A Computational Study of Chaotic Flow and Heat Transfer within a Trapezoidal Cavity

Md. Mahafujur Rahaman, Sidhartha Bhowmick (), Rabindra Nath Mondal and Suvash C. Saha ()
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Md. Mahafujur Rahaman: Department of Mathematics, Jagannath University, Dhaka 1100, Bangladesh
Sidhartha Bhowmick: Department of Mathematics, Jagannath University, Dhaka 1100, Bangladesh
Rabindra Nath Mondal: Department of Mathematics, Jagannath University, Dhaka 1100, Bangladesh
Suvash C. Saha: School of Mechanical and Mechatronic Engineering, University of Technology Sydney, Ultimo 2007, Australia

Energies, 2023, vol. 16, issue 13, 1-18

Abstract: Numerical findings of natural convection flows in a trapezoidal cavity are reported in this study. This study focuses on the shift from symmetric steady to chaotic flow within the cavity. This cavity has a heated bottom wall, a cooled top wall, and adiabatic inclined sidewalls. The unsteady natural convection flows occurring within the cavity are numerically simulated using the finite volume (FV) method. The fluid used in the study is air, and the calculations are performed for different dimensionless parameters, including the Prandtl number (Pr), which is kept constant at 0.71, while varying the Rayleigh numbers (Ra) from 10 0 to 10 8 and using a fixed aspect ratio ( AR ) of 0.5. This study focuses on the effect of the Rayleigh numbers on the transition to chaos. In the transition to chaos, a number of bifurcations occur. The first primary transition is found from the steady symmetric to the steady asymmetric stage, known as a pitchfork bifurcation. The second leading transition is found from a steady asymmetric to an unsteady periodic stage, known as Hopf bifurcation. Another prominent bifurcation happens on the changeover of the unsteady flow from the periodic to the chaotic stage. The attractor bifurcates from a stable fixed point to a limit cycle for the Rayleigh numbers between 4 × 10 6 and 5 × 10 6 . A spectral analysis and the largest Lyapunov exponents are analyzed to investigate the natural convection flows during the shift from periodic to chaos. Moreover, the cavity’s heat transfers are computed for various regimes. The cavity’s flow phenomena are measured and verified.

Keywords: natural convection; trapezoidal cavity; unsteady flow; bifurcations; heat transfer (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
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