Lemonergy · Studio block

U-channel plate

Fixed 2 × 2 metal mesh with four contact ports, finite metal/coolant heat capacities, reversible coolant enthalpy transport and linear hydraulic resistance. Constant properties; single-phase coolant; ports require explicit reservoir boundaries..

Implementation ID: u-cooling-plate
Reviewed: 2026-10-27

Behavior

Four metal temperature nodes form a fixed 2 × 2 conduction mesh with four thermal contact ports. Coolant follows one four-segment U path. Metal and coolant have finite heat storage. Pressure difference drives reversible mass and enthalpy transport; hydraulic dissipation enters the coolant energy balance. Each liquid boundary requires an explicit pressure/temperature reservoir.

Interface

Original Lemonergy interface view. Lines identify ports; they are not a completed simulation circuit.

Ports and observed outputs
Name	Direction	Unit	Meaning
`a`	terminal	Pa / kg/s / K / W	Thermal-liquid conserving connection. Across variables are shared at a node; through flows balance.
`b`	terminal	Pa / kg/s / K / W	Thermal-liquid conserving connection. Across variables are shared at a node; through flows balance.
`h1`	terminal	K / W	Thermal conserving connection. Across variables are shared at a node; through flows balance.
`h2`	terminal	K / W	Thermal conserving connection. Across variables are shared at a node; through flows balance.
`h3`	terminal	K / W	Thermal conserving connection. Across variables are shared at a node; through flows balance.
`h4`	terminal	K / W	Thermal conserving connection. Across variables are shared at a node; through flows balance.
`massFlow`	output	kg/s	Observed massFlow.
`pressureDrop`	output	Pa	Observed pressureDrop.
`hydraulicPower`	output	W	Observed hydraulicPower.
`contactHeat`	output	W	Observed contactHeat.
`outletTemperature`	output	K	Observed outletTemperature.
`storedEnergy`	output	J	Observed storedEnergy.

Parameters

Defaults are initial model values. Select values for your own model and operating conditions.

Configuration fields
Parameter	Unit	Default	Meaning and limits
Total plate heat capacity `plateCapacityJK`	J/K	900	Total plate heat capacity. Numerical bounds are model-validation limits, not physical operating ratings. Minimum 1e-06; Maximum 1000000000
Total coolant heat capacity `coolantCapacityJK`	J/K	420	Total coolant heat capacity. Numerical bounds are model-validation limits, not physical operating ratings. Minimum 1e-06; Maximum 1000000000
Conductance between metal nodes `plateConductanceWK`	W/K	10	Conductance between metal nodes. Numerical bounds are model-validation limits, not physical operating ratings. Minimum 0; Maximum 1000000
Thermal contact conductance `contactConductanceWK`	W/K	100	Thermal contact conductance. Numerical bounds are model-validation limits, not physical operating ratings. Minimum 1e-06; Maximum 1000000000
Metal-to-coolant conductance per segment `coolantConductanceWK`	W/K per segment	20	Metal-to-coolant conductance per segment. Numerical bounds are model-validation limits, not physical operating ratings. Minimum 0; Maximum 1000000000
Hydraulic resistance per channel `hydraulicResistance`	Pa s/kg per channel	1000000	Hydraulic resistance per channel. Numerical bounds are model-validation limits, not physical operating ratings. Minimum 0.001; Maximum 1000000000000000
Coolant specific heat `specificHeatJkgK`	J/(kg K)	4200	Coolant specific heat. Numerical bounds are model-validation limits, not physical operating ratings. Minimum 1; Maximum 1000000
Coolant density `densityKgM3`	kg/m3	1000	Coolant density. Numerical bounds are model-validation limits, not physical operating ratings. Minimum 1; Maximum 100000
Initial plate temperature `initialPlateTemperatureK`	K	310	Initial plate temperature. Numerical bounds are model-validation limits, not physical operating ratings. Minimum 0; Maximum 5000
Initial coolant temperature `initialCoolantTemperatureK`	K	300	Initial coolant temperature. Numerical bounds are model-validation limits, not physical operating ratings. Minimum 0; Maximum 5000

Equations and rules

mass flow per channel = (pressureA-pressureB)/hydraulicResistance
contact heat[j] = contactConductance*(contactTemperature[j]-plateTemperature[j])
metal heat capacity per node = plateCapacity/4
hydraulicPower = totalMassFlow*(pressureA-pressureB)/density
coolant heat capacity*dT/dt = metal-to-coolant heat + advective enthalpy + hydraulic heat

Worked example

U-channel plate worked example

The bundled model connects four 320 K thermal loads to a 310 K plate, with 300 K coolant reservoirs at 200 kPa and 100 kPa. With channel resistance 10^6 Pa s/kg, the total flow is 0.1 kg/s and hydraulic dissipation is 10 W. After 0.2 s all four loads cool below their initial temperature.

Open Studio example after release →

Numerical checks for the bundled synthetic example
Output	Time (s)	Expected value	Unit	Absolute tolerance
Total coolant mass flow `massFlow`	0.2	`0.1`	kg/s	1e-06
Hydraulic dissipation `hydraulicPower`	0.2	`10`	W	1e-06

Use in a workflow

U-channel plate worked example

U-channel plate: Four metal temperature nodes form a fixed 2 × 2 conduction mesh with four thermal contact ports. Coolant follows one four-segment U path. Metal and coolant have finite heat storage. Pressure difference drives reversible mass and enthalpy transport; hydraulic dissipation enters the coolant energy balance. Each liquid boundary requires an explicit pressure/temperature reservoir.
- Use the parameter values in the block reference.
- Implementation tested locally; public release pending.

Open Studio example after release

Connected concepts

Limits and interpretation

Fixed 2 × 2 metal mesh and the stated coolant path. Constant properties and single-phase incompressible coolant. No arbitrary liquid junction solver, configurable grid, resolved channel geometry or phase change.

Scientific and mathematical references

These sources explain the scientific and mathematical background. The behavior, interface and limits above define the Lemonergy implementation; a citation does not imply every model option in the source is implemented.

University Physics Volume 2, §1.6: Mechanisms of Heat Transfer
OpenStax, Rice University
Technical reference · Conduction, convection, radiation and thermal resistance.

Implementation sources

This reference follows the public interface and locally verified numerical checks for an upcoming release.

Contract: Lemonergy Studio public contract · Verification record: verification-2026-10-27

docs/glossary/native-block-verification.json

This implementation and its workflow uses (JSON) · Knowledge graph (JSON-LD)