Biot Number Calculator - Heat Transfer Analysis
Calculate Biot number for transient heat conduction to see if lumped capacitance model applies. Free heat transfer calculator with charts and breakdowns.
About This Calculator
The Biot Number Calculator computes the dimensionless Biot number (Bi) for transient heat transfer analysis, comparing internal conduction resistance within a solid to external convection resistance at its surface. The Biot number determines whether the lumped capacitance model can be applied, which assumes uniform temperature throughout the solid. This calculator is essential for mechanical engineers, chemical engineers, HVAC professionals, physics students, and anyone working with heat transfer problems involving cooling, heating, or thermal processing of solid objects.
How the Biot Number Works
The Biot number is calculated using the formula Bi = h × Lc / k, where h is the convective heat transfer coefficient (W/m²K), Lc is the characteristic length defined as volume divided by surface area (m), and k is the thermal conductivity of the solid material (W/mK). The characteristic length varies by geometry: for a sphere Lc = r/3, for a long cylinder Lc = r/2, and for a slab or flat plate Lc = half-thickness.
Interpreting Biot Number Results
Bi < 0.1: The lumped capacitance model is valid — internal conduction is much faster than surface convection, so the solid can be considered to have a uniform temperature. The error from this assumption is less than 5%. This applies to small, high-conductivity objects like thin aluminum plates, copper wires, or small bearings cooling in air.
0.1 ≤ Bi < 10: Intermediate regime — neither conduction nor convection can be neglected. A full transient temperature distribution analysis using Heisler charts or the one-term approximation method is required. Most real-world engineering objects fall in this range.
Bi ≥ 10: Surface resistance dominates — conduction within the solid is the limiting factor. The surface temperature quickly approaches the fluid temperature while the interior changes slowly. Fins and extended surfaces are beneficial in this regime to enhance heat transfer.
Regional Notes
India: The Biot number is applied in the design of heat exchangers for process industries, cooling of electronic components, and thermal analysis of solar thermal collectors. ISHRAE guidelines reference Biot-based lumped analysis for HVAC component sizing. Common Indian construction materials like fly ash brick (k ≈ 0.35 W/mK) and autoclaved aerated concrete blocks (k ≈ 0.18 W/mK) have different thermal properties affecting their Biot numbers.
United States: ASHRAE Handbook chapters on transient heat transfer use Biot number analysis for building envelope thermal response and HVAC system design. Common US construction materials like fiberglass insulation (k ≈ 0.04 W/mK) and concrete (k ≈ 1.8 W/mK) span different Biot regimes depending on thickness. The NEC and IECC reference thermal time constants derived from Biot-Fourier analysis.
United Kingdom: CIBSE Guide A provides environmental design data incorporating Biot-based transient analysis for building services. UK Building Regulations Part L thermal bridging calculations benefit from understanding whether lumped or distributed temperature models apply. Typical UK solid wall constructions (brick k ≈ 0.6 W/mK, stone k ≈ 2.0 W/mK) may require full transient analysis unless very thin.
Frequently Asked Questions
What is the Biot number?
The Biot number (Bi) is a dimensionless quantity in heat transfer that compares internal conduction resistance within a solid to external convection resistance at its surface. It is defined as Bi = hL/k, where h is the convective heat transfer coefficient (W/m²K), L is the characteristic length (volume/surface area in meters), and k is the thermal conductivity of the solid (W/mK). A low Biot number (Bi < 0.1) means internal conduction is much faster than surface convection.
When can the lumped capacitance model be used?
The lumped capacitance model is valid when Bi ≤ 0.1. In this regime, internal conduction resistance is negligible compared to surface convection resistance, so the solid can be assumed to have a uniform temperature throughout. The error from this assumption is less than 5%. This typically applies to small objects with high thermal conductivity, such as aluminum spheres in air or thin metal plates.
What is characteristic length in Biot number calculation?
The characteristic length Lc is defined as the volume of the solid divided by its surface area (Lc = V/A). For common geometries: a sphere has Lc = radius/3, a long cylinder has Lc = radius/2, and a slab or flat plate has Lc = half-thickness. Choosing the correct characteristic length based on geometry is essential for accurate Biot number calculation.
What is a typical Biot number for metals in air?
For small aluminum objects (k ≈ 237 W/mK) in still air (h ≈ 10-25 W/m²K), the Biot number is typically under 0.1, making the lumped capacitance model valid. Stainless steel (k ≈ 15 W/mK) has a higher Biot number for the same size due to lower conductivity. In water (h ≈ 100-1000 W/m²K), even aluminum objects may exceed Bi = 0.1, requiring a full transient analysis.
How does the Biot number relate to the Fourier number?
The Biot number (Bi) and Fourier number (Fo) are both dimensionless numbers used together in transient heat transfer analysis. The product Bi × Fo = (h² × α × t)/(k²) relates time to thermal resistance, where α is thermal diffusivity and t is time. Heisler charts and one-term approximation methods use both Bi and Fo to determine temperature distribution in solids over time.
What does the Biot number mean in cooking?
In cooking, the Biot number explains why large items like a turkey (Bi > 0.1) have non-uniform cooking temperatures where outer layers cook faster than the center. This is why meat thermometers must reach the center for accurate doneness. Small items like shrimp or thin steaks (Bi < 0.1) cook more uniformly since internal conduction is fast enough to maintain near-uniform temperature.
How do you interpret Biot number in heat exchanger design?
A high Biot number (Bi ≥ 10) indicates conduction resistance dominates over convection, making fins or extended surfaces beneficial for improving heat transfer. A low Biot number (Bi < 0.1) means convection at the surface is the limiting factor, so improving fluid flow or increasing the heat transfer coefficient has a bigger impact than adding surface area.
What is the difference between Biot number and Nusselt number?
Both Biot number and Nusselt number have the same formula hL/k, but they use different thermal conductivities. The Biot number uses the thermal conductivity of the solid (k_solid) and describes internal temperature gradients. The Nusselt number uses the thermal conductivity of the fluid (k_fluid) and describes convective heat transfer at the fluid-solid boundary. They serve different purposes in heat transfer analysis.