Chapter 4, Problem 1CP

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?

To determine

To discuss: The Physical significance of Biot number and define whether its value is larger for highly conducting solids or poorly conducting solids.

Explanation of Solution

The Biot number is defined as the ratio of internal conduction resistance to the external convection resistance of the body.

  $\begin{array}{l}\text{Bi =}\frac{\text{Internal conduction resistance}}{\text{External convection resistance}}\\ Bi=\frac{\raisebox{1ex}{$L_C$}\!\left/ \!\raisebox{-1ex}{$kA$}\right.}{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$hA$}\right.}=\frac{h{L}_C}{k}\\ Where:-\\ L_C\to characteristiclength\\ k\to Thermalconductivityofthesystem\\ h\to Convectionheattransfercoefficient.\end{array}$

The Biot number is used for the analysis of lumped heat capacitive systems, in which thermal internal conduction resistance is much lesser than the external convection resistance. And the condition for its applicability is Bi ? 0.1.

From the formula of Biot number, it can be defined that its value is inversely proportional to the thermal conductivity of the body.

  $Bi\propto \frac{1}{k}$

Thus, with a larger value of k, the Biot number will be lesser. Hence, due to lower thermal conductivity, the value of the Biot number will be larger for poorly conducting solids. Also, the poorly conducting materials possess high conduction resistance, resulting in the larger value of the Biot number.