Analytical solution of buoyancy-driven flow and heat transfer in a vertical channel with spatially periodic boundary conditions

Hasan Gunes*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

In this study, we derive analytical expressions describing the variation of field variables in steady, 2-D and 3-D natural convection in a vertical channel with discrete in-space, flush-mounted heat sources. The expressions are valid for sufficiently small Gras of numbers. The solution are governed by the following dimensionless parameters: aspect ratios defining the geometry of the problem, Prandtl number, Grashof number and dimensionless channel reference temperature. Test case solutions are obtained numerically to assess the accuracy of the derived expressions. For small values Gr, the derived expressions are in excellent agreement with the numerical solutions in the entire computational domain. Analytical expressions for the net volume flow rate through the channel and Nusselt number variation are also given.

Original languageEnglish
Pages (from-to)33-45
Number of pages13
JournalHeat and Mass Transfer
Volume40
Issue number1-2
DOIs
Publication statusPublished - Dec 2003

Keywords

  • Analytical methods
  • Buoyancy-driven flow
  • Natural convection
  • Perturbation methods
  • Three-dimensional flow

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