Correlations/Excel Spreadsheets for Flow across a Circular Cylinder or a Bank of Tubes
For flow across a circular cylinder or across a bank of tubes, the following definitions apply to the Reynolds number and Nusselt number:
Reλ = λVρ/μ, Nuλ = hλ/k, and λ = πD/2, where:
D = cylinder diameter; V = free stream fluid velocity; and all fluid properties are at the bulk mean fluid temperature [ (Tin + Tout)/2 ].
Following is a correlation (Gnielinski, Ref #5) for flow past a single circular cylinder:
Nuλo = 0.3 + ( (Nuλ lam)2 + (Nuλ turb)2 )1/2, where
Nuλ lam = 0.664(Reλ)1/2(Pr)1/3, and Nuλ turb = (0.037 Reλ0.8 Pr)/[ 1 + 2.44 Reλ-0.1 (Pr2/3 - 1) ]
This correlation is valid for 10 < Reλ < 107 and 0.6 < Pr < 1000
Flow past a bank of tubes approximates the flow pattern in the shell side of a shell and tube heat exchanger with baffles. For flow past a bank of tubes, the correlations above are used with some modification, but additional definitions are needed as follows:
Transverse pitch ratio: a = SQ/D
Longitudinal pitch ratio: b = SL/D (SQ and SL are shown in the diagrams at the right.)
Void ratio: ψ = 1 - π/(4a), for b > 1 ; ψ = 1 - π/(4ab), for b < 1
The Nusselt number for a tube bank is then: Nuo bank = fA Nuλo with Nuλo calculated with the equation for flow past a single cylinder given above, with Reλ replaced by Reψλ = λVρ/ψμ (Gnielinski, Ref #5).
The equations for fA for in-line and staggered tube banks are included in the diagrams at the right.
The spreadsheet template shown in the two images at the left above is set up to calculate Nuλo, ho, and h for flow past a single cylinder and flow past a bank of tubes. The Excel formulas in this spreadsheet use the correlations and equations given in this section.
To download one of these Excel spreadsheets (U.S. units or S.I. units) click one the links below:
Click here to download this Excel spreadsheet in U.S. units.
Click here to download this Excel spreadsheet in S.I. units.