{ "node": { "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" ] } }, "edges": [ { "id": "edge:4634", "source": "term:biot-number", "target": "topic:topic-thermal", "type": "belongsTo", "properties": { "sourceFile": "terms.json" } }, { "id": "edge:4635", "source": "term:biot-number", "target": "term:heat-transfer-coefficient", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:4636", "source": "term:biot-number", "target": "term:thermal-conductivity", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:4637", "source": "term:biot-number", "target": "term:thermal-model", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:4638", "source": "term:biot-number", "target": "term:thermal-gradient", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:mentions/biot-number/heat-transfer-modes", "source": "term:biot-number", "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:4640", "source": "term:biot-number", "target": "visual:biot", "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:heat-transfer-coefficient", "type": "Term", "label": "Heat transfer coefficient", "properties": { "id": "heat-transfer-coefficient", "name": "Heat transfer coefficient", "abbr": "h", "aka": [ "convection coefficient", "film coefficient" ], "section": "topic-thermal", "definition": "The heat carried away per unit area per kelvin of difference between a surface and the fluid passing it. Typical values are 5–25 W/(m²·K) for still air, 25–250 for forced air and hundreds to thousands for pumped liquid, which is why fast-charging packs are liquid-cooled. Thermal models use it as their cooling boundary.", "formula": "Q = h·A·ΔT", "unit": "W/(m²·K)", "related": [ "heat-transfer-modes", "heat-flux", "biot-number", "thermal-model", "cooling-plate", "coolant" ], "example": { "title": "Estimate convective cooling", "text": "For an illustrative h = 20 W/(m²·K), area 0.1 m² and surface-to-fluid temperature difference 10 K, hAΔT gives 20 W of cooling. The coefficient depends on the actual flow and geometry." }, "url": "https://lemonergy.com/learn/glossary/heat-transfer-coefficient/", "mentions": [] } }, { "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: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": "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: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:biot", "type": "Visual", "label": "Compare internal and surface thermal resistance", "properties": { "title": "Compare internal and surface thermal resistance", "summary": "Increasing surface cooling can make internal gradients more important.", "readout": "At h = 100 W/(m²·K), Bi = 0.5. The 0.1 line is a modeling heuristic, not a pass/fail safety limit.", "formula": "Bi = h L_characteristic / k", "note": "Declare characteristic length consistently, often volume/cooled area. Uses one scalar conductivity and convection coefficient.", "software": { "status": "reference", "label": "Reference concept", "body": "This dimensionless check helps choose a thermal model. It does not validate a lumped model for an anisotropic or internally heated battery.", "href": "../chapter-1/" }, "html": "
Biot number versus cooling coefficient
Biot number versus cooling coefficientSurface coefficient h (W/(m²·K)) versus Biot number. Bi; 0.1 rule-of-thumb marker. Interpretation follows the graphs.000.6251251.252501.883752.5500Surface coefficient h (W/(m²·K))Biot number
Bi0.1 rule-of-thumb marker (dashed)
" } } ] }