Mixed convection in a lid-driven cavity containing triangular block with constant heat flux: Effect of location of block
Graphical abstract
Introduction
The study of internal flows has been a topic of great scientific research all over the years. A classical example of internal flows is system of lid-driven cavity. It constitutes an illustrious research area in the field of fluid dynamics, owing to its great pragmatic as well as theoretical importance. The applications of the lid-driven cavity are diverse, such as cooling of electronic gadgets, oil extraction, design of heat exchangers, solar ponds, float glass productions, insulation materials, multi-screen gadgets for nuclear reactors, coating, food processing crystal growth, etc [1], [2], [3]. In mixed convection, the shear driven flow as well as the buoyancy driven flow are of corresponding magnitude [4], [5]. Hence making the flow characteristics much more complex. Therefore, it is beneficial to adopt the numerical strategies for the fundamental understanding of such kind of flow systems. Moreover, the presence of heated blocks/obstacle/cylinder inside the lid-driven cavity bring-in the fundamental interaction of shear and buoyancy driven flows, which enhances the overall complexity of flow and heat transfer. It demands a comprehensive analysis to elucidate the underlying physics [6]. The lid-driven cavity problem has been considered as a notable research field, owing to its simple geometry (hence low computational efforts) associated with the strong theoretical foundation (multiple steady states, flow bifurcation, etc.). Extensive research have been reported in the recent past on the lid-driven hydrodynamics. Relatively the information on the mixed convection in lid-driven cavity containing heated block is still to the modest. It has also been asserted that the use of detached bodies/cylinders (adiabatic, heated, conducting, etc.) can effectively use to control/limit the fluid flow and thereby heat transfer [7]. Therefore, it is required to understand the flow physics affected by use of obstacle/cylinder of different cross-sections.
All-embracing research is now usable on the various aspects of hydrodynamics and heat transfer characteristics in a lid-driven cavity. But the data exploring the gross and local flow characteristics in a lid-driven cavity containing obstacle/block is still to a lessor extent comparatively. To exemplify, Billah et al. [8] studied the combined convection in a lid-driven cavity with heated circular-hollow cylinder for range of cylinder diameters (0.2–0.5) and Richardson number (0 ≤ Ri ≤ 5). Sun et al. [9] explored the control of mixed convective fluid flow by using conductive triangular fins in a lid-driven cavity. The study were based on the effect of variation of location fins and Richardson number . Islam et al. [10] studied the effect of heated ‘square’ blockage on the mixed convection characteristics inside a lid-driven cavity for range of governing parameters, such as, location of block, Richardson number, etc. Chatterjee et al. [11] studied the effect of rotating cylinder of circular cross-section for nanofluid on mixed convection in lid-driven cavity, for rotational speed (0–5), solid nanoparticle volume fraction (0–0.2) and . Similar kind of work was performed by Esfe et al. [12], [13] for heated square block in cavity. Chamkha et al. [14] numerically analyzed the convection hydrodynamics inside porous cavity due to inner rotating circular cylinder. The effects of Re, Gr and Pr on the mixed inside lid-driven cavity with heated triangular cylinder (either with constant temperature or heat flux conditions) were given by Gangawane [15], [16]. A critical Reynolds number (Recr) was identified in these studies. Hammami et al. [17] presented a computational work based on a system of two sided lid-driven cavity containing circular cylinder. The critical Reynolds number for the considered problem was found to be . Khanafer and Aithal [18] examined the effects of Ri, angular rotational speed on the heat transfer due to convection in a cavity. Their study shown improvement in the heat transfer characteristics for the cavity containing cylinder than absence of cylinder. Similarly, Mehmood et al. [19] studied the mixed convection for Al2O3 nanofluid in a lid-driven cavity containing a heated square shaped obstacle under the effect of magnetic field. For illustrating, the heat transfer characteristics in a lid-driven, non-square shaped cavity, Selimefendigil et al. [20] studied the cavity of trapezoidal shape for nanofluids. The cavity contained a circular cylinder. Ababaei et al. [21] shown the detailed analysis of a double diffusive, mixed convection with entropy generation in a lid-driven cavity. The cavity contained a heat source. The study predicted deterioration of the rate of heat transfer with increasing Lewis number. The effect of size of the square blockage on the conjugate mixed convection behavior in a double lid-driven cavity for nanofluid was ascertained by Alsabery et al. [22]. The study were based on the numerical experimentation of physical parameters, such as, Reynolds number, Richardson number, thermal conductivity of square blockage, etc. Higher heat transfer results were achieved at higher Re, Ri and larger block size. In extension to this work, Alsabery et al. [23] studied the effect of two-phase nanofluid model on the mixed convection characteristics in the lid-driven cavity subjugated to magnetic field and also containing a square block. The consequences caused by the heat-conducting solid wall and