Numerical Simulation Of Natural Convection Research Articles

Numerical simulation of natural convection in a differentially heated cubical cavity with solid fins

Purpose The performance of solid fins inside a differentially heated cubical cavity is numerically studied in this paper. The main purpose of the study is to make an optimization to reach the maximum heat transfer in the enclosure having the solid fins with studied parameters. Design/methodology/approach The considered domain of interest is a differentially heated cube having heat-conducting solid fins placed on the heated wall while an opposite wall is a cooled one. Other walls are adiabatic. Governing equations describing natural convection in the fluid filled cube and heat conduction in solid fins have been written using non-dimensional variables such velocity and vorticity taking into account the Boussinesq approximation for the buoyancy force and ideal solid/fluid interfaces between solid fins and fluid. The formulated equations with appropriate initial and boundary conditions have been solved by the finite difference method of the second of accuracy. The developed in-house computational code has been validated using the mesh sensitivity analysis and numerical data of other authors. Analysis has been performed in a wide range of key parameters such as Rayleigh number (Ra = 104–106), non-dimensional fins length (l = 0.2–0.8), non-dimensional location of fins (d = 0.2–0.6) and number of fins (n = 1–3). Findings From numerical methods point of view the used non-primitive variables allows to perform numerical simulation of convective heat transfer in three-dimensional (3D) regions with two advantages, namely, excluding difficulties that can be found using vector potential functions and reducing the computational time compared to primitive variables and SIMPLE-like algorithms. From a physical point of view, it has been shown that using solid fins can intensify the heat transfer performance compared to cavities without any fins. Fins located close to the bottom wall of the cavity have a better heat transfer rate than those placed close to the upper cavity surface. At high Rayleigh numbers, increasing the fins length beyond 0.6 leads to a reduction of the average Nusselt number, and one solid fin can be used to intensify the heat transfer. Originality/value The present numerical study is based on hybrid approach for numerical analysis of convective heat transfer using velocity and vorticity that has some mentioned advantages. Obtained results allow intensifying the heat transfer using solid fins in 3D chambers with appropriate location and length.

Numerical simulation of natural convection in a rectangular enclosure filled with porous medium saturated with magnetic nanofluid using Buongiorno's two‐component model

AbstractMotivated by studying emerging nanofluid‐based magnetic fuel cells and hybrid direct absorber solar collectors, a numerical study is presented for buoyancy‐driven flow in a vertical enclosure containing a porous medium saturated with magnetized nanofluid flow under a transverse static magnetic field. The enclosure features adiabatic side walls and vertical heat slits, ensuring consistent cold temperatures on the lower and upper bounded walls. The side walls of the regime are insulated, and the hot slits are centrally located on these walls. The finite difference method (FDM) is applied to employ the transformed dimensionless vorticity–stream function (VSF) formulation of the transport equations. The impact of pertinent parameters on isotherm, streamline, iso‐concentration, and average Nusselt and Sherwood numbers are visualized with contour plots and graphs. Increasing Darcy number values tend to amplify the isotherm magnitudes. Higher Hartmann (magnetic) number values, on the other hand, lead to a reduction in local Nusselt number profiles but do not significantly modify the local Sherwood number. The porous medium permeability, as simulated via the Darcy number, has a strong impact on streamlines, thermal contours, and iso‐concentrations. A reduction in Darcy's number suppresses local Nusselt and Sherwood numbers, whereas an elevation in Rayleigh's number enhances them. Increasing the Buongiorno nanoscale Brownian motion parameter enhances local Nusselt and Sherwood numbers at both cold walls of the enclosure. The simulations provide a deeper insight into enclosure flows involving electrically conducting nanofluids in advanced processing systems for nanomaterials and hybrid fuel cells utilizing electromagnetic and liquid fuel technologies.

A numerical simulation of natural convection in a porous enclosure with nanofluid

In day-to-day life, heat transfer has several applications and hence we have many research areas of interest to learn new things. Nanoparticles improve the characteristics of heat transfer due to the random motion of particles. In this study, a computational approach is used to study natural convection in a porous enclosure with nanofluid. The convective term is solved by the QUICK scheme, and the finite difference method is used to solve the stream function with a 60 × 60 mesh size. CuO-water nanofluid is used in this work since nanoparticles are widely used in almost all engineering fields. In this study, we considered a two-dimensional complex cavity which is solved mathematically by using the Boussinesq approximation method. For validation of the software code, the obtained results are compared with the existing results in the literature and are found to be in good agreement. We see distortion of isotherms increases with an increase in the Rayleigh number and the nanoparticle content. That is, heat transfer takes place by natural convection very fast. Nusselt number increases with increasing nanofluid particles and the Rayleigh number. Also, it can be concluded that the heat transfer is a strong function of the Darcy number and The Rayleigh number.

