Mixed Convective Heat Transfer Analysis by Heatlines on a Lid-Driven Cavity Having Heated Wavy Wall Containing Tilted Square Obstacle

Ali, Md. Yousuf; Alim, M. A.; Karim, Md. Mashud

doi:https://doi.org/10.1155/2023/1374926

Mathematical Problems in Engineering

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Abstract Introduction Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 1374926 | https://doi.org/10.1155/2023/1374926

Mixed Convective Heat Transfer Analysis by Heatlines on a Lid-Driven Cavity Having Heated Wavy Wall Containing Tilted Square Obstacle

Md. Yousuf Ali,¹M. A. Alim,¹and Md. Mashud Karim²

Academic Editor: Waqas Abbasi

Received05 Mar 2023

Revised14 Jun 2023

Accepted20 Jun 2023

Published26 Jul 2023

Abstract

The current problem studies the mixed convective heat transport by heatlines in lid-driven cavity having wavy heated walls with two diamond-shaped obstacles. The left and right vertical walls are both cold, whereas the top wall is adiabatic, and the bottom wavy wall is heated. The relevant governing equation has been calculated through using the finite element method as well as the Galerkin weighted residual approach. The implications of the Reynolds number , Richardson number , Hartman number , Prandtl number , Undulations number , and inner diamond shape obstacle are depicted by the streamlines, isotherms, and the heatlines. The convection heat transfer is observed to be fully developed at a high Prandtl number, whereas heat conduction happens at poor Pr. In particular, the undulations number has the greatest effect on the streamlines and isotherm contrast to a flat area. The Nusselt numbers increase as the Reynolds and Prandtl numbers rise as well. The isotherm, streamlines, heatlines, Nusselt number, and fluid flow are shown graphically for several relevant dimensionless parameters. The result demonstrates that a single oscillation of a heated wall with such a poor Richardson number is optimal heat transport in the cavity. The presence of undulations minimizes the cavity area; the case N = 3 makes quicker fluid motions and better heat transfer in the present research. Additionally, the interior obstacle size reduces the amount of space it takes up within the wavy cavity, and it was observed that the obstacle with diamond size D = 0.15 is better than that with any other size.

1. Introduction

It is fascinating to learn about the mixed convection technique with a lid-driven cavity since it has so many applications, including crystal growth, electrical devices, energy transmission between rooms and units, cooling of industrial machinery, nuclear reactor technology, and food processing [1–3]. The force of convection and natural convection, both of these factors, contribute to mixed convection. Several research papers on mixed convection have been considered with various geometry types. Ali et al. [4] established the heat transmission speed is dominant with a higher Ri and a lower Ha. The Richardson and Hartmann numbers have been discovered to significantly impact the flow structure and field of temperature. Azizul et al. [5] analyzed the heatline visualize on mixed convection apparatus and heat transmission in cavity with double lid-driven. Also, compared to the flat surface, the undulations number significantly influences the streamlines and isotherm. The result shows that a single wavy surface oscillation achieves the most effective heat transport in the cavity with low Ri.

The transport technique of laminar mixed convection is explored numerically in shear- and buoyancy-driven setup with a generally hot lower wall and progressively cold sidewalls by Aydin and Yang [6]. Al-Amiri et al. [7] mixed convective and heat transfer processes within a lid-driven chamber with a bottom-heated curved wall were taken into consideration. Their research used the Galerkin method to solve equations using the finite element method (FEM) formulation. They also discovered that heat transport was optimized due to two undulations with low Richardson values. Rahman et al. [8] established a strong thermal field and flowed dependency on the magnetic field. Basak et al. [9] explored mixed convective flow in a lid-driven cavity with a porous substance. Nasrin [10] numerically investigated the mixed convective flow and heat transport in a lid-driven cavity with a sinusoidal wall. Saha et al. [11] investigated various dimensionless groups. The lattice Boltzmann approach is used to analyze flow through four square cylinders placed in an in-line square contableuration in 2D numerical research. A similar issue with wavy wall, discovered an important application in several technical fields [12–16]. Omari [17] studied mixed convective flow in a lid-driven cavity while heat transfer was improved by reducing the aspect ratio raising the Re. Hossain et al. [18] researched the fluid object of the dust with a magnetic field and a heat source, radiation, etc. Khanafer et al. [19] studied the impact of heat transport on mixed convection in heated cavity with two rotating cylinders. Sarkar et al. [20] analyzed magnetohydrodynamics (MHD) mixed convective in lid-driven rectangular cavities with wavy top wall and bottom heater. Geridonmez and Oztop [21] hydromagnetic behavior influence of mixed convective flow and a uniform partial magnetic force are analyzed in a lid-driven cavity. Hossain et al. [22], the flow of MHD mixed convective in a lid-driven trapezoidal enclosure with nonuniform lower wall heating numerically analyzed. The numerical computations were performed over a wide variety of parameters, including Re , Pr , Ra , and Ha for various rotations of a heated triangular obstacle. When a magnetic field is present, Ali et al. [23] use the heat transmission and fluid flow characteristics of mixed convection in a chamber with two lids and a heat-conducting solid impediment to numerically investigate. Recently, Fayz-Al-Asad et al. [24], Fayz-Al-Asad et al. [25], Majeed et al. [26], Islam et al. [27], and Rehman et al. [28] studied the convective heat transport in various enclosures using Finite element analysis, A numerical analysis was carried out on the impact of mixed convective heat transport on a bottom wavy wall in a lid-driven cavity heated from the top.

