Question

What is the physical significance of the Biot number? Is the Biot number more likely to be larger for highly conducting solids or poorly conducting ones?

Short answer

Answer: The Biot number (Bi) is a dimensionless parameter representing the ratio of conductive heat resistance within a solid body to the convective heat transfer resistance at the surface. It is used to determine whether the heat transfer within a solid object is dominated by conduction or convection. Solids with a larger Biot number have significant temperature gradients within them and are more likely to be poor conductors, while solids with a smaller Biot number have negligible temperature gradients and are more likely to be good conductors.

Step-by-step solution

Understanding the Biot Number

The Biot number (Bi) is a dimensionless parameter that represents the ratio of the conductive heat resistance within a solid body to the convective heat transfer resistance at the surface. Mathematically, the Biot number is defined as: Bi = (h * L_c) / k where: - h is the convective heat transfer coefficient, - L_c is the characteristic length (usually the object's volume divided by the surface area), - k is the thermal conductivity of the solid. The Biot number is used to determine whether the heat transfer within a solid object is dominated by conduction or convection.

Physical Significance of Biot Number

The physical significance of the Biot number can be understood by examining the critical values it can take: 1. If Bi << 1, the solid has a small Biot number, indicating that the conductive heat resistance within the solid is much smaller than the convective heat transfer resistance at the surface. In this case, the temperature gradients within the solid are negligible, resulting in a nearly uniform temperature throughout the solid. 2. If Bi >> 1, the solid has a large Biot number, indicating that the conductive heat resistance within the solid is much larger than the convective heat transfer resistance at the surface. In this case, there are significant temperature gradients within the solid, and heat transfer is predominantly due to conduction within the solid.

Biot Number and Conductive Properties of Solids

The Biot number is more likely to be larger for poorly conducting solids compared to highly conducting ones. This is because the thermal conductivity (k) of a poorly conducting material is lower, which would result in a higher Biot number using the above equation. A higher Biot number suggests that there are significant temperature gradients within the solid, and heat transfer is dominated by conduction within the solid. Conversely, a lower Biot number would mean that heat transfer at the surface via convection is more significant in the case of highly conducting solids.