A Novel Thermal Lattice Boltzmann Method for Numerical Simulation of Natural Convection of Non-Newtonian Fluids

A modified thermal Bhatnagar–Gross–Krook Lattice Boltzmann (BGK-LB) model was developed to study the convection phenomenon of non-Newtonian fluids (NNFs). This model integrates the local shear rate into the equilibrium distribution function (EDF) of the flow field and keeps the relaxation time from varying with fluid viscosity by introducing an additional parameter. In addition, a modified temperature EDF was constructed for the evolution equation of the temperature field to ensure the precise recovery of the convection–diffusion equation. To validate the accuracy and effectiveness of the proposed model, numerical simulations of benchmark problems were performed. Subsequently, we investigated the natural convection of power–law (PL) fluids and examined the impact of the PL index (n = 0.7–1.3) and Rayleigh number (Ra = 103–5 × 105) on the flow and temperature fields while holding the Prandtl number (Pr = 7) constant. The obtained results indicate that, for a given value of n, the convective intensity exhibits a positive correlation with Ra, which is illustrated by the rising trend in the average Nusselt number (Nu¯) with increasing Ra. Additionally, shear-thinning fluid (n < 1) exhibited increased Nu¯ values compared to the Newtonian case, indicating an enhanced convection effect. Conversely, shear-thickening fluid (n > 1) exhibits reduced Nu¯ values, indicating weakened convective behavior.

Numerical simulation of natural convection around the dome in the passive containment air-cooling system

The Passive containment Air-cooling System (PAS) can effectively remove the decay heat of the modular small nuclear reactor after an accident. The details of natural convection around the dome, which is a key part of PAS, were investigated numerically in the present study. The thermal dynamics around the dome were studied through the temperature, pressure and velocity contours and the streamlines. Additionally, the formation of the buoyant plume at the top of the dome was investigated. The results show that with the increase of Ra, the lift-off point moves toward the bottom of the dome, and the eddy under the buoyant plume grows larger gradually, which enhances the heat transfer. And the heat transfer along the dome surface with different truncation angles was investigated. As the angle increases, the heat transfer coefficient becomes stronger as well. Consequently, a newly developed heat transfer correlation considering the influence of truncation angle for the dome is proposed based on the simulated results. This study could provide a better understanding of natural convection around the dome of PAS and the proposed correlation could also offer more predictive value in the improvement of nuclear safety.

Frequency response of three-dimensional natural convection of nanofluids under microgravity environments with gravity modulation

The present study performed three-dimensional numerical simulations of natural convection generated by nanofluids between plates under microgravity with gravity modulation. The Rayleigh number was fixed at and the dimensionless frequency of the gravity modulation was varied from F = 0 to 102 for the volume fraction –0.05. From an unsteady analysis, we clarified the time variation of three-dimensional thermal convection structures under gravity modulation and the frequency response of the heat transfer characteristics to the gravity modulation. When the frequency of gravity modulation and the volume fraction of nanoparticles are changed, two- or three-dimensional roll-shaped thermal convection occurs, and vortex pairs form between thermal plumes. For a low volume fraction of the fluid follows the low-frequency gravity modulation of F = 1 well. Therefore, the thermal convection repeatedly develops and decays as the gravity acceleration increases and decreases. At high-frequency gravity modulation of since the followability of the fluid is poor, the convection remains during one cycle of gravity modulation. At the low frequency of F = 1 and low volume fraction of the instantaneous Nusselt number is 1.0–1.1 times higher than that at over one period. For the time-averaged characteristics, the heat transfer coefficient is lower at low frequencies than at high frequencies regardless of the volume fraction. At the low volume fraction of the average Nusselt numbers for the low frequencies of F = 1 and F = 5 are 1.0–1.01 times higher than that at and the decrease in heat transfer coefficient owing to nanoparticles is suppressed. At for each frequency, the Nusselt number is much lower than that for Therefore, for low-frequency gravity modulations that make damping difficult, using nanofluids with a low volume fraction of can prevent the decrease in the heat transfer coefficient.

