Double-diffusive buoyancy induced flow in a triangular cavity with corrugated bottom wall: Effects of geometrical parameters

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Abstract

A numerical study has been carried out to present flow field, temperature and concentration distribution in a triangular enclosed space with corrugated base surface using finite element method. The cavity consists of an absorber plate and two inclined glass covers. At the base corrugated wall high concentrations and temperature are considered. The study was done for various wave lengths (0.1, ≤, λ, ≤, 1.0), thermal Rayleigh number (103  Ra  105) and Prandtl number (0.071, ≤, Pr, ≤, 7). Isotherms, iso-concentration, streamlines, overall Nusselt and Sherwood numbers are obtained for the aforesaid parameters. It is found that wave length plays a dominant role on flow strength for any Rayleigh numbers. Variation of Prandtl number becomes significant for greater values of Rayleigh numbers and multiple cells are formed at the lowest value of Prandtl number.

Introduction

Buoyancy induced heat and mass transfer occurred inside the enclosure for many engineering applications such as solar collectors, heating and cooling of building, fire in buildings, natural ventilation, heat exhangers and cooling of electronical equipments. These applications are reviewed by many authors in the literature [1], [2], [3], [4].

Geometry of the enclosure is the most effective parameter for natural convection studies in enclosure. Thus, sloping surface shows completely different phenomena. In this context, heat and mass transfer inside the triangular cavities are very important for cooling of electronic equipments, attic-shaped space as given by Saha and Khan [5], and desalination [6], [7]. Solar energy is a common phenomenon in many engineering and technological problems. It is required to transfer solar energy into a conventional energy. Building energy system mostly depends on solar energy. In the solar energy system, the main piece of solar collectors is rectangular, triangular or trapezoidal etc. among the different shapes of solar collectors.

Flack [8] and Poulikakos and Bejan [9], [10] are the pioneers of study of the natural convection in a triangular cavity. Then, Salmun [11] investigated the convection patterns in triangular domain and Asan and Namli [12], [13] modeled the winter and summer day boundary conditions inside a roof of triangular cross-section. Varol et al. [14] solved the natural convection problem with flush mounted heater on one wall of a triangular cavity. They showed the effects of location of heater on thermal and flow field. Then, entropy generation due to free convection inside the porous isosceles triangle at the different positions of the non-uniformly heater is studied by Varol et al. [15]. Other studies on natural convection in triangular enclosures can be found in the literature as Varol et al. [16], Kent [17], Ridouane and Campo [18], Ridouane et al. [19], Basak et al. [20] and Roy et al. [21]. Other related studies are also presented in [22], [23], [24], [25], [26], [27], [28].

Double-diffusive natural convection occurs due to the thermal and mass diffusion buoyancy effects between cover and absorber within the solar collector. It is required to progress the performance of the solar collector with a competitive price for its practical importance. In this case numerical study is easy and economical over the experimental investigation for various important parameters. Numerical analysis is also useful to test the performance of the different component of the collectors.

The effect of buoyancy ratio on the flow structure is analyzed numerically by Nishimura et al. [29] for a binary mixture gas in a rectangular enclosure subject to opposing horizontal thermal and compositional buoyancies. The effect of double-diffusive natural convection of water in a partially heated enclosure with Soret and Dufour coefficients was investigated by Nithyadevi and Yang [30] using control volume method around the density maximum. They presented comprehensive Nusselt and Sherwood numbers data as functions of the studied governing parameters. Other related studies can be found in ref. [31], [32], [33], [34], [35].

Studies on double-diffusive natural convection inside the triangular enclosure are extremely limited. Hajri et al. [36] analyzed a numerical study of heat and mass transfer due to natural convection inside a triangular enclosure. The governing equations of the two-dimensional flow problem consist of a velocity–pressure (UVP) formulation along with the energy and concentration flow equations. These equations are solved numerically by control volume based finite element method using the equal-order method without pressure correction. They found that the buoyancy ratio and the Lewis number values have a profound influence on the thermal, concentration and dynamic fields. Chamkha et al. [37] studied effect of heat generation/absorption on double-diffusive natural convection inclined finned triangular porous enclosures.

The main aim of this work is to examine the double diffusive convection inside the triangular cavity with corrugated bottom wall. This geometry is useful to control heat and mass transfer in case of desalination process.

Section snippets

Physical description

The considered physical model is given in Fig. 1 with boundary conditions and coordinate system. Indeed, the model is a triangular type solar collector with corrugated bottom wall with changes by wave length. The wave length is defined as in the figure. The height and length of triangular cavity are shown by H and L, respectively. The gravity acts in negative –y direction. An absorber plate and two inclined glass covers form a cavity. Both concentration and temperature are higher on corrugated

Solution procedure

The finite element formulation of Galerkin weighted residual technique is considered for this study. The coupled governing Eqs. (2), (3), (4), (5) are transformed into sets of algebraic equations using finite element method. The considered geometry is discretized into numerous simple shaped regions called elements. These elements may be different shapes and sizes. In this analysis, the second-order triangular type elements are considered. The dependent variables are approximated over each

Results and discussion

Finite element analysis was used to solve governing equations of heat, mass and fluid flow for different Rayleigh number, Prandtl number and wave length of the geometry. Streamlines, isotherms, isoconcentration, overall Nusselt and Sherwood numbers are plotted. The study of this problem for different values of Lewis number and buoyancy ratio has been conducted and published in Rahman et al. [38]. In this case, Lewis number and buoyancy ratio were fixed as 2 and 10, respectively.

Streamlines are

Conclusions

A numerical study has been carried out to simulate double diffusive natural convection inside a triangular enclosure with corrugated bottom wall. Results are presented for different Rayleigh numbers, Prandtl numbers and wave length. In general, it can be said that conduction mode of heat transfer becomes a dominant role at the lower Rayleigh number. In this case, symmetrical cells are formed and they turned different direction but same flow strength. The symmetricity is distorted for the lowest

Acknowledgment

The 2nd author would like to acknowledge the financial support from the High Impact Research Grant (HIRG) scheme (UM-MoHE) project (Project no: UM.C/HIR/MoHE/ENG/40) to carry out this research.

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