Heat transfer coefficients in thermally fully developed, laminar flow

3 Heat transfer coefficients in thermally fully developed, laminar flow 

In the following we will show how heat transfer coefficients are calculated for thermally fully developed, laminar flow. In a corresponding manner the mass transfer coefficients with regard to fully developed concentration profile can be obtained. In order to show this fundamentally we will consider tubular flow. The explanations can easily be transferred to cover other types of channel flow. 

When we neglect the dissipation and the thermal conduction in the direction x of flow and under the assumption that the properties of the materials are temperature independent, the energy balance in cylindrical coordinates x,r is 

In fully developed flow we have wr = 0, so that the second term on the left hand side drops out. The velocity profile wx r) is given by the Hagen-Poiseuille parabola (3.223). 

Separating the variables gives, after integration, the general solution of the differential equation 

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