Mechanism of nodular growth in copper electrorefining with the inclusion of impurity particles under natural convection

Nodular growth behavior with the inclusion of impurity particles in copper electrorefining was investigated herein by quantitative analyses of impurity elements inside nodules, observations of crystal structures, and numerical simulations of natural convection based on the tertiary current distribution. Impurity contents were higher in the upper half of the nodule than in either the lower half or electrolytic copper with non-nodulous growth. Impurity particles, such as suspended slime, were considered to be preferentially taken into the upper part of nodules due to frequent collisions with the upper part as they circulated along the convection vortex that emerged above the nodule. The inclusion of impurity particles changed the electrodeposition morphology and growth direction, and eventually produced granular irregularities and buds of new nodules on the upper surface of the initial nodule.

Numerical simulation of natural convection and heat transfer in a molten pool with embedded cooling tubes

This study described the natural circulation and heat transfer of a molten pool in a specifically designed core catcher conceived for a pressurized water reactor. In addition to external cooling, the core catcher features internal cooling tubes embedded in the molten pool. To investigate the coolability in such a configuration, first, a full-scale core catcher simulation is conducted to give a preliminary study under a real SA situation. Results illustrated that cooling efficiency can be remarkably enhanced due to the inner tubes. Then a test facility of the 2D slice with the geometrical scaled factor of 1:4 has been developed, and molten salt (NaNO3–KNO3) experiments will be implemented in the near future. This study also performed a pre-test simulation using molten NaNO3–KNO3 as a stimulant to study the heat transfer and flow characteristics of the salt pool. The melt convection in the test section was represented by a two-dimensional mesh with a WMLES turbulence model using the FLUENT code. The simulation captured the heat transfer enhancement by the cooling tubes as expected, and the results would help decide the proper test matrix and improvement of instrumentation required to obtain the necessary data for code validation.

A multi-resolution particle method with high order accuracy for solid-liquid phase change represented by sharp moving interface

This paper develops a highly accurate, multi-resolution particle method to simulate solid-liquid phase change coupled with the thermal flow. Instead of including the latent heat in the governing equation, the heat equations for solid and liquid phases are solved separately. A sharp interface model is proposed to represent the solid-liquid interface explicitly. The sharp interface, represented by discrete nodes, provides the Neumann boundary condition for pressure and the Dirichlet boundary condition for velocity/temperature, respectively. Based on temperature gradients in the solid and liquid phases, the positions of these interface nodes are updated every time step. The Eulerian-based formulation, rather than the conventional Lagrangian-based one, is utilized to minimize time step-dependent error. Up to 4th order spatial discretization scheme is adopted based on the Least Square Moving Particle Semi-implicit (LSMPS) scheme. Moreover, a geometry-based multi-resolution scheme is introduced to dynamically refine the spatial resolution near the interface for saving computational cost. The 1-D Stefan problem is firstly simulated to verify the accuracy of the proposed sharp interface model. Then, the consistency of the multi-resolution scheme is investigated by a convergence study of the Taylor-Green vortex problem. After that, numerical simulations of natural convection in a cavity are performed with different spatial resolutions and high order schemes. Resulted computational costs are compared and discussed. Finally, the problems of melting by natural convection with different Rayleigh numbers are investigated. The results achieved so far indicate that the multi-resolution and high order schemes have great potential to save computational cost.

Direct numerical simulation of natural convection between an enclosure and multiple circular cylinders: An influence of horizontal arrangement of cylinders

The work involves a three-dimensional numerical analysis of the buoyancy-driven heat transfer in an enclosure having four heated cylinders for Rayleigh number, Ra = 10 4 -10 6 , and Prandtl number, Pr = 0.7. An in-house direct numerical simulation code, finite volume-based immersed boundary method incorporates the inner cylinder's virtual wall boundary and computes the governing transport equations. Heat and flow characteristics at different Ra and spacing between cylinders are discussed by using three-dimensional vortices and isotherms. The effect of heat and flow on three-dimensionality and heat transfer features are captured and reported. Limitations of two-dimensional simulation for capturing the physics of the problem and the importance of the three-dimensional analysis for the present study are highlighted.

The Baffle Length Effects on the Natural Convection in Nanofluid-Filled Square Enclosure with Sinusoidal Temperature.

