Question: For the Biot problem in a slab by expanding the sin and cos term and keeping only terms up to (lambda^{2}) the following approximate relation

For the Biot problem in a slab by expanding the sin and cos term and keeping only terms up to $\lambda^{2}$ the following approximate relation can be obtained for the eigenvalues for small Biot number:

\[\lambda=\sqrt{B i /(1+B i / 2)}\]

Verify the result.

Find the value for a Biot number of 1 , and estimate the error in the time constant if the above equation were used.

What are the corresponding expressions for a long cylinder and a sphere?

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