Natural convection in differentially heated enclosures subjected to variable temperature boundaries

Abstract

Purpose Natural convection in differentially heated enclosures has been extensively investigated due to its importance in many industrial applications and has been used as a benchmark solution for testing numerical schemes. However, most of the published works considered uniform heating and cooling of the vertical boundaries. This paper aims to examine non-uniform heating and cooling of the mentioned boundaries. The mentioned case is very common in many electronic cooling devices, thermal storage systems, energy managements in buildings, material processing, etc. Design/methodology/approach Four cases are considered, the left-hand wall’s temperature linearly decreases along the wall, while the right-hand wall’s temperature is kept at a constant, cold temperature. In the second case, the left-hand wall’s temperature linearly increases along the wall, while the right-hand wall’s temperature is kept a constant, cold temperature. The third case, the left-hand wall’s temperature linearly decreases along the wall, while the right-hand wall’s temperature linearly increases along the wall. In the fourth case, the left-hand and the right-hand walls’ temperatures decrease along the wall, symmetry condition. Hence, four scenarios of natural convection in enclosures were covered. Findings It has been found that the average Nusselt number of the mentioned cases is less than the average Nusselt number of the uniformly heated and cooled enclosure, which reflects the physics of the problem. The work quantifies the deficiency in the rate of the heat transfer. Interestingly one of the mentioned cases showed two counter-rotating horizontal circulations. Such a flow structure can be considered for passively, highly controlled mechanism for species mixing processes application. Originality/value Previous works assumed that the vertical boundary is subjected to a constant temperature or to a sinusoidal varying temperature. The subject of the work is to examine the effect of non-uniformly heating and/or cooling vertical boundaries on the rate of heat transfer and flow structure for natural convection in a square enclosure. The temperature either linearly increases or decreases along the vertical coordinate at the boundary. Four scenarios are explored.

The Influence of linear Heating on Free Convection in a Cylindrical Enclosure

“…Moreover, the obstacle, characterized by high thermal conductivity, led to a reduction in heat exchanges with the lower wall and an increase in heat exchanges with the side walls. In their study [14], inspected heat transfer induced by free convection in a square differentially-heated cavity, where variations in the temperature of the left wall either increased or decreased linearly along the wall, along with similar variations in the right wall temperature. Particularly noteworthy is the outcome observed when the right wall's temperature rises linearly and the left wall's temperature diminishes linearly, resulting in the formation of two flow cells within the enclosure, one at the bottom and the other at the top.…”

Natural convection and entropy generation in square and skew cavities due to large temperature differences: A Gay–Lussac‐type vorticity stream‐function approach

“…The simplicity of ignoring density variations except in buoyancy term and treating the flow field as incompressible while its existence is due to density variations makes the classic Boussinesq approximation popular. [2][3][4][5][6][7][8][9][10][11][12][13][14][15] Another advantage of the Boussinesq approximation that justifies its application for a broad range of the natural convection simulations is its simple implementation and accuracy of performance for problems having small temperature differences. The Boussinesq approximation, accompanied by a linear relation between density and temperature via a volumetric thermal expansion coefficient, is the basis of many numerical simulations of natural convection benchmark problems such as rectangular, 2-7 triangular [8][9][10][11] and annular [12][13][14] enclosed geometries.…”

Can the shape influence entropy generation for thermal convection of identical fluid mass with identical heating? A finite element introspection

“…Natural convection occurs when the fluid motion is induced by the density variations based on the temperature difference within the fluid (also termed as buoyancy-driven convection). Applications of natural convection involve material processing (Mohamad et al , 2019), phase change materials (Ben Salah and Ben Hamida, 2019), cooling of electronic equipment (Bairi et al , 2019), heat exchangers (KhakRah et al , 2019) and nanofluids (Mahmoudi et al , 2013; Cho et al , 2013; Selimefendigil et al , 2016; Bondareva et al , 2017; Mansour et al , 2017; Shirvan et al , 2017; Sabour et al , 2017; Sheremet et al , 2017; Alsabery et al , 2018; Armaghani et al , 2019a, 2019b; Biswal et al , 2019; Cimpean and Pop, 2019; Dogonchi et al , 2019; Dutta et al , 2019; Ghalambaz et al , 2019; Gireesha and Sindhu, 2019; Hajiyan et al , 2019; Ishak et al , 2019; Izadi et al , 2019; Khan et al , 2019a; Mohebbi et al , 2019; Rashidi et al , 2019; Shashikumar et al , 2019; Shahsavar et al , 2019; Sreedevi et al , 2019; Tayebi and Chamkha, 2019). Das et al (2017) highlight the importance of natural convection associated with the thermal performance of various process applications.…”