# Normal mode analysis of the fully developed free convection flow in a vertical slot with open to capped ends

- 76 Downloads
- 7 Citations

## Abstract

The fully developed free convection flow in a differentially heated vertical slot with open to capped ends investigated recently by Bühler (Heat Mass Transf 39:631–638, 2003) and Weidman (Heat Mass Transf Online First, February 2006) is revisited in this paper. A new method of solution of the corresponding fourth order boundary value problem, based on its reduction to “normal modes” by a complex matrix similarity transformation is presented. As a byproduct of the method, some invariant relationships involving the heat flux and the shear stress in the flow could be found.

## Keywords

Normal Mode Wall Heat Flux Free Convection Flow Invariant Relationship Vertical Slot## Notes

### Acknowledgments

The author is indebted to Prof. P. D. Weidman of University of Colorado at Boulder for prolific discussions during the preparation of this paper.

## References

- 1.Bühler K (2003) Special solutions of Boussinesq-equations for free convection flows in a vertical gap. Heat Mass Transf 39:631–638CrossRefGoogle Scholar
- 2.Weidman PD (2006) Convection regime flow in a vertical slot: continuum solutions from capped to open ends. Heat Mass Transf. Online first, February 2006Google Scholar