A combined spectral-amplitude-perturbation approach for systematic mode selection in thermal convection

Abstract

Purpose -The post-critical convective state for Rayleigh-Benard (RB) convection is studied using a nonlinear spectral-amplitude-perturbation approach in a fluid layer heated from below. The paper aims to discuss these issues. Design/methodology/approach -In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A combined amplitude-perturbation approach is developed to solve the nonlinear spectral system in the post-critical range, even far from the linear stability threshold. Also, to leading order, the Lorenz model is recovered. Findings -It is found that very small Prandtl numbers (Pro 0.1) can change the Nusselt number, when terms to O(ε 5/2 ) and higher are considered. However, to lower orders the Prandtl number does not affect the results. Variation of the Nusselt number to different orders is found to be highly consistent. Comparison with experimental results is made and a very good qualitative agreement is observed, even far from the linear threshold. Originality/value -Unlike existing nonlinear formulations for RB thermal convection, the present combined spectral-perturbation approach provides a systematic method for mode selection. The number and type of modes to be included are directly related to the post-critical Rayleigh number. The method is not limited to the weakly nonlinear range.

Role of heatlines on thermal management during Rayleigh-Bénard heating within enclosures with concave/convex horizontal walls

“…The Bénard-type flow during natural convection with heat transfer in porous media was considered for the study and the Nusselt-Rayleigh correlation was determined for various Rayleigh numbers by Canovas et al (2015). Niknami et al (2015) investigated the post-critical convective state for Rayleigh-Bénard convection using a nonlinear spectral-amplitude-perturbation approach for a fluid layer heated from below.…”

“…Conventionally, the rectangular cavities with the flat isothermal walls were considered by the researchers for the study of Rayleigh-Bénard convection (Ramaswamy, 1993;Pallares et al, 1999Pallares et al, , 2002Davis and Carey, 2000;Crunkleton and Anderson, 2006;Kao and Yang, 2007;Turan et al, 2012;Aghighi et al, 2015;Canovas et al, 2015;Niknami et al, 2015). The slight perturbation in the aspect ratio, inclination angle and other geometrical parameter may result in the drastic change in the distribution of the fluid and heat flow features during Rayleigh-Bénard convection.…”

Heatlines visualization of convective heat flow during differential heating of porous enclosures with concave/convex side walls

“…In the past few decades, an enormous expansion in the research on convection heat transfer is observed due to versatile natural, industrial and engineering applications such as solidification (Damronglerd et al , 2012; Stapor, 2016), chemical reactions (Chamkha et al , 2012), melting (Wu and Lacroix, 1992, 1993; Lacroix and Benmadda, 1998; Kousksou et al , 2014), cooling (Shuja et al , 2010), thermo-bioconvection (Kuznetsov, 2013) and pool boiling (Elrais et al , 1992). The knowledge of heat and flow characteristics during natural convection within various enclosed cavities is important, and a number of works on natural convection within enclosed cavities for the fluid media via different computational techniques are found in the literature (Turk and Tezer-Sezgin, 2013; Rahman et al , 2014; Salama et al , 2014; Aghighi et al , 2015; Canovas et al , 2015; Miroshnichenko and Sheremet, 2015; Niknami et al , 2015; Yapici and Obut, 2015; Noghrehabadi et al , 2015). In addition to the clear fluid media, the analysis of convection within porous enclosures has been a self-sustained area of research in the heat transfer community and the extensive discussions on natural convection in porous media with the mathematical aspects are documented in various books (Holzbecher, 1998; Bejan, 2013; Ingham and Pop, 1998; Vafai and Hadim, 2000; Pop and Ingham, 2001; Nield and Bejan, 2016).…”