Mathematical Methods in the Physical Sciences · Problem 7.8

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · sphere-temperature-legendre-piecewise

Problem

Find the steady-state temperature distribution inside a sphere of radius 1 when the surface temperature is:

\begin{cases} 100^\circ, & 0 < \theta < \pi/3, \\ 0^\circ, & \text{otherwise.} \end{cases}

Hint

: See Problem 9.8 of Chapter 12.