For the Biot problem in a slab by expanding the sin and cos term and keeping only terms up to λ2 the following approximate relation can be obtained for the eigenvalues for small Biot number: λ = Bi/(1 + Bi/2) Verify the result

Management Oct 27, 2020

For the Biot problem in a slab by expanding the sin and cos term and keeping only terms up to λ2 the following approximate relation can be obtained for the eigenvalues for small Biot number: λ = Bi/(1 + Bi/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?