Heat transfer 1D

Consider the equation \[ -(r^{n-1}cT')'=\dot q(r),\qquad T(r_l) = T_l, \ T(r_r) = T_r, \ r\in [r_l,r_r], n=1,2,3\] to describe the (static) heat transfer (static) in

• a bar (1d, \(n=1\))
• a cross-section of a tube (2d, \(n=1\))
• a spherical shell (3d, \(n=1\))

• move around the points \(x_r,x_l\)
• change the boundary condition \(T_r, T_l\)
• change the discretization \(N\)
• change the considered space dimension \(n=1,2,3\)
• change the constant heat source/sink in the interval \((x_l,x_r)\)