the vertical temperature gradient inside a lid-driven cavity on the mixed convection along with entropy generation were analyzed by Gibanov et al. [24]. In this study, authors highlighted the importance of the thickness of the bottom wall on convection behavior. Goodarzi et al. [25] used lattice Boltzmann method (LBM) to study flow and thermal characteristics in the inclined lid-driven cavity with a centrally placed heat source for pure natural as well as mixed convection cases. On the other hand, the effects of the rotating, adiabatic circular cylinder on the overall convection in a lid-driven cavity for turbulent flow was given by Kareem and Gao [26], [27]. Authors determined the impact of surface roughness of cylinder [26] as well as direction of rotation of cylinder [27] on rate of heat transfer by convection. The effects of a heated elliptical cylinder inside a lid-driven cavity on the combined convection characteristics were given by Karbasifar et al. [28], [29]. Manchanda and Gangawane [30] explored the mixed convection in the double lid-driven cavity containing a centrally placed heated triangular block (for constant temperature) for non-Newtonian power law fluids. The governing parameters used for the study were Reynolds number non-Newtonian power-law index (n = 0.2–1.8), Richardson number (0.01–10), size of block (10% or 30% of characteristic length) for . Higher heat transfer rate were attained by using higher size of block at higher Ri. Some recent works exploring similar phenomenon in a lid-driven cavity with blockage were given by [31], [32], [33], [34], [35], [36], [37], [38].
Hence, after having completed a prompt review of recent literature (most relevant to the problem under consideration), it can be affirmed that extensive details covering the local and global flow characteristics are now available on the mixed convection in a lid-driven cavity with circular or square obstacle/cylinder. But the studies performing a comprehensive analysis of the mixed convection the lid-driven cavity with obstacle of other cross-sections (than circular and square) are to a lesser level. Also, the majority of such studies were targeted for the constant wall temperature condition of heated block. Very limited information is available on triangular block/cylinder [4], [9], [15], [16] subjected to constant heat flux thermal condition. No study, as much known to authors, have explored the combined effects of location as well as size of heated triangular cylinder for constant heat flux (CHF) condition in a lid-driven cavity. The lapse available in the literature has prompted the authors to research this problem. The work is an extension of our earlier study [4], in which the influence of location as well as size of blockage have been elucidated for lid-driven cavity containing triangular block maintained at constant temperature condition. In this work, the mixed convection in lid-driven cavity containing heated triangular block with constant heat flux (CHF) has been examined. The location of triangular block has been varied along vertical center-line of cavity (Ly). The flow governing parameters used in this work as similar as used in [4], such as Reynolds number (1 ≤ Re ≤ 1000), Prandtl number, (1 ≤ Pr ≤ 100), location of block size of blockage (0.1H, 0.3H) and Richardson number (0.01 ≤ Ri ≤ 10).
Section snippets
Problem statement and mathematical formulation
Consider a square cavity (Fig. 1) containing heated triangular block (edge, b) placed at horizontal geometric center . The top wall of the cavity is maintained at adiabatic condition and moving with uniform horizontal velocity of . All other walls (both vertical) of the cavity are stationary (no-slip). The triangular block is subjugated to constant heat flux thermal condition (q). Both vertical walls of the cavity are exposed to the ambient (Tc). The blockage (B) is defined by
Numerical simulation procedure
The linear form of algebraic equations are obtained by the discretization of mass, momentum and energy equations (in partial differential form). A finite volume method (FVM) based on commercial CFD solver (ANSYS FLUENT 15) has been used to carry out the iterative solution of the governing equations. The structured grid consists of ‘quadrilateral cells’ of uniform grid spacing was generated (Fig. 2(a)). A semi-implicit method for the pressure linked equations (SIMPLE) scheme is used to solve the
Results and discussion
The present computational work has been accomplished to explore the hydrodynamics and thermal characteristics due to mixed convection in the lid-driven square cavity with centered heated triangular block subjugated to constant heat flux (CHF) thermal condition. The location of triangular block is varied along the vertical center-line of the cavity (0.5, y*). The influence of location of the block size of block Reynolds number Richardson
Conclusion
The present numerical simulation study is performed to investigate the 2D, steady, laminar mixed convection characteristics inside the lid-driven cavity containing heated triangular block for Newtonian fluids. The heated triangular block is subjected to thermal condition of constant heat flux (CHF). The study is basically targeted to elucidate the impact of location of triangular block and blockage (size of block, ) on overall fluid flow patterns and heat
Acknowledgment
Second and third authors extend their appreciation to the International Scientific Partnership Program ISPP at King Saud University for funding this research work through .
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