Solid sphere,steady 1-D.

RS01 Solid sphere, 0 $\leq$ r $\leq$ b, with G < $\infty$ (natural boundary) at r = 0, and G = 0 (Dirichlet) at r = b.

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

RS02 Solid sphere, 0 $\leq$ r $\leq$ b, with G < $\infty$ (natural boundary) at r = 0, and $\partial$G/$\partial$r = 0 (Neumann) at r = b . Note that this geometry requires a pseudo GF, denoted H. The temperature solution found from a pseudo GF requires that the total volumetric heat flow is equal to the boundary heat flow, and the spatial average temperature in the body must be supplied as a known condition.

4$$\pi$$G_RS20(r $$\left\vert\vphantom{ \,r^{\prime }}\right.$$ r^$\prime$$$\left.\vphantom{ \,r^{\prime }}\right.$$) = $$\left\{\vphantom{ \begin{array}{cc} 1/r^{\prime }+[r^{2}+(r^{\... ...}+(r^{\prime })^{2}]/(2b^{3}) & \text{for }r>r^{\prime } \end{array} }\right.$$$$\begin{array}{cc} 1/r^{\prime }+[r^{2}+(r^{\prime })^{2}]/(2b^{3... ... 1/r+[r^{2}+(r^{\prime })^{2}]/(2b^{3}) & \text{for }r>r^{\prime } \end{array}$$ $$\left.\vphantom{ \begin{array}{cc} 1/r^{\prime }+[r^{2}+(r^{\p... ...}+(r^{\prime })^{2}]/(2b^{3}) & \text{for }r>r^{\prime } \end{array} }\right.$$

RS03 Solid sphere, 0 $\leq$ r $\leq$ b, with G < $\infty$ (natural boundary) at r = 0 and k$\partial$G/$\partial$r + h₂G = 0 (convection) at r = b. Note B₂ = h₂b/k.

4$$\pi$$G_RS03(r $$\left\vert\vphantom{ \,r^{\prime }}\right.$$ r^$\prime$$$\left.\vphantom{ \,r^{\prime }}\right.$$) = $$\left\{\vphantom{ \begin{array}{cc} 1/r^{\prime }+(1/B_{1}-1)/... ...rime } \\ 1/r+(1/B_{1}-1)/b & \text{for }r>r^{\prime } \end{array} }\right.$$$$\begin{array}{cc} 1/r^{\prime }+(1/B_{1}-1)/b & \text{for }r<r^{\prime } \\ 1/r+(1/B_{1}-1)/b & \text{for }r>r^{\prime } \end{array}$$ $$\left.\vphantom{ \begin{array}{cc} 1/r^{\prime }+(1/B_{1}-1)/b... ...rime } \\ 1/r+(1/B_{1}-1)/b & \text{for }r>r^{\prime } \end{array} }\right.$$