A compact closed-form Nusselt formula for laminar longitudinal flow between rectangular/square arrays of parallel cylinders with unequal row temperatures

• A compact closed-form easy-to-use formula for Nusselt number estimation.
• Longitudinal flow between rectangular array of parallel cylinders was modeled.
• Cylinders temperatures can vary from one row to another.
• The present model can be used for almost any porosity of parallel cylinders.

Axial flows over cylinders are frequently encountered in practice, e.g. in tubular heat exchangers and reactors. Using the Integral method, closed-form relationships are developed for heat transfer coefficients or Nusselt number inside a fluid flowing axially between a rectangular/square array of parallel cylinders with unequal temperatures. The model considers the temperature variations of cylinders from one row to another while assuming the same temperature for all the cylinders in each row. The model could well capture several sets of numerical data, which can be regarded as excellent in light of the simplicity and comprehensiveness of the model. The compact and accurate formulae developed in this work can be readily employed, and also implemented into any software or tools, for the estimation of Nu in tubular heat exchangers, fins systems, porous media and composite manufacturing.

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