{ "node": { "id": "term:thermal-model", "type": "Term", "label": "Thermal model", "properties": { "id": "thermal-model", "name": "Thermal model", "aka": [ "lumped thermal model" ], "section": "topic-thermal", "definition": "A model of cell temperature: at its simplest one thermal mass with heat generation inside and convection outside, at its most detailed a 3D simulation of the pack. Temperature feeds back into every rate, so electrical and thermal models are usually solved together.", "related": [ "heat-generation", "thermal-management", "arrhenius", "newman-model", "thermal-characterisation" ], "url": "https://lemonergy.com/learn/glossary/thermal-model/", "mentions": [ "thermal-mass", "heat-transfer-modes" ] } }, "edges": [ { "id": "edge:109", "source": "term:thermal-model", "target": "workflow:charge-thermal", "type": "usedIn", "properties": { "sourceFile": "wiki-blocks.json" } }, { "id": "edge:2192", "source": "term:thermal-model", "target": "topic:topic-thermal", "type": "belongsTo", "properties": { "sourceFile": "terms.json" } }, { "id": "edge:2193", "source": "term:thermal-model", "target": "term:heat-generation", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:2194", "source": "term:thermal-model", "target": "term:thermal-management", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:2195", "source": "term:thermal-model", "target": "term:arrhenius", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:2196", "source": "term:thermal-model", "target": "term:newman-model", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:2197", "source": "term:thermal-model", "target": "term:thermal-characterisation", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:mentions/thermal-model/thermal-mass", "source": "term:thermal-model", "target": "term:thermal-mass", "type": "mentions", "properties": { "sourceFile": "terms.json", "method": "build_glossary.mention_index + mentions", "field": "definition", "meaning": "Text mention; not a causal claim" } }, { "id": "edge:mentions/thermal-model/heat-transfer-modes", "source": "term:thermal-model", "target": "term:heat-transfer-modes", "type": "mentions", "properties": { "sourceFile": "terms.json", "method": "build_glossary.mention_index + mentions", "field": "definition", "meaning": "Text mention; not a causal claim" } }, { "id": "edge:2200", "source": "term:thermal-model", "target": "visual:thermal", "type": "illustratedBy", "properties": { "sourceFile": "visual-pages.json" } }, { "id": "edge:2201", "source": "term:thermal-model", "target": "reference:bernardi-energy", "type": "cites", "properties": { "sourceFile": "wiki-references.json", "scope": "direct technical reference" } } ], "neighbors": [ { "id": "workflow:charge-thermal", "type": "Workflow", "label": "Inspect pack temperature", "properties": { "id": "charge-thermal", "title": "Inspect pack temperature", "kind": "protocol", "summary": "The separate Charge session can include a lumped thermal node.", "steps": [ "Provide thermal mass and conductance.", "Compare two ambient temperatures." ], "example": "100 kJ/K thermal mass and 100 W/K conductance give a 1000 s no-source temperature-difference time constant.", "observe": "Temperature limits can pause charge; heater and mass are separate.", "limits": "One node does not resolve gradients, coolant geometry or runaway. Studio’s native charger instead uses external temperature.", "url": "https://design.lemonergy.com/", "label": "Open Design → Charge session", "evidence": [ "js/charger.js" ] } }, { "id": "topic:topic-thermal", "type": "Topic", "label": "Thermal management and heat transfer", "properties": { "id": "topic-thermal", "name": "Thermal management and heat transfer", "lede": "How heat is made, moved and removed in cells and packs, and the hardware that keeps a battery at the right temperature.", "context": "Select spatial detail for the question.", "example": "Equal total heat in different layouts can produce different gradients. Average temperature can miss a