The extended Graetz problem with piecewise constant wall temperature for laminar and turbulent flows through a concentric annulus

The effect of axial heat conduction on the heat transfer is of importance if the flow Peclet number is small or if the axial extension of the heating zone is small. This paper therefore presents an analytical solution to the extended Graetz problem in a concentric annulus with piecewise constant temperature at the outer wall. The solution is based on a selfadjoint formalism which results from the decomposition of the elliptic energy equation into two first-order partial differential equations. The gained solution is exact and simple.