG | Algebraic MultiGrid | Low | Very High |
| SSOR | Symmetric SOR | Low | Low-Medium |
Convergence and Mesh Independence
Mesh refinement strategies:
- h-refinement: Decrease element size $h$ for higher accuracy. Convergence rate $O(h^p)$ where $p$ is element order
- p-refinement: Increase polynomial order within elements
- hp-refinement: Combine both simultaneously for optimal efficiency
Always verify mesh convergence with 2–3 refinement levels. Extrapolate to zero-mesh-size solution using Richardson extrapolation.
Nonlinear Coupling Iterations
Newton-Raphson iteration for electromagnetic-thermal coupling:
where residual $\mathbf{R}(\{T\}) = [K]\{T\} - \{Q(T)\}$ includes temperature-dependent loss. Convergence requires $\|\mathbf{R}\|/\|\mathbf{R}_0\| < 10^{-4}$.
Practical Application of Motor Thermal Management
Implementation Guide by Software
What's the step-by-step procedure for actually running a motor thermal analysis?
The general workflow is:
- Preprocessing: CAD import → shape cleanup → material definition → meshing → BC setup
- Solving: Solver configuration → job submission → convergence monitoring
- Postprocessing: Result visualization → validation → reporting
Common Failure Modes and Remedies
Convergence Failure
| Symptom | Cause | Remedy |
|---|---|---|
| Solver quits after N iterations without solution | Poor mesh quality; inappropriate BCs; nonlinear instability | Check mesh metrics; review constraints; increase substeps |
| Oscillating residual | Strong nonlinearity or feedback | Apply relaxation factor; reduce load step size |
| Residual stagnates but doesn't converge | Solver singularity or ill-conditioning | Check for duplicate nodes; review material data |
Unphysical Results
- Negative temperature: Boundary condition error (wrong sign on heat flux)
- Extreme temperature spike: Boundary isolation or element inversion
- Large temperature gradients: Check for missing contact resistance or material mismatch
Quality Assurance Checklist
- Energy balance closure: $\sum P_{loss} = Q_{coolant} + \Delta U$ (transient)
- Mesh quality metrics: aspect ratio < 5, Jacobian > 0.3, skewness < 45°
- Material property range: conductivity 1–500 W/(m·K) typical
- Result sensitivity: ±10–15% variation in uncertain parameters acceptable
- Benchmark against known solutions or prior tests