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Determination of the Number of Tube Rows to Obtain Closure for Volume Averaging Theory Based Model of Fin-and-Tube Heat Exchangers

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Modelling of fin-and-tube heat exchangers based on Volume Averaging Theory (VAT) requires proper closure of the VAT based governing equations. Closure can be obtained from reasonable lower scale solutions of a CFD code, which means the tube row number chosen should be large enough so that the closure can be evaluated for a representative elementary volume (REV) that is not affected by the entrance or re-circulation at the outlet of the fin gap. To determine the number of tube rows, three-dimensional numerical simulations for plate fin-and-tube heat exchangers were performed, with the Reynolds number varying from 500 to 6000 and the number of tube rows varying from 1 to 9. A clear perspective of the variations of both overall and local fiction factor and Nusselt number as the tube row number increases are presented. These variation trends are explained from the view point of the Field Synergy Principle (FSP). Our investigation shows that 4+1+1 tube rows is the minimum number to get reasonable lower scale solutions. A computational domain including 5+2+2 tube rows is recommended, so that the closure formulas for drag resistance coefficient and heat transfer coefficient could be evaluated for the sixth and seventh elementary volumes to close the VAT based model.

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