Advertisement

A Numerical Investigation of Mixed Convection on a Horizontal Semi-Infinite Plate

  • Valod Noshadi
  • Wilhelm Schneider

Abstract

The laminar mixed convection flow above a semi-infinite horizontal plate is studied for large Reynolds and Grashof numbers. To permit similarity solutions of the boundary-layer equations, the plate temperature, T w , is assumed to differ from the free-stream temperature, T , according to the relation (T T w ) ∝ x −1/2, where x is the distance from the leading edge. This corresponds to a plate that is strongly cooled near the leading edge while thermally insulated everywhere else. There are two branches of similarity solutions of the boundary-layer equations if the non-dimensional buoyancy parameter is larger than a critical value, which is negative and depends on the Prandtl number. Non-similar solutions connecting the self-similar solutions have also been found analytically. In the present work a finite-element package is used to solve the full NavierStokes and energy equations. The numerical results resemble the analysis in a certain regime of the buoyancy parameter. In other regimes, however, neither the self-similar solutions nor the connecting solutions are found numerically.

Keywords

Mixed convection numerical solutions Navier-Stokes equations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Afzal, N. & Hussain, T. 1984 Mixed convection over a horizontal plate. ASME J. Heat Transfer 106, 240–241.CrossRefGoogle Scholar
  2. De Hoog, F. R., Laminger, B. & Weiss, R. 1984 A numerical study of similarity solutions for combined forced and free convection. Acta Mech. 51, 139–149.CrossRefzbMATHGoogle Scholar
  3. Merkin, J. H. & Ingham, D. B. 1987 Mixed convection similarity solutions on a horizontal surface. J. Appl. Math. Phys. (ZAMP) 38, 102–116.CrossRefzbMATHGoogle Scholar
  4. Schneider, W. 1979 A similarity solution for combined forced and free convection flow over a horizontal plate. Int. J. Heat Mass Transfer 22, 1401–1406.CrossRefzbMATHGoogle Scholar
  5. Schneider, W. 1995 Laminar mixed convection flows on horizontal surfaces. Proc. 3rd Caribbean Cong. on Fluid Dynamics. Vol. II, Simon Bolivar University, Caracas.Google Scholar
  6. Steinrück, H. 1995 Mixed convection over a horizontal plate: self-similar and connecting boundary-layer flows. Fluid Dyn. Res. 15, 113–127.CrossRefzbMATHGoogle Scholar
  7. Steinrück, H. 1997 Recent investigations on buoyant boundary layer flows over horizontal surfaces. Submitted to Z. angew. Math. Mech. (ZAMM).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Valod Noshadi
    • 1
  • Wilhelm Schneider
    • 1
  1. 1.Institute of Fluid Dynamics and Heat TransferTechnical University of ViennaViennaAustria

Personalised recommendations