Question

The characteristic length (\(\text{L}_{\text{c}}\)) for the calculation of Biot number (\(\text{Bi}\)) for a sphere of radius 'R' subjected to Newtonian cooling is

• A. R
• B. \(\frac{\text{R}}{2}\)
• C. \(\frac{\text{R}}{3}\)
• D. 3R

Hint:

Standard Characteristic Lengths (\(L_c = V/A_s\)) to memorize: - Cube (side length $a$): \(L_c = \frac{a^3}{6a^2} = \frac{a}{6}\) - Long Solid Cylinder (radius $R$): \(L_c = \frac{\pi R^2 L}{2\pi R L} = \frac{R}{2}\) - Solid Sphere (radius $R$): \(L_c = \frac{\frac{4}{3}\pi R^3}{4\pi R^2} = \frac{R}{3}\)

Answer 1

The Correct Option is C