Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-06T14:00:18.262Z Has data issue: false hasContentIssue false
  • English
  • Français

Free convective heat transfer in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel flat wall

Published online by Cambridge University Press:  12 April 2006

K. Vajravelu  and
K. S. Sastri
K. Vajravelu
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kharagpur 721302
K. S. Sastri
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kharagpur 721302 Present address: Department of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853.
Get access Rights & Permissions [Opens in a new window]

Abstract

Analyses of fluid flow over a wavy wall are of interest because of their applications to the physical problems mentioned in § 1. The authors have therefore devoted their attention to the effect of waviness of one of the walls on the flow and heat-transfer characteristics of an incompressible viscous fluid confined between two long vertical walls and set in motion by a difference in the wall temperatures. The equations governing the fluid flow and heat transfer have been solved subject to the relevant boundary conditions by assuming that the solution consists of two parts: a mean part and a disturbance or perturbed part. To obtain the perturbed part of the solution use has been made of the long-wave approximation. The mean (zeroth-order) part of the solution has been found to be in good agreement with that of Ostrach (1952) after certain modifications resulting from the different non-dimensionalizations employed by Ostrach and the present authors respectively. The perturbed part of the solution is the contribution from the waviness of the wall. The zeroth-order, the first-order and the total solution of the problem have been evaluated numerically for several sets of values of the various parameters entering the problem. Certain qualitatively interesting properties of the flow and heat transfer, along with the changes in the fluid pressure on the wavy and flat wall, are recorded in §§ 5 and 6.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 86 , Issue 2 , 29 May 1978 , pp. 365 - 383
Copyright
© 1978 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Lekoudis, S. G., Nayfeh, A. H. & Saric, W. S. 1976 Compressible boundary layers over wavy walls. Phys. Fluids 19, 514–519.Google Scholar
Lessen, M. & Gangwani, S. T. 1976 Effect of small amplitude wall waviness upon the stability of the laminar boundary layer. Phys. Fluids 19, 510–513.Google Scholar
Ostrach, S. 1952 Laminar natural convection flow and heat transfer of fluids with and without heat sources in channels with constant wall temperature. N.A.C.A. Tech. Note no. 2863.Google Scholar
Shankar, P. N. & Sinha, U. N. 1976 The Rayleigh problem for a wavy wall. J. Fluid Mech. 77, 243–256.Google Scholar