hot spot.", "lesson_url": "https://lemonergy.com/learn/fundamentals/battery-aging/", "lesson_label": "Open temperature and aging" } }, { "id": "term:heat-generation", "type": "Term", "label": "Heat generation", "properties": { "id": "heat-generation", "name": "Heat generation", "aka": [ "Bernardi equation" ], "section": "topic-thermal", "definition": "The heat a cell produces in operation: an irreversible part equal to current times overpotential, and a reversible part from the entropy change, I·T·dE/dT. The Bernardi equation sums them and feeds every thermal model.", "formula": "q = I(V − E_OCV) + I·T·(dE/dT)", "unit": "W", "related": [ "entropy-coefficient", "internal-resistance", "thermal-model", "thermal-management", "exothermic" ], "example": { "title": "Keep reversible and irreversible heat separate", "text": "With charging current +5 A and terminal voltage 0.10 V above OCV, the irreversible term is 0.50 W. At 300 K with dE/dT = +0.1 mV/K, the reversible contribution is +0.15 W, giving 0.65 W under this sign convention." }, "url": "https://lemonergy.com/learn/glossary/heat-generation/", "mentions": [ "overpotential" ] } }, { "id": "term:thermal-management", "type": "Term", "label": "Thermal management", "properties": { "id": "thermal-management", "name": "Thermal management", "abbr": "TMS", "aka": [ "battery thermal management system", "BTMS" ], "section": "topic-thermal", "definition": "Keeping cells in their comfortable range, roughly 15–35 °C, and within a few degrees of each other: liquid cooling plates, refrigerant plates or immersion for heat removal, and heaters or waste heat for warming before fast charging in the cold.", "related": [ "cooling-plate", "thermal-interface-material", "operating-temperature", "heat-generation", "preconditioning", "temperature-sensor" ], "url": "https://lemonergy.com/learn/glossary/thermal-management/", "mentions": [ "fast-charging" ] } }, { "id": "term:arrhenius", "type": "Term", "label": "Arrhenius law", "properties": { "id": "arrhenius", "name": "Arrhenius law", "section": "topic-aging", "definition": "The rule that a rate constant is proportional to exp(−Ea/RT), so a thermally activated reaction speeds up steeply with temperature. Near room temperature many degradation reactions roughly double their rate for every +10 °C.", "formula": "k = A·exp(−Eₐ/RT)", "related": [ "activation-energy", "calendar-aging", "operating-temperature", "accelerated-aging", "celsius-kelvin" ], "lesson": "fundamentals/battery-aging/#arrhenius", "example": { "title": "Compare reaction-rate factors", "text": "For an illustrative activation energy of 40 kJ/mol, increasing temperature from 25 °C to 35 °C multiplies the modeled rate by about 1.69. Convert both temperatures to kelvin before evaluating the exponential." }, "notes": [ "A reaction-rate factor alone is not a prediction of battery lifetime." ], "url": "https://lemonergy.com/learn/glossary/arrhenius/", "mentions": [] } }, { "id": "term:newman-model", "type": "Term", "label": "Newman model", "properties": { "id": "newman-model", "name": "Newman model", "abbr": "P2D", "aka": [ "pseudo-two-dimensional model", "Doyle–Fuller–Newman", "DFN" ], "section": "topic-transport", "definition": "The standard physics-based lithium-ion cell model: porous-electrode theory across the cell thickness, with solid diffusion solved in a representative spherical particle at every point — hence pseudo-two-dimensional. It predicts voltage from first principles but needs dozens of parameters.", "related": [ "porous-electrode-theory", "single-particle-model", "butler-volmer", "ficks-second-law", "parameterisation", "pybamm" ], "url": "https://lemonergy.com/learn/glossary/newman-model/", "mentions": [ "diffusion" ] } }, { "id": "term:thermal-characterisation", "type": "Term", "label": "Thermal characterisation", "properties": { "id": "thermal-characterisation", "name": "Thermal characterisation", "aka": [ "heat capacity test", "entropy test" ], "section": "topic-testing", "definition": "Measuring