In a two-dimensional cylindrical configuration, the radial \((\Delta r)\) and angular \((\Delta \phi)\) spacings of the nodes are uniform. The boundary at \(r=r_{i}\) is of uniform temperature \(T_{i}\). The boundaries in the radial direction are adiabatic (insulated) and exposed to surface convection \(\left(T_{\infty}, h\right)\), as illustrated. Derive the finite-difference equations for (i) node 2, (ii) node 3 , and (iii) node 1 .

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5 Th 2 Uniform temperature surface, T +