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

Gunes H.

HEAT AND MASS TRANSFER, vol.40, pp.33-45, 2003 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40
  • Publication Date: 2003
  • Doi Number: 10.1007/s00231-003-0417-0
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.33-45
  • Istanbul Technical University Affiliated: No


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 Grasof 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.