Numerical study of buoyancy‐driven transitional flow in a square cavity with partially heated and cooled vertical walls
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 21 September 2010
Abstract
Purpose
The purpose of this paper is to numerically study transient natural convective flow in a square cavity with partially heated and cooled vertical walls, thermally insulated top wall and linearly heated bottom wall.
Design/methodology/approach
The governing equations of motion are non‐dimensionalized and reformulated using stream function‐vorticity approach. Alternating direction implicit finite difference scheme is used to solve the coupled equations.
Findings
The transient results obtained for different values of Grashof number (Gr) and fixed Prandtl number Pr = 0.733 are presented in the form of isotherms, streamlines, bifurcation diagram and time series. The transition from steady to oscillatory motions is analyzed in detail with respect to Gr. The flow is observed to be steady up to Gr ≈ 2 × 104. A time‐periodic unsteady solution first appears at Gr = 20,900 and the amplitude of the fluctuation grows as Gr is increased.
Research limitations/implications
The study is limited to laminar flow in a square cavity. Further extension of this work could include the influence of various choices of Prandtl number and the effect of aspect ratio. Buoyancy‐driven convection in a sealed cavity with differentially heated walls is a prototype of many industrial applications such as energy‐efficient design of buildings and rooms, convective heat transfer associated with boilers, etc.
Originality/value
The paper presents an original computer program written in FORTRAN to solve the partial differential equations.
Keywords
Citation
Navamani, R. and Murugan, N. (2010), "Numerical study of buoyancy‐driven transitional flow in a square cavity with partially heated and cooled vertical walls", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 20 No. 7, pp. 744-758. https://doi.org/10.1108/09615531011065548
Publisher
:Emerald Group Publishing Limited
Copyright © 2010, Emerald Group Publishing Limited