1. Component Heat Generation
Q̇loss,i = |Pcycle · fi| · (1 − ηi)
Vehicle power is distributed to each cooled component using its power fraction. Efficiency converts the non-useful portion into heat.
- Q̇loss,i: heat generated by component i.
- Pcycle: drive-cycle power at the current time step.
- fi: fraction of total power assigned to component i.
- ηi: efficiency of component i.
2. Component Temperature
Ci · dTi/dt = Q̇loss,i − UAi · (Ti − Tc)
Thermal mass slows temperature rise. Component-to-coolant conductance controls how strongly heat moves into the coolant loop.
- Ci: thermal capacitance of component i.
- Ti: component temperature.
- UAi: component-to-coolant thermal conductance.
- Tc: coolant temperature.
3. Coolant Energy Balance
Cc · dTc/dt = Σ[UAi · (Ti − Tc)] − Q̇rad
The coolant lump collects component heat and rejects heat through the radiator.
- Cc: coolant thermal capacitance.
- Σ[UAi(Ti − Tc)]: total heat transferred from components into coolant.
- Q̇rad: heat rejected by the radiator.
4. Radiator Rejection
Q̇rad = UArad · Fṁ · Fair · max(Tc − Tamb, 0)
Radiator effectiveness scales with coolant flow and air speed. Fan duty adds equivalent air speed at low vehicle speed.
- UArad: radiator conductance at reference flow and air speed.
- Fṁ: correction factor for coolant flow rate.
- Fair: correction factor for air speed through the radiator.
- Tamb: ambient air temperature.
5. Pump and Fan Control
u = clamp((Tc − Ton) / (Tfull − Ton), 0, 1)
Pump flow and fan power ramp linearly between on and full temperature setpoints.
- u: pump or fan duty command from 0 to 1.
- Ton: coolant temperature where the device starts ramping.
- Tfull: coolant temperature where the device reaches full command.
- clamp: limits the command between 0 and 1.
6. Numerical Method
Tk+1 = Tk + Δt · (dT/dt)k
The model uses explicit time stepping. It is a lumped-parameter model for design studies, not CFD or final validation.
- Tk: temperature at the current time step.
- Tk+1: temperature at the next time step.
- Δt: simulation time step.
- (dT/dt)k: temperature rate of change evaluated at the current step.