A heatline approach, first described by Kimura and Bejan [29], can be used to illustrate convective heat transmission. The method they utilized is based on an energy analog in fluid flow velocity and temperature circulation. The heatline can also be mathematically expressed by a heat function associated with the Nusselt number. Costa [30] also looked at heatlines; a heatline is similar to a streamline but visualizes net energy flow in a convection or conduction heat transfer situation and mass lines. Basak et al. [31] exposed streamlines, isotherms, and heatlines on trapezoidal chambers. Considering the impact of distinct surface heating, the problem of natural convection flow was numerically solved with biquadratic elements using the FEM. Moreover, a study of natural convection by Basak et al. [32] observed the heatline visualization in square cavities using FE approach. They discovered that the heatlines traveled from the temperature of cold wall, with a circulation of heatlines in a clockwise motion occurring in the bottom half of the hole, resulting in thermal mixing.

Meanwhile, Bondareva et al. [33] described the identical issue with a rectangular followed by a compact wall. The outcome was that increasing the significant wall thickness decreased the average Nusselt number. They agreed that using visualization and analysis tools to visualize and analyze heat transport was beneficial, and it quickly became a hot topic of forced convection heat transfer in the research area.

Depending on the results of the previous surveys, researchers have yet to investigate the effects of a double lid-driven cavity on mixed convection. Although new investigations have yet to be investigated, there are a variety of challenges among several geometries of enclosures, including varying temperatures. As a result, the current research examines how heatlines can be used to visualize a heated bottom wavy wall and adiabatic upper lid-driven cavity. When it comes to studying heating solutions for cavities with wavy surfaces, the heatline approach is very useful. Cooling wavy solar panels, nuclear reactor technology, electronic chips, and manipulating materials are just a few of the engineering possibilities for such a method. Therefore, the heatline visualize on mixed convective flow inside a heating bottom wall and upper wall adiabatic lid-driven cavity are investigated in this study, and an inner obstacle is inserted inside the cavity. As a result, this research investigates the isotherms, streamlines, and heatlines of heat transport while adjusting nondimensional parameters of Re, Gr, undulations number, and obstacle size. So, in this proposed study, a numerical investigation of heatlines on mixed convective heat transport in a lid-driven cavity having heated wall with a tilted square obstacle will be carried out.

2. Mathematical Framework

A 2D geometric model of mixed convective heat transport in wavy lid-driven cavity with sides of length, L, and having inner obstacles with length, D, is depicted schematically in Figure 1. The bottom wall is heated (T_h) and develops a sinusoidal shape of the type of cos (2Nπy), where N is undulations number. The hollow’s two vertical walls are kept at T_c, but the top wall is allowed to move at a constant speed from left to right. The hollow is surrounded by water, and its borders are thought to be impenetrable. The dimensionless parameters are calculated using the Boussinesq approximation. The prior presumptions are used to obtain the governing equations of continuity, momentum, and energy for laminar and steady-state convection:

Continuity equation

Momentum equation

Energy equationswhere u and v are velocity components through x and y are represented by the Cartesian coordinates of the vertical and horizontal planes, respectively. β is the volumetric thermal expansion coefficient, σ is the electrical conductivity, B₀ is the magnitude of a magnetic field, and is the thermal diffusivity.

2.1. Nondimensional Boundary Conditions

The boundary conditions for the current phenomena are definite as follows: On the bottom wavy wall: At the top moving adiabatic wall: At the left and right vertical wall: where A is the amplitude and N is the undulation number.

Now, we are using the following parameters, the governing Equations (1)–(4) can be converted to the dimensionless forms:

Here, the dimensionless quantities X and Y are the coordinates along horizontal and vertical directions, respectively, U and V are the velocity properties along the X and Y directions, respectively, θ is the temperature of fluid and P is the nondimensional pressure, and is the temperature difference and α is the thermal diffusivity.

