Biot Number Calculator

The Biot number (Bi) is a dimensionless parameter used in heat transfer calculations. To compute it, the calculator first determines the characteristic length (L_c) of the object by dividing its volume (V) by its surface area (A): L_c = V / A. Once the characteristic length is known, the Biot number is derived using the formula: Bi = (L_c * h) / k, where h represents the convective heat transfer coefficient of the surrounding fluid, and k denotes the thermal conductivity of the solid material.

Consider a steel component undergoing rapid cooling in an industrial oil bath. Suppose the solid object has a volume of 0.002 cubic meters and a surface area of 0.2 square meters. First, we compute the characteristic length: L_c = 0.002 / 0.2 = 0.01 meters. Next, assume the convective heat transfer coefficient (h) is 250 W/(m²K) and the thermal conductivity of the steel (k) is 50 W/(m·K). Plugging these values into the Biot equation yields: Bi = (0.01 * 250) / 50 = 2.5 / 50 = 0.05. Because the resulting Biot number is well below the standard threshold of 0.1, internal temperature gradients are negligible, confirming that lumped capacitance assumptions can be safely applied.

Always ensure your input units are consistent before running the computation, preferably utilizing the International System of Units (SI). When analyzing complex geometries, double-check that the characteristic length is defined correctly as volume divided by surface area, rather than simply half-thickness or radius. Finally, remember that a Biot number significantly smaller than 0.1 indicates that conduction inside the solid is much faster than convection at the surface, simplifying your thermal modeling dramatically.