Question 1:

Solve the transient one-dimensional heat conduction in a spherical coordinate system. Consider a solid sphere with radius of ‘ro’ and a uniform initial temperature of ‘Ti’. It is exposed to a fluid with a temperature of ‘T∞’ and the convective heat transfer coefficient between the fluid and the surface of the sphere is ‘h’. Assuming that there is no internal heat generation and constant thermophysical properties, find how the temperature inside the sphere varies with r and t.

 How would the one-term approximation look like for a sphere?

Show your working steps clearly.