Tube with Constant Temperature of the Wall

Statement of the problem. Let us consider laminar steady-state fluid flow in a circular tube of radius a with Poiseuille velocity profile (see Section 1.5). We introduce cylindrical coordinates 1Z, Z with the Z-axis in the direction of flow. We assume that for Z 0 the temperature on the wall is equal to the constant T2. In the entry area Z 0, the temperature on the wall is also constant but takes another value T.  

The convective heat transfer in a tube is described by the equation 

The following dimensionless variables have been used  

Mass Transfer in Films, Tubes, and Boundary Layers 

The corresponding dimensionless local jr and total It heat fluxes have the form [269] 

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