The proper process of applying heat to many technological devices is a significant challenge. There are many nanofluids of different sizes used inside the system. The current study combines this potential to improve convection effects, considering numerical simulations of natural convection using Cu/water nanofluids in a square enclosure with bottom blocks embedded in baffles. The enclosure consists of two vertical walls with isothermal boundary conditions; the left wall is the sinusoidal heat source, whereas the right wall is cooled. The investigations dealt with the influences of nanoparticle concentration, Rayleigh number, baffle length, and thermal conductivity ratioon isotherms, stream functions, and average Nusselt number. The results present that, when the Rayleigh number rises, the fluid flow velocity increases, and the heat transfer improves. Furthermore, the baffle length case (Lb = 0.3) provides higher heat transfer characteristics than other baffle height cases.

Direct numerical simulation of natural convection in a square cavity at high Rayleigh numbers via the Lagrange interpolating polynomial scheme

Direct numerical simulation (DNS) is a powerful research technique to solve the Navier–Stokes equations based on turbulent flows. DNS delivers highly reliable physical solutions with extreme accuracy. Unfortunately, present hardware and computing technologies remain limited, making it difficult to implement DNS in practice. The recently proposed Lagrange interpolating polynomial (LIP) scheme is a discretization technique for the finite-volume method. The LIP scheme is easy to use with nonuniform grid simulations and can flexibly increase or decrease the order of accuracy. The objective of this study is to verify that the LIP scheme is suitable for DNS of natural convection in a square cavity at high Rayleigh numbers (Ra). Accordingly, code was developed in-house using a second-order LIP scheme with the finite-volume method and the semi-implicit method for pressure-linked equations (SIMPLE) algorithm. Simulations were performed at Ra values of 109 and 1.58 × 109. The solutions were then verified against experimental benchmark data and published numerical solutions. The maximum differences in the Nusselt numbers between the computed solutions and the experimental benchmark data and published numerical solutions are 19.23% and 5.51%, respectively. However, the comparison results indicate that most of the computed solutions are in good agreement with experimental benchmark data and published numerical solutions.

Numerical simulation of natural convection in a porous cavity with internal hot and cold sources using the lattice Boltzmann method

Based on the non-orthogonal multiple-relaxation-time lattice Boltzmann method (MRT–LBM), natural convection in a porous square cavity with a pair of isothermally hot and cold blocks inside was studied numerically in the current study. The influence of arrangements (Cases 1, 2, 3, 4, and 5), spacing ratio (S), and size ratio (A) of the hot and cold sources and the Rayleigh number (Ra) on the heat exchange efficiency were studied. The results show that different arrangements produce different heat-transfer effects. Two arrangements, hot and cold blocks placed horizontally (Case 1) and a cold block located in the upper left corner while a hot block is located in the bottom right corner (Case 4), have better heat exchange performance than the other three cases because the flow directions of hot and cold fluids are closer to that of the heat transfer. Then, the influence of the spacing between blocks and the size of the blocks on the heat transfer rate was further studied in Cases 1 and 4. Heat transfer performance improved with increasing A. Additionally, the variation in the heat transfer performance with spacing is related to the arrangement and size ratio of the blocks. For Ra = 104, 105, and 106, the best heat transfer characteristics were obtained in Case 1 when S = 0.05 and A = 0.20. For Ra = 107, Case 4 exhibited the best heat transfer effect when S = 0.35 and A = 0.20.

Buoyancy-driven flows beyond the Boussinesq approximation: A brief review

The well-known Boussinesq (also known as Oberbeck—Boussinesq) approximation is still the most common approach for the numerical simulation of natural convection problems. However, the accurate performance of this approximation is mainly restricted by small temperature differences. This encourages researchers and engineers to use other approaches beyond the range of validity of the Boussinesq approximation, especially when buoyancy-driven flows are generated by large temperature differences. This paper assembles and classifies the various approaches for numerical simulation of laminar natural convection, including Boussinesq and non-Boussinesq approximations for Newtonian fluids. These classifications reside under two overarching classes capturing compressible and incompressible approaches, respectively. This review elaborates on the different approaches and formulations adopted within each category.

