The thermal entry flow with fully developed velocity profile

4 The thermal entry flow with fully developed velocity profile 

3 Convective heat and mass transfer. Single phase flow 

We presume negligible axial heat conduction, constant wall temperature i90 and a constant temperature i9a of the fluid at the inlet of the tube. All material properties are temperature independent. 

This problem was first dealt with by Graetz (1850-1891) in 1883 [3.27], later in 1910 by Nusselt (1882-1957) [3.28] and by many other authors. It is also known as a Graetz or Graetz-Nusselt problem. It is described by the energy equation (3.232), in which, according to the suppositions made, the radial velocity component disappears, wr = 0, and the axial velocity is that of a Hagen-Poiseuille flow (3.223). With that the energy equation becomes 

The temperature profile should satisfy the following boundary conditions 

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