Chapter 5.2, Problem 29E

Additional Boundary-Value Problems

Temperature in a Sphere Consider two concentric spheres of radius r = a and r = b, a < b. See Figure 5.2.10. The temperature u(r) in the region between the spheres is determined from the boundary-value problem

$r\frac{d^{2}u}{d{r}^2}+2\frac{du}{dr}=0,u\left(a\right)=u_0,u\left(b\right)=u_1$,

where u₀ and u₁ are constants. Solve for u(r).

FIGURE 5.2.10 Concentric spheres in Problem 29