Numerical study of buoyancy‐driven transitional flow in a square cavity with partially heated and cooled vertical walls

Abstract

PurposeThe 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/approachThe 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.FindingsThe 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/implicationsThe 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/valueThe paper presents an original computer program written in FORTRAN to solve the partial differential equations.