Question

In the lumped mass system of transient analysis, for calculation of Biot number, the characteristic length should be considered as the ratio of

• A. Surface area and perimeter
• B. Volume and surface area
• C. Volume and perimeter
• D. Perimeter and surface area

Hint:

In transient heat transfer problems, the Biot number is used to determine whether temperature gradients within the object are negligible. The characteristic length is calculated as the ratio of volume to surface area.

Answer 1

The Correct Option is B

Step 1: Understanding the Biot number
The Biot number (\( \text{Bi} \)) is a dimensionless quantity that measures the relative resistance to heat flow within a solid and the heat flow across its boundary. It is defined as: \[ \text{Bi} = \frac{h L_c}{k} \] Where:
\( h \) is the convective heat transfer coefficient,
\( L_c \) is the characteristic length,
\( k \) is the thermal conductivity of the material.
Step 2: Definition of characteristic length
In the lumped capacitance model, the characteristic length is typically taken as the ratio of the volume of the object to its surface area. This ratio is important because it characterizes how well the object can store heat relative to how easily it can lose heat. \[ L_c = \frac{\text{Volume}}{\text{Surface Area}} \]
Step 3: Conclusion
For the lumped mass system, the characteristic length is indeed the ratio of volume to surface area. This ratio is crucial for determining the Biot number and helps assess whether the lumped capacitance model is applicable.