The bottom wall of a sinusoidal form is thought to resemble the following pattern. , where A denotes nondimensional amplitude of the wavy surface and N is the undulation number.

The following nondimensional equations are obtained by substituting the dimensionless variables into Equations (1)–(4):

Continuity equation

Momentum equation

Energy equations

The nondimensional parameters are the Prandtl number (Pr), Grashof number (Gr), Reynolds number (Re), and Hartmann number (Ha).

2.2. Nusselt Number

To determine the heat transfer rate, it is required to calculate the Nusselt numbers. First, conduction heat transmission was compared to convection heat transfer.

Equation (11) is adjusted to include the nondimensional variables and the local Nusselt number is defined as follows:

On the temperature of cold wall, the average Nusselt number is calculated as follows:

Also, the expression of a heatline is used as follows:

3. Numerical Technique and Model Validation

The Galerkin weighted residual approach with FEM has been employed to solve nondimensional governing equations (Equations (7)–(10)) with the help of boundary conditions. The following method is used to perform the momentum equations’ finite element analysis (Equations (8) and (9)):

Using the finite element penalty approach in order to remove pressure (P) along with the penalty parameter () defined as follows:

Equation (15) yields to the momentum equations listed below:

And then, the modified momentum and energy equations take the new form as represented by Equations (16) and (17). Applying the boundary conditions in Equation (11) and Equations (16) and (17) together with Galerkin finite element approach, the solution has been determined. The interpolation functions have been approximated with the velocity elements u, v, and temperature distributions (θ) by employing the basic set as follows:

The Nonlinear residual equations (Equations (11), (16), and (17)) converted into the following form and employing the residual finite element technique with Galerkin weights internally oriented (Ω):

Here i, q, and r are the residual, nodes, and number of iterations, respectively.

Through the use of the Newton–Raphson iteration method, the nonlinear elements of the momentum equations are clarified. The percentage error to any variables fulfilling the following convergence conditions allow to converge the solution:

The momentum equations weighted-integral representation is produced by multiplying the equation with an internally oriented domain Ω and integrating it across the computational domain.

The Newton–Raphson approach has been implemented via PDE solver with MATLAB interface to solve the sets of global nonlinear mathematical equations in the form of a matrix. The convergence of solutions is considered when the percentage error for each variable across consecutive iterations is less than the convergence criteria, such thatwhere n is the iteration number and . The convergence technique was set to .

The experimental and numerical analysis are compared of Islam et al. [34] to validate of the current work, as shown in Figure 2 for natural convectve heat transport in a prismatic enclosure. For ensuring more accuracy of the solution, a comparison was made within the attainment of the average Nuselt number (Nu_av) from study by Pirmohammadi and Ghassemi [35], and Jani et al. [36] with the current investigation as shown in Table 1. The Nu_av has been calculated at Ra = 10⁴ and 10⁵ for different Hartman numbers. It can be shown from 1 that an average Nusselt number demonstrates great agreement between these two experiments.

4. Mesh Generation and Grid Independency Test

Grid dependency analysis was conducted to evaluate the correctness of the numerical solution. To establish the numerical findings verification, the grids of various sizes have been analyzed, as illustrated in Figure 3. To assure the independency of the solution, the models were designed by using five different grid sizes for the computational domain (Figure 4). The mean Nusselt number (Nu_av) was calculated for several elements are presented in Figure 4. Based on the results obtained from grid dependency test simulation, insignificance differences in the adjacent the grids G4 and above were observed. To reduce computational cost and optimum accuracy of the solution, the grid G4 was used to generate reliable results. Therefore, the G4 grid was considered to solve the underlying models for this study unless stated otherwise.

