Question

Lumped system analysis of transient heat conduction situations is valid when the Biot number is (a) very small (b) approximately one (c) very large (d) any real number (e) cannot say unless the Fourier number is also known

Short answer

Question: For lumped system analysis of transient heat conduction situations to be valid, the Biot number should be: Answer: (a) very small.

Step-by-step solution

Understand Lumped System Analysis

Lumped system analysis assumes that the temperature within a solid is uniform, and heat transfer occurs only at its surface. This assumption is valid when internal conduction resistance is much smaller than the surface heat transfer resistance.

Relation between Biot number and Lumped System Analysis

The Biot number (Bi) is defined as the ratio of internal conductive resistance to surface convective resistance in a solid. Mathematically, it is given by: \(Bi = \frac{h L_c}{k}\), where \(h\) is the surface heat transfer coefficient, \(L_c\) is the characteristic length of the system, and \(k\) is the thermal conductivity of the material.

Identify the Appropriate Range of Biot Number for Lumped System Analysis

For lumped system analysis to be valid, the internal conductive resistance must be much smaller than the surface convective resistance, so the Biot number should be very small. In practice, a Biot number less than 0.1 is considered to satisfy this criterion.

Choose the Correct Option based on the Appropriate Range of Biot Number

The lumped system analysis of transient heat conduction situations is valid when the Biot number is very small. Therefore, the correct option is (a) very small.