Solid cylinder, steady 1-D.

R01 Solid cylinder, 0 $\leq$ r $\leq$ b, with G < $\infty$ (natural boundary) at r = 0, and G = 0 (Dirichlet) at r = b.

2$$\pi$$G_R01(r $$\left\vert\vphantom{ \,r^{\prime }}\right.$$ r^$\prime$$$\left.\vphantom{ \,r^{\prime }}\right.$$) = $$\left\{\vphantom{ \begin{array}{cc} ln(b/r^{\prime }) & \text{for }r<r^{\prime } \\ ln(b/r) & \text{for }r>r^{\prime } \end{array} }\right.$$$$\begin{array}{cc} ln(b/r^{\prime }) & \text{for }r<r^{\prime } \\ ln(b/r) & \text{for }r>r^{\prime } \end{array}$$ $$\left.\vphantom{ \begin{array}{cc} ln(b/r^{\prime }) & \text{for }r<r^{\prime } \\ ln(b/r) & \text{for }r>r^{\prime } \end{array} }\right.$$

R02 Solid cylinder, 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.

2$$\pi$$H_R02(r $$\left\vert\vphantom{ \,r^{\prime }}\right.$$ r^$\prime$$$\left.\vphantom{ \,r^{\prime }}\right.$$) = $$\left\{\vphantom{ \begin{array}{cc} \left( r^{2}+(r^{\prime })... ...\right) /(2b^{2})+\ln (b/r) & \text{for }% r>r^{\prime } \end{array} }\right.$$$$\begin{array}{cc} \left( r^{2}+(r^{\prime })^{2}\right) /(2b^{2}... ...ime })^{2}\right) /(2b^{2})+\ln (b/r) & \text{for }% r>r^{\prime } \end{array}$$ $$\left.\vphantom{ \begin{array}{cc} \left( r^{2}+(r^{\prime })^... ...\right) /(2b^{2})+\ln (b/r) & \text{for }% r>r^{\prime } \end{array} }\right.$$

R03 Solid cylinder, 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.

2$$\pi$$G_R03(r $$\left\vert\vphantom{ \,r^{\prime }}\right.$$ r^$\prime$$$\left.\vphantom{ \,r^{\prime }}\right.$$) = $$\left\{\vphantom{ \begin{array}{cc} \ln (b/r^{\prime })+1/B_{2... ...rime } \\ \ln (b/r)+1/B_{2} & \text{for }r>r^{\prime } \end{array} }\right.$$$$\begin{array}{cc} \ln (b/r^{\prime })+1/B_{2} & \text{for }r<r^{\prime } \\ \ln (b/r)+1/B_{2} & \text{for }r>r^{\prime } \end{array}$$ $$\left.\vphantom{ \begin{array}{cc} \ln (b/r^{\prime })+1/B_{2}... ...rime } \\ \ln (b/r)+1/B_{2} & \text{for }r>r^{\prime } \end{array} }\right.$$