5. Result Discussion

5.1. Effect of Reynolds Number

Figure 5 shows the impact of streamlines, isotherms, and heatlines for Pr = 0.71, Ri = 10, N = 3, and D = 0.15, while the left wall and right wall move upward and downward, respectively. When the right cell spins counterclockwise and another cell rotates counterclockwise on the left side of the cavity, there are two distinct flowing vortices. The low Re generated a powerful viscous force that forced the fluid flow to follow the motion of the top lid-driven surface. The flow depicted at Re = 100 in Figure 5(Ψ) is controlled by the laminar flow and begins to move with a significant inertia force. Increasing Re to 250 causes the tiny eddy flow to circulate from the left side to the cavity around the diamond-shaped obstacle. Due to the increase in inertial force within the cavity, several vortices were generated, and the velocity of the fluid’s circulation slowed. As seen in Figure 5(θ), the contours of the temperature distributions reveal that heat is transported from the undulating hot bottom wall to the cool walls. At low Re, the isotherms have an essentially asymmetric shape that occupies the entire cavity above two diamond-shaped obstacles. Because of the greater temperature variation, a rise Re results in a highly compressed plume pattern between the first and third oscillations. For the heatlines visualization, Figure 5(Π) is demonstrated. Two path circulations occur inside the cavity, transporting heat from the left and bottom interfaces. The enormous right circulation cell shrinks steadily and concentrates in the upper part of the wavy cavity as the Re rises. The density of heatlines rises as the Re increases, lowering the intensity of the heat flow. The heat transfer rate rises as Re increases, as seen in Figure 5. As the Re rises, the anticlockwise cell on the left cavity becomes increasingly evident.

Figure 6 depicts the impact of modifying the Re on heat transfer contacts with the oscillating bottom wall for Ri = 10, Pr = 0.71, and N = 3. For the local Nusselt number, the contour routes are ranked from Re = 10 to Re = 100, 250, and 500. This sign indicates that increasing Re improves the distribution of the local Nusselt number. This graph trend has a sinusoidal pattern for all Re, reaching its maximum faster around the local Nusselt number edge than in the prior case. Because of the existence of lid-driven laminar force from the wavy bottom wall to side wall, heat convection manipulates the process. The fluid in upper area follows the top lid motion, as indicated by the stream function’s negative values. In addition, results indicate the local Nusselt number falls with increasing Re and reaches a minimum at Re = 500.

Along the wavy wall, the five graphs form a symmetry transition trend. Figure 7 depicts the impact of the Re on the surface of four undulations. The low Re, ranging from 10 to 50, gives the same mean Nusselt number as the wavy wall. Following that are Re = 250 and Re = 500. It demonstrates that a larger Re results in better heat transfer performance for the cavity. The average Nusselt number progressively rises because the maximum height of the heat convection is largely concentrated along both edges because of the movement of the top lid.

5.2. Effect of Richardson Number

Generally, the Ri influences the kind of convection heat transmission inside the cavity. For a lower Ri, i.e., Ri = 0.01, mixed convection predominates the structure inside the lid-driven cavity, as seen in Figure 8(Ψ). The buoyancy force is generated by the outer two cells of circulation to combine, which can result in fluid density and thermal temperature variations. In contrast to Figure 8(Ψ), the middle of the undulating wall is heated that of the surrounding area of the obstacle, and the isotherm distributions shift smoothly. At Ri = 1 and 10, the outer two cells begin to detach from one another. Due to mixed convection, the circulations of isotherms and heatlines shown in Figure 8(θ) and Figure 8(Π)) are not obviously changing. Moreover, the streamlines and heatlines indicate that flow circulation is increasing, as well as the isotherms show that mixed convection predominates. When the Ri approaches infinity, the forced convection effects the heat transmission, which may cause several cells of rotating to occur in the cavity’s center and between its wavy wall. Because of internal factors and the flow shear effect, the isotherms display a dismal line within the wavy wall. As a result, the visualization of the heatlines is identical to the visualization of the streamlines, and the left circulating cell is larger compared to the other circulations. It has been found that mixed convection dominates the mechanism of heat transport at low Ri. On the other hand, natural convection predominates when the Ri is high. Thus, the streamlined contour across the cavity region produces respective primary vortices when the Ri stays equal to or larger than unity.

The results of different Ri on the wavy bottom wall for local heat transfer for Re = 100, N = 3, and Pr = 0.71 are interpreted in Figure 9. The maximal stream in the hot–cold connection appears to be a similar goal in five examples of Ri. Because of the greater heating impact of shear force at Ri = 10, all the supreme edges are modified. The upper curve indicates the proportion of heat transmission remains exceptionally high towards the borders before gradually diminishing inside a sinusoidal pattern and beginning to grow toward the wavy bottom walls center. Significant heat flux adjacent to the temperature of hot–cold wall junction, impacted by an increase in magnitude from the heat function near the curved base turns, causes this behavior.

Furthermore, the heat transmission rate remains extraordinarily high toward the right edge before rapidly decreasing through the middle of the bottom wall. Due to the dominance of transmission heat transfer, the local Nusselt number distribution is virtually uniform, with a sinusoidal pattern that has a similar trend throughout the bottom wall, as shown by the heatlines. The local Nusselt number towards the intersection of the temperature of heated wall grows steadily in a sinusoidal pattern. Due to convection, the process is altered, allowing more heat pass into the cavity.

