Infinite body with a spherical void, steady 1-D.

RS10 Infinite body surrounding a spherical void, a $\leq$ r < $\infty$, with G = 0 (Dirichlet) at r = a.

4$$\pi$$G_RS10(r $$\left\vert\vphantom{ \,r^{\prime }}\right.$$ r^$\prime$$$\left.\vphantom{ \,r^{\prime }}\right.$$) = $$\left\{\vphantom{ \begin{array}{cc} (1-a/r)/r^{\prime } & \tex... ...me } \\ (1-a/r^{\prime })/r & \text{for }r>r^{\prime } \end{array} }\right.$$$$\begin{array}{cc} (1-a/r)/r^{\prime } & \text{for }r<r^{\prime } \\ (1-a/r^{\prime })/r & \text{for }r>r^{\prime } \end{array}$$ $$\left.\vphantom{ \begin{array}{cc} (1-a/r)/r^{\prime } & \text... ...me } \\ (1-a/r^{\prime })/r & \text{for }r>r^{\prime } \end{array} }\right.$$

RS20 Infinite body surrounding a spherical void, a $\leq$ r < $\infty$, with $\partial$G/$\partial$r = 0 (Neumann) at r = a.

4$$\pi$$G_RS20(r $$\left\vert\vphantom{ \,r^{\prime }}\right.$$ r^$\prime$$$\left.\vphantom{ \,r^{\prime }}\right.$$) = $$\left\{\vphantom{ \begin{array}{cc} -1/r^{\prime } & \text{for }r<r^{\prime } \\ -1/r & \text{for }r>r^{\prime } \end{array} }\right.$$$$\begin{array}{cc} -1/r^{\prime } & \text{for }r<r^{\prime } \\ -1/r & \text{for }r>r^{\prime } \end{array}$$ $$\left.\vphantom{ \begin{array}{cc} -1/r^{\prime } & \text{for }r<r^{\prime } \\ -1/r & \text{for }r>r^{\prime } \end{array} }\right.$$

RS30 Infinite body surrounding a spherical void, `a < r < $\infty$, with - k$\partial$G/$\partial$r + h₁G = 0 (convection) at r = a. Note B₁ = h₁a/k.

4$$\pi$$G_RS30(r $$\left\vert\vphantom{ \,r^{\prime }}\right.$$ r^$\prime$$$\left.\vphantom{ \,r^{\prime }}\right.$$) = $$\left\{\vphantom{ \begin{array}{cc} 1/r^{\prime }-B_{1}a/[(1+B... ..._{1}a/[(1+B_{1})rr^{\prime }] & \text{for }r>r^{\prime } \end{array} }\right.$$$$\begin{array}{cc} 1/r^{\prime }-B_{1}a/[(1+B_{1})rr^{\prime }] &... ...\\ 1/r-B_{1}a/[(1+B_{1})rr^{\prime }] & \text{for }r>r^{\prime } \end{array}$$ $$\left.\vphantom{ \begin{array}{cc} 1/r^{\prime }-B_{1}a/[(1+B_... ..._{1}a/[(1+B_{1})rr^{\prime }] & \text{for }r>r^{\prime } \end{array} }\right.$$