Set the model in motion.
From thermal and vehicle response to switching parasitics, motor identification and the MCU. Change conditions and compare calculated diagrams, waveforms and values.
Each chapter documents its assumptions, equations and limits.
Heat changes the next loss.
Go beyond fixed loss and an isothermal coolant boundary: calculate temperature–loss feedback and the coolant’s stored-energy state.
ELECTROTHERMAL / FLOW & STORAGE
Heat changes loss, and accumulates in the coolant.
Compare the same 120-second heating and 60-second cooling interval in three models. One time cursor links junction, plate and fluid temperatures with loss and current.
All temperatures and losses are synthetic teaching-model results. Linear resistance, constant properties and single-phase fluid assumptions are extended across the input range; large temperature rises are linear extrapolations, not physical temperature predictions or an allowable operating envelope. All three modes use the same coolant energy storage.
Input conditions
At each thermal calculation instant, this is on-state device RMS over an entire short electrical averaging cycle. Off intervals within that cycle count as zero, so conduction duty is already included. It is neither RMS over the 180-second thermal history nor motor phase RMS. The request becomes zero at 120 seconds.
Input conditions
Synthetic linear resistance, 12 mΩ at 25°C. At α = 0, unrestricted temperature feedback matches the fixed-loss reference.
Input conditions
Converted to kg/s internally. At 0 g/s, no heat leaves the system; heat moves between the junction, plate and fluid and remains stored. Plate-to-fluid thermal resistance stays fixed independently of flow.
At 1×, the full range plays in 12 screen seconds. Cursor conditions and calculated results are independent of playback speed.
Synthetic model calculation · Feedback + current limit · Heating interval · Current reduced by temperature
Thermal network for the selected mode
Arrows show calculated heat-flow direction and magnitude. Color uses a fixed 25–110°C scale; outside it the color saturates while the numerical temperature remains visible.
Fixed loss uses constant resistance without current limiting. Feedback varies resistance without limiting. Limited mode adds a synthetic linear current reduction from 80°C to zero at 110°C to that same feedback model.
Switching off does not make every node cool immediately. The fluid can still receive stored heat from the plate. At zero flow, total stored heat remains constant after switch-off.
Equations, units, assumptions and verification
Pcond = I²rms,on R(Tj) · Psw = fsw ke Irep
Cj dTj/dt = Ploss − (Tj − Tp)/Rjp
Cp dTp/dt = (Tj − Tp)/Rjp − (Tp − Tf)/Rpf
Cf dTf/dt = (Tp − Tf)/Rpf − ṁ cp (Tf − Tin)
T is in °C; temperature differences equal those in K. C is in J/K, Rjp and Rpf in K/W, ṁ in kg/s, cp in J/(kg·K), and P in W. Tin = 25°C, initially Tj = Tp = Tf = 25°C. Fluid mass 20 g × cp 4180 J/(kg·K) gives Cf = 83.6 J/K. The outlet equals the perfectly mixed fluid temperature Tf.
R₂₅ = 12 mΩ, fsw = 20 kHz, ke = 4 µJ/A. For this synthetic switching model only, representative switching current Irep is assigned the same numerical value as device RMS current. Actual switching current and RMS current generally differ. Gate, auxiliary and off-state losses are omitted; zero current produces zero heat.
Properties, thermal resistances and capacities stay constant. This is a single-phase, perfectly mixed fluid model. It omits spatial fluid temperature gradients, pressure losses, pump power, flow-dependent h, ambient losses and device stress history. The linear resistance law cannot be extrapolated as an actual device characteristic over a wide temperature range. The 80/110°C settings are not product ratings or a protection guarantee.
Rtotal = Rjp + Rpf + 1/(ṁ cp)
g = Rtotal I² R₂₅ α
Ploss,ss = (I²R₂₅ + fsw ke I)/(1 − g)
The last two expressions give the steady solution only for positive flow, continuous constant current, no current limiting, and g < 1. This playback switches off at 120 seconds, so it need not reach that steady state. Current unrestricted steady Tj = 102.6 °C; g = 0.225.
Integration uses RK4 with 0.05-second steps aligned to the 120-second transition. Outputs are every 0.5 seconds; intermediate cursor temperatures and energies are linearly interpolated. Checks cover heat balance, recovery of fixed loss at α = 0, analytic steady states, independent midpoint integration and zero-flow storage. A small energy residual confirms numerical conservation, not physical accuracy.
TI · On-resistance and transient thermal impedance ↗ · Nexperia AN11261 · RC thermal models ↗ · MathWorks · Fluid energy accumulation ↗