Biot Number Calculator

The Biot number is a dimensionless heat-transfer ratio that compares resistance to conduction inside a solid with resistance to convection at its surface. It is calculated as the convection heat-transfer coefficient multiplied by a characteristic length and divided by the material's thermal conductivity. Because the units cancel, the result can compare objects of different sizes, materials, and boundary conditions on a common basis. A small Biot number means heat conducts through the object much more readily than heat crosses the surrounding fluid boundary layer. Internal temperature gradients are then relatively small, and the object's temperature may be approximated as spatially uniform. The widely used lumped-capacitance method is generally considered suitable when Bi is below 0.1, subject to the required engineering accuracy. Larger values indicate meaningful temperature variation inside the solid and may require transient conduction charts, analytical series solutions, or numerical simulation. Characteristic length must be chosen correctly. For lumped transient analysis it is commonly the object's volume divided by its convecting surface area. A long cylinder, sphere, wall, or finite body therefore has a characteristic length related to geometry, not automatically its largest dimension. Some heat-transfer correlations define length differently, so always follow the convention used by the chosen equation or reference. The convection coefficient depends on fluid properties, velocity, surface orientation, and whether convection is natural or forced. Thermal conductivity depends on material composition and temperature. Use values representative of the actual operating condition rather than generic room-temperature values when precision matters. The calculator expects watts per square meter-kelvin for convection coefficient, meters for characteristic length, and watts per meter-kelvin for conductivity. Biot number should not be confused with the Nusselt number: Bi uses the solid's conductivity and evaluates internal temperature uniformity, whereas Nusselt uses fluid conductivity and describes convection relative to conduction in the fluid. This result is a screening and modeling aid; critical thermal designs should also evaluate geometry, radiation, changing properties, contact resistance, and time-dependent boundary conditions.