{ "node": { "id": "term:thermal-diffusivity", "type": "Term", "label": "Thermal diffusivity", "properties": { "id": "thermal-diffusivity", "name": "Thermal diffusivity", "abbr": "α", "section": "topic-thermal", "definition": "How quickly temperature evens out inside a material: thermal conductivity divided by density times specific heat. Heat spreads a distance L in roughly L²/α, so crossing a 10 mm cell at about 0.2 mm²/s through-plane takes several minutes, while aluminium, near 100 mm²/s, equalises almost at once.", "formula": "α = k / (ρ·cₚ)", "unit": "m²/s", "related": [ "thermal-conductivity", "specific-heat-capacity", "thermal-gradient", "biot-number", "thermal-model" ], "example": { "title": "Compare heat-spreading rates", "text": "For an illustrative material with k = 1 W/(m·K), density 2000 kg/m³ and cₚ = 1000 J/(kg·K), α = 5×10⁻⁷ m²/s. A higher α means a temperature disturbance spreads faster for the same geometry." }, "url": "https://lemonergy.com/learn/glossary/thermal-diffusivity/", "mentions": [] } }, "edges": [ { "id": "edge:4572", "source": "term:thermal-diffusivity", "target": "topic:topic-thermal", "type": "belongsTo", "properties": { "sourceFile": "terms.json" } }, { "id": "edge:4573", "source": "term:thermal-diffusivity", "target": "term:thermal-conductivity", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:4574", "source": "term:thermal-diffusivity", "target": "term:specific-heat-capacity", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:4575", "source": "term:thermal-diffusivity", "target": "term:thermal-gradient", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:4576", "source": "term:thermal-diffusivity", "target": "term:biot-number", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:4577", "source": "term:thermal-diffusivity", "target": "term:thermal-model", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:4578", "source": "term:thermal-diffusivity", "target": "visual:thermal-spreading", "type": "illustratedBy", "properties": { "sourceFile": "visual-pages.json" } } ], "neighbors": [ { "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:thermal-conductivity", "type": "Term", "label": "Thermal conductivity", "properties": { "id": "thermal-conductivity", "name": "Thermal conductivity", "abbr": "k", "aka": [ "λ", "through-plane conductivity", "in-plane conductivity" ], "section": "topic-thermal", "definition": "How readily a material conducts heat: the heat flux per unit temperature gradient. Cells are strongly anisotropic — around 25–45 W/(m·K) in-plane, along the metal foils, but below 1 W/(m·K) through-plane, across separators and coatings — so the side a cell is cooled from decides how hot its core runs.", "formula": "q″ = −k·dT/dx", "unit": "W/(m·K)", "related": [ "thermal-resistance", "thermal-diffusivity", "thermal-characterisation", "thermal-interface-material", "biot-number", "thermal-model" ], "example": { "title": "Calculate a slab heat flow", "text": "An illustrative 2 mm layer with k = 1 W/(m·K), area 0.01 m² and a 10 K temperature difference transfers 50 W in steady one-dimensional conduction. Contact resistances and edge losses are omitted." }, "url": "https://lemonergy.com/learn/glossary/thermal-conductivity/", "mentions": [ "heat-flux", "thermal-gradient" ] } }, { "id": "term:specific-heat-capacity", "type": "Term", "label": "Specific heat capacity", "properties": { "id": "specific-heat-capacity", "name": "Specific heat capacity", "abbr": "cₚ", "aka": [ "heat capacity", "specific heat" ], "section": "topic-thermal", "definition": "The heat needed to raise one kilogram of a material by one kelvin; multiplied by mass it gives a body’s heat capacity in J/K. Lithium-ion cells sit near 1,000 J/(kg·K), so a 0.5 kg pouch cell absorbs about 500 J per degree — the figure a thermal model uses to turn heat into temperature rise.", "formula": "Q = m·cₚ·ΔT", "unit": "J/(kg·K)", "related": [ "thermal-mass", "thermal-characterisation", "thermal-model", "heat-generation", "thermal-diffusivity" ], "example": { "title": "Estimate a temperature rise", "text": "A 0.5 kg body with cₚ = 900 J/(kg·K) requires 4500 J for a 10 K temperature rise if heat loss and phase change are neglected. The heat capacity of the whole body is 450 J/K." }, "url": "https://lemonergy.com/learn/glossary/specific-heat-capacity/", "mentions": [ "pouch-cell" ] } }, { "id": "term:thermal-gradient", "type": "Term", "label": "Thermal gradient", "properties": { "id": "thermal-gradient", "name": "Thermal gradient", "aka": [ "temperature gradient", "temperature spread", "temperature uniformity" ], "section": "topic-thermal", "definition": "A change of temperature with position — within a cell from core to surface, or across a pack from coolant inlet to outlet. Packs are commonly designed to keep cells within about 5 °C of each other, because warmer cells age faster and, in parallel, carry more current, so a gradient grows into an imbalance.", "related": [ "hot-spot", "cell-to-cell-variation", "cooling-plate", "thermal-management", "biot-number" ], "url": "https://lemonergy.com/learn/glossary/thermal-gradient/", "mentions": [] } }, { "id": "term:biot-number", "type": "Term", "label": "Biot number", "properties": { "id": "biot-number", "name": "Biot number", "abbr": "Bi", "section": "topic-thermal", "definition": "The ratio of the resistance to heat conduction inside a body to the resistance to convection at its surface. Below about 0.1 the body heats almost uniformly and a lumped thermal model is adequate; large, strongly cooled cells with poor through-plane conductivity exceed it and need a model that resolves the internal gradient.", "formula": "Bi = h·L / k", "related": [ "heat-transfer-coefficient", "thermal-conductivity", "thermal-model", "thermal-gradient" ], "example": { "title": "Check a lumped-temperature assumption", "text": "For h = 10 W/(m²·K), characteristic length L = 0.005 m and k = 1 W/(m·K), Bi = 0.05. Small Bi supports a lumped-temperature approximation; the characteristic length must match the geometry." }, "url": "https://lemonergy.com/learn/glossary/biot-number/", "mentions": [ "heat-transfer-modes" ] } }, { "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" ] } }, { "id": "visual:thermal-spreading", "type": "Visual", "label": "Length sets the diffusion time scale", "properties": { "title": "Length sets the diffusion time scale", "summary": "The characteristic spreading time grows with thickness squared; ideal laser-flash half-rise time has a different coefficient.", "readout": "Thermal diffusivity is 1 mm²/s. At 5 mm, L²/α = 25 s and the ideal half-rise time is 3.47 s.", "formula": "α = k/(ρc_p); t_characteristic = L²/α; t_half = 0.1388 L²/α", "note": "Laser-flash coefficient assumes a homogeneous slab, instantaneous uniform pulse and negligible heat loss. L²/α is a characteristic scale, not an exact equilibration time.", "software": { "status": "reference", "label": "Reference concept", "body": "These analytical relations explain material measurements and thermal time scales. The glossary does not fit a laser-flash experiment or solve a cell temperature field.", "href": "../chapter-1/" }, "html": "
Thickness and response time
Thickness and response timeThickness L (mm) versus Time (s). L²/α characteristic scale; Ideal laser-flash half-rise. Interpretation follows the graphs.00252.5505757.510010Thickness L (mm)Time (s)
L²/α characteristic scaleIdeal laser-flash half-rise (dashed)
" } } ] }