the thermal properties a model needs: specific heat capacity in a calorimeter, thermal conductivity through and along the layers, the entropy coefficient from OCV against temperature, and heat generation under load. Without them a thermal model is a guess.", "related": [ "heat-generation", "entropy-coefficient", "thermal-model", "accelerating-rate-calorimetry" ], "url": "https://lemonergy.com/learn/glossary/thermal-characterisation/", "mentions": [ "open-circuit-voltage", "thermal-conductivity", "specific-heat-capacity" ] } }, { "id": "term:thermal-mass", "type": "Term", "label": "Thermal mass", "properties": { "id": "thermal-mass", "name": "Thermal mass", "aka": [ "thermal inertia", "thermal time constant" ], "section": "topic-thermal", "definition": "A body’s total heat capacity seen as a buffer against temperature change. A 500 kg pack at about 1 kJ/(kg·K) stores roughly 500 kJ per kelvin, so 10 kW of uncooled heat warms it only about 1.2 K a minute. Together with the thermal resistance to the coolant it sets the pack’s thermal time constant.", "formula": "τ = m·cₚ·R_th", "related": [ "specific-heat-capacity", "thermal-resistance", "thermal-model", "phase-change-material", "thermal-management" ], "example": { "title": "Calculate a thermal time constant", "text": "With mass 0.5 kg, cₚ = 900 J/(kg·K) and R_th = 2 K/W, the lumped thermal time constant is 900 s, or 15 min. The calculation assumes a nearly uniform internal temperature." }, "url": "https://lemonergy.com/learn/glossary/thermal-mass/", "mentions": [] } }, { "id": "term:heat-transfer-modes", "type": "Term", "label": "Heat transfer modes", "properties": { "id": "heat-transfer-modes", "name": "Heat transfer modes", "aka": [ "conduction", "convection", "thermal radiation" ], "section": "topic-thermal", "definition": "The three ways heat moves: conduction through solids and still fluids, convection carried by a moving fluid, and radiation emitted as infrared by every warm surface. In a pack, conduction takes heat from the cell into the cooling plate and convection carries it away in the coolant; radiation matters mainly at the high temperatures of thermal runaway.", "related": [ "thermal-conductivity", "heat-transfer-coefficient", "thermography", "cooling-plate", "thermal-propagation" ], "url": "https://lemonergy.com/learn/glossary/heat-transfer-modes/", "mentions": [ "thermal-runaway" ] } }, { "id": "visual:thermal", "type": "Visual", "label": "Heat approaches an equilibrium", "properties": { "title": "Heat approaches an equilibrium", "summary": "Thermal resistance sets the steady temperature rise; thermal mass sets the response time.", "readout": "Steady rise: 10 K. Time constant: 8.333 min.", "formula": "ΔT = P R_th [1 − exp(−t / (C_th R_th))]", "note": "C_th = 500 J/K, fixed ambient and heat input, uniform temperature.", "software": { "status": "reference", "label": "Reference concept", "body": "Analysis → Charge session supports optional lumped thermal behavior. This independent explanation uses a 500 J/K thermal mass and constant heat input; it is not an application simulation result.", "href": "https://design.lemonergy.com/" }, "html": "
Temperature above ambient
Temperature above ambientTime (min) versus Temperature rise (K). Lumped response. Interpretation follows the graphs.001515303045456060Time (min)Temperature rise (K)
Lumped response
" } }, { "id": "reference:bernardi-energy", "type": "Reference", "label": "A General Energy Balance for Battery Systems", "properties": { "title": "A General Energy Balance for Battery Systems", "publisher": "Journal of The Electrochemical Society", "url": "https://doi.org/10.1149/1.2113792", "type": "Research article", "scope": "Battery energy balance and irreversible and reversible heat contributions. Reduced thermal models require explicit assumptions and current-sign conventions.", "year": 1985, "authors": [ "Dawn Bernardi", "Ellen Pawlikowski", "John Newman" ], "accessed": "2026-10-27" } } ] }