Theory and Application
The thermodynamic behaviour of concentric tube heat exchangers can be described by both empirical and numerical analysis. The simplest of these involve the use of correlations to model heat transfer; however the accuracy of these predictions varies depending on the design. For turbulent, non-viscous fluids the Dittus-Boelter Equation can be used to determine the heat transfer coefficient for both the inner and outer streams; given their diameters and velocities (or flow rates). For conditions where thermal properties vary significantly, such as for large temperature differences, the Seider-Tate Correlation is used. This model takes into consideration the differences between bulk and wall viscosities. Both correlations utilize the Nusselt number and are only valid when the Reynolds number is greater than 10,000. While Dittus-Boelter requires the Prandtl number to be between 0.7 and 160, Seider-Tate applies to values between 0.7 and 16,700.
For calculations involving the outer stream, the equivalent diameter (or mean hydraulic radius) is used in place of the geometric diameter, as the cross-sectional area of the annulus is not circular. Equivalent diameters are also used for irregular shapes such as rectangular and triangular ducts. For concentric tubes, this relationship simplifies to the difference between the diameters of the shell and the outer surface of the inner tube.
After the heat transfer coefficients (h_{i} and h_{o}) are determined, and knowing the resistance due to fouling and thermal conductivity of the boundary material (k_{w}), the Overall Heat Transfer coefficient (U_{o}) can be calculated.
The length of heat exchanger required can then be expressed as a function of the rate of heat transfer:
Where A is the surface area available for heat transfer and ∆T is the log mean temperature difference. From these results, the NTU method can be performed to calculate the heat exchanger’s effectiveness.
where
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