The influence of changing oscillation number N on is shown in Figure 10(a), and that of different Pr is demonstrated in Figure 10(b) with the Ri where Re = 100. The increases when the Pr grows, and the Ri rises. However, lower wavy wall oscillation results in the highest , which is associated with the development of the Ri. The grows as the Ri increases, as shown in the graph.

(a)

(b)

5.3. Effect of Prandtl Number

The effect of the Pr on the isotherms, streamline, and heatlines contours is displayed in Figure 11 for Re = 100, Ri = 10, H = 10, and N = 3. The streamlines demonstrate in Figure 11(Ψ) that two circulations are produced at Pr = 0.01 to Pr = 1 and merge into many circulations at Pr = 10. The streamlines yield two vortices of circulation together with clockwise rotation. However, in Figure 11 (θ), the circulation of isotherms transfers linearly because of thermal diffusivity, and this procedure is known as conduction. As the Pr rises, the circulation becomes complex by the diffusion of momentum. As a result, the Pr strongly influences thermal diffusivity and the fluid momentum. The heatline in Figure 11(Π) displays cell at the bottom of two adjacent cavities. It begins to produce more significantly as it moves toward the sidewall of the cavity. It is obvious from Figure 11 that thermal diffusivity prevails when the Pr is less than 1, and most of the heat transfer happens through conduction. A convection process with momentum diffusivity happens when the Pr is greater than one. So the convection of heat transfer inside the wavy cavity is controlled by the value of the Pr.

Due to decreased conductivity, the local Nusselt number in Figure 12 remains constant throughout the surface at Pr = 0.015 and 0.16. But at Pr = 0.7, the contour lines for the local Nusselt number begin to progressively climb, and at Pr = 1, the local Nusselt number exceeds the other Prandtl values. The local Nusselt number graph in Figure 12 also displays a sinusoidal form with the same trend, but Pr = 1 takes a larger local Nusselt number followed by Pr = 0.71, 0.16, and 0.015. This pattern demonstrates that the Nusselt number is larger when the Pr values are substantial.

Figure 13 depicts that the compares Pr along the wavy temperature of heated wall for various Re while maintaining a stable value for the remaining parameters. It is evident from this graph that increases as the Re rises. At a fixed Re, a reduction in Pr increases buoyancy force and enhances heat transfer.

5.4. Effect of Inside Diamond Size (D)

Figure 14 (Ψ–Π) delimitates the impacts of the inner two diamond-shaped obstacles on the streamlines, isotherms, and heatlines for Ri = 10, N = 3, Pr = 0.71, H = 10, and Re = 100. In Figure 14(Ψ), two circulation vortices occur in different cavity parts. The fluid in the top portion follows the top lid’s motion, which is confirmed by the stream function’s negative results. Rising D up to 0.10, there appear to be two separate revolving vortices inside the cavity. The area inside the hollow is constrained by the greater inner obstruction. Consequently, the fluid flows more rapidly. At D = 0.2, circulation is more intense than in the event of a modest inner obstruction. No heat transmission occurs within the innermost block. As the size of the inner obstruction rises, but the isothermal lines start to pass through the internal barrier.

The heat transfer starts from the hot bottom wall and is held on both vertical walls because the heat is transferred from the wavy heated wall and then released to the temperature of cold walls. As a result, the top right corner of the cavity has a clockwise eddy. A clockwise vortex starts to form at D = 0.15 and intensifies. In other words, a hollow with increased heat transfer efficiency is produced by enlarging the inner block size.

Figure 15 shows the as a function of the Re for different thicknesses of inner obstacle at Ri = 10 and N = 3. The lowest found is D = 0.2 at Re = 10, which starts to increase quickly as the Re rises. As expected, the increases in heat transfer rate are reflected by D = 0.05, 0.10, 0.15 at low Re. For Reynolds number less than 250, the decreases with the increasing Re. However, the curve for D = 0.20 crosses the curve for D = 0.15 at Re = 250, the curve for D = 0.10 at Re = 320, and the curve for D = 0.05 at Re = 375. Therefore, the rate of increase in is greater than that for D = 0.15, 0.10, and 0.05. It is obvious that the inner obstacle with D = 0.15, the rate of increase in heat transfer with an increase in Re is preferable to any other size.

5.5. Effect of Undulation (N)

Figure 16 (Ψ–Π) shows the impacts of undulations number on the streamlines, isotherms, and heatlines with Re = 100, Ri = 10, Pr = 0.71, and D = 0.15. The flow field in the whole cavity is formed by various distinct circulation cells. This behavior is indicative of a substantial buoyancy force, which is the control mechanism of mixed convection. Figure 16(Ψ