Q$3.$ Given a spherical container with an inner radius $\backslash ($ r$\_\{1\}\backslash ),$ outer radius $\backslash ($ r$\_\{2\}\backslash ),$ and thermal conductivity k $,$ state the boundary condition at the inner surface for steady one$-$dimensional heat conduction under the following scenarios:

a$)$ The inner surface is maintained at a constant temperature $\backslash (\backslash$mathrm$\{$T$\}\_\{1\}\backslash ).$

b$)$ The inner surface is subjected to a constant heat flux $\backslash (\backslash$mathrm$\{$q$\}\_\{1\}\backslash ).$

c$)$ The outer surface is insulated $($no heat transfer$).$

d$)$ The outer surface experiences convective heat transfer with a surrounding fluid at temperature $\backslash (\backslash$mathrm$\{$T$\}\_\{\backslash$infty$\}\backslash )$ and a convection coefficient $\backslash (\backslash$mathrm$\{$h$\}\_\{0\}\backslash ).$