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

AbstractIn this study, a benchmark natural convection problem is studied under a Gay–Lussac‐type approximation incorporating centrifugal effects in the context of a new vorticity‐stream‐function approach. This approximation differs from the classic Boussinesq approximation in that density variations are considered in the advection term as well as the gravity term in the momentum equations. Such a treatment invokes Froude number as a non‐Boussinesq parameter deviating results from the classic Boussinesq approximation. It is also shown how the Gay–Lussac parameter may be expressed by its equivalent relative temperature difference. Numerical simulation of natural convection in square and skewed cavities are performed up to Ra = 106 and ϵ = 0.3 at Pr = 0.71. Results obtained with new approximation are compared against the weakly compressible approach and the conventional Boussinesq approximation in terms of the average and local Nusselt number, coefficient of friction and entropy generation. Comparing the local Nusselt number indicates a negligible difference between Gay–Lussac type and the Boussinesq approximations even at a high relative temperature difference, with both deviating from the weakly compressible approach. Comparing coefficient friction results obtained by the Gay–Lussac‐type approximation against the weakly compressible approach confirms superior numerical data in some regions of the physical domain with less deviation for rotating flows in comparison with the Boussinesq approximation. Finally, comparing the computational cost of the numerical simulation shows at least 8% less computational cost when governing equations are solved via secondary variables using a central scheme rather than primitive variables.

Numerical simulation of natural convection within wavy square enclosure filled with nanofluid under magnetic field using EFGM with parallel algorithm

Purpose This paper aims to study the flow and heat transfer inside a wavy enclosure filled with Cu-water nanofluid under magnetic field effect by parallel implemented meshfree approach. Design/methodology/approach The simulation has been carried out for a two-dimensional model with steady, laminar and incompressible flow of the nanofluid filled inside wavy enclosure in which one of the walls is sinusoidal such that the amplitude (A = 0.15) and number of undulations (n = 2) are fixed. A uniform magnetic field B0 has been applied at an inclination angle γ. The governing equations for the transport phenomena have been solved numerically by implementing element-free Galerkin method (EFGM) with the sequential as well as parallel approach. The effect of various parameters, namely, nanoparticle volume fraction (φ), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ) has been studied on the natural convection flow of nanofluid. Findings The results are obtained in terms of average Nusselt number calculated at the cold wavy wall, streamlines and isotherms. It has been observed that the increasing value of Rayleigh number results in increased heat transfer rate while the Hartmann number retards the fluid motion. On the other hand, the magnetic field inclination angle gives rise to the heat transfer rate up to its critical value. Above this value, the heat transfer rate starts to decrease. Originality/value The implementation of the magnetic field and its inclination has provided very interesting results on heat and fluid flow which can be used in the drug delivery where nanofluids are used in many physiological problems. Another important novelty of the paper is that meshfree method (EFGM) has been used here because the domain is irregular. The results have been found to be very satisfactory. In addition, parallelization of the scheme (which has not been implemented earlier in such problems) improves the computational efficiency.

Effect of inclination on nonlinear evolution and bifurcation of thermal convection in a square cavity

Heat transfer of natural convection in inclined cavities is one of the hot research topics in nonlinear non-equilibrium systems. In this paper, direct numerical simulations of natural convection in an inclined square cavity are carried out by using a high-accuracy numerical method. The effects of the different trends of inclination angle in a range of 0°–180° on the nonlinear evolution of flow field, heat transfer efficiency, and bifurcation are investigated. The Rayleigh number varies in a range from 10<sup>3</sup> to 10<sup>6</sup>. The results show that the heat transfer efficiency characterized by Nusselt number is highly dependent on the Rayleigh number, Prandtl number, and the inclination angle. When the Rayleigh number is high, the Nusselt number will have a small jump near the inclination angle in a range of 80°–100°. The evolution of the flow field and temperature field are more complicated at high Rayleigh number. There are one to three vortices of different intensities in the cavity. At low Rayleigh number and inclination angle of the cavity being close to 90°, the flow state is composed mainly of heat conduction state. In addition, it is found that there exist two stable branches of solutions in a range of Rayleigh number (4949, 314721) when the inclination angle is in the interval of (70°, 110°).

Growth of Nodules in Copper Electrorefining: Numerical Simulation of Natural Convection

