Weakly non-linear stability of stratified natural convection in a vertical cavity with lateral temperature gradient |
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| Affiliation: | 1. School of Mechanical Engineering, Yeungnam University, 280 Daehak-ro, Gyeongsan-si, Gyeongbuk, 712-749, South Korea;2. School of Mechanical Engineering, Korea University, Anam-dong, Seongbuk-gu, Seoul, 136-713, South Korea;3. Department of Mechanical Engineering, Dr. B.R. Ambedkar National Institute of Technology Jalandhar, Punjab, 144011, India;1. School of Mechanical Engineering, Yeungnam University, 280 Daehak-ro, Gyeongsan-si, Gyeongbuk, 38541, South Korea;2. Department of Mechanical Engineering, Dr B R Ambedkar National Institute of Technology, Jalandhar, Punjab, 144011, India;1. Faculty of Engineering and Built Environment, SEGi University, 47810 Petaling Jaya, Malaysia Selangor Darul Ehsan, Malaysia;2. Solar Energy Research Institute, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia;1. Solar Energy Research Institute, Universiti Kebangsaan Malaysia (UKM), 43600 Bangi, Selangor, Malaysia;2. Al-Musaib Technical College, Al-Furat Al-Awsat Technical University, 51009 Babylon, Iraq;1. High-Tech Construction Materials Center, Korea Conformity Laboratories, Seoul 08503, South Korea;2. Department of Architectural Engineering, Gachon University, 1342 Seongnamdaero, Sujeong-gu, Seongnam-si, Gyeonggi-do 13120, South Korea |
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| Abstract: | Stability of free convection is examined in a vertical cavity with a fixed lateral temperature difference on the walls, which is also heated from the bottom by a constant heat flux causing vertical stratification of the base flow. Weakly nonlinear stability equations are derived, under the assumption of fully developed flow conditions. Critical Rayleigh numbers and Landau coefficients are determined in terms of the Prandtl number and stratification parameter. It is found that critical disturbances are always two-dimensional, for stationary and oscillating instabilities as well. Alternatives are considered for the calculation of the Landau coefficient. Analysis reveals that unstationary instability is the preferred mode at the codimension point. |
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