It is well known that copper can be electrodeposited with 100 % current efficiency without hydrogen evolution. In modern copper electrorefining process, however, the current utilization rate for copper electrorefining is generally 93-98 %. This is because nodulation occurs on cathode to cause short circuits and lose currents [1]. In other words, when nodules on the cathode grow to reach anode, current can flow but electrochemical reaction can not occur. There are various studies on the mechanism of nodule formation [2], and it is considered that suspended particles (e.g. floating slime) adhering to the cathode are an origin of nodule formation or nodule outbreak (see Fig. 1a).Previously we investigated the effect of current concentration on a nodule by experiments and numerical simulations [3-5]. Based on the secondary current distribution model, i.e. without considering the effect of natural convection, it was found that the experimental growth rate cannot be explained by the effect of current concentration on nodules only.Upward and downward natural convection occurs near the cathode and anode, respectively, as the density of the electrolyte solution near the electrode changes due to electrolysis (see Fig. 1a). Although natural convection can affect mass transfer, its contribution to the nodule formation has not been clarified. In this study, we focused on the natural convection as a factor for nodule growth in the early stages of nodule formation or after nodule outbreak.We performed numerical simulations based on the tertiary current distribution model. Using the FEM simulation software COMSOL Multiphysics®, we calculated the natural convection behavior and the cupric ion concentration distribution. Cylindrical protrusions were considered to mimic the nodules. The partially simplified governing equations for electrochemical model, mass transfer and computed fluid dynamics (CFD) were solved simultaneously (see Fig. 2). In CFD, laminar flow was assumed. The calculation was performed in 3D area of the electrolyte solution between the single pair of vertical anode and cathode plates.Figures 1b and 1c confirmed that the flow behaviors changed as a function of the protrusion length. When the protrusion length was 0.2 mm or less, natural convection along the cathode surface flowed over the protrusion. By contrast, when it was about 0.5 mm or more, the flow was divided into both sides of the protrusion, implying that natural convection is weakened at the protrusion tip. It is also notable that the simulated thickness of the diffusion layer at the protrusion tip decreased as the protrusion length increased. Thus, as the protrusion length increases, more Cu2+ ions are supplied by diffusion at the protrusion tip. This effect may promote the nodule growth above a certain size under natural convection.[1] M. E. Schlesinger, M. J. King, K. C. Sole and W. G. Davenport, Extractive metallurgy of copper 5th, Elsevier (2011), pp. 251-279.[2] T. N. Andersen, C. H. Pitt and L. S. Livingston, J. Appl. Electrochem., 13(4), 429 (1983).[3] K. Adachi, Y. Nakai, A. Kitada, K. Fukami and K. Murase, TMS Annual Meeting & Exhibition, Springer, Cham (2018), pp. 215-222.[4] Y. Nakai, K. Adachi, A. Kitada, K. Fukami and K. Murase, TMS Annual Meeting & Exhibition, Springer, Cham (2018), pp. 319-323.[5] K. Adachi, Y. Nakai, S. Mitsuno, M. Miyamoto, A. Kitada, K. Fukami and K. Murase, Journal of MMIJ (in Japanese), 136(2), 8 (2020). Figure 1

Numerical Simulation of Natural Convection in A Cavity Filled with A Nanofluid Who’s Wall Containing the Heat Source Is Inclined

In this work, we study by numerical simulation the natural convection in a trapezoidal cavity filled with a nanofluid whose wall containing the heat source is successively inclined at an angle varying from 0 to 60 ° at the most (in order to maintain a valid model straight vertical wall) with respect to the horizontal. The upper and lower walls on either side of the heat source are adiabatic while the other walls are subjected to a constant cold temperature. The hydrodynamic and thermal phenomena are described by the equations of Navier-Stockes and energy. The models Brinkman and Wasp are used to describe the thermo-physical properties of the nanofluid (water- ).The finite element method; based on the Galerkin principle; is used to solve the system of partial differential equations. We consider the effect of the solid volume fraction for different values ??of the Rayleigh number on the results obtained, in the form of isotherms and local, modified Nusselt numbers.

Numerical simulation of natural convection of dusty nanofluids within a curve-shaped enclosure

The current research expounds the numerical simulation of a two phase dusty nanofluid flow in a curve-shaped enclosure surrounded by three straight walls and a curved wall. The flow is generated in the enclosure because of the buoyancy force due to the heated lower curved wall. An apt variable transform that transfigures the curve-shaped domain into a rectangular domain is introduced in this study. The governing equations for the nanofluid phase and the dusty phase in transformed coordinates are solved by incorporating a finite difference technique with a successive over-relaxation method. The requisite results to analyze the flow and heat transfer are blazoned for physically significant parameters, namely, the nanoparticles’ volume fraction, the Rayleigh number, the amplitude, the density ratio, and the dusty parameter. The results assert that the flow strength can be decreased slightly by increasing the nanoparticles’ volume fraction and the amplitude but can be increased notably by incrementing the Rayleigh number. Besides, heat transfer can be enhanced about 4.33% at the lower wall and about 5.13% at the upper wall by incrementing the nanoparticles’ volume fraction 4% for the Rayleigh number 105. Moreover, the increment in the Rayleigh number and decrement in the density ratio and the dusty parameter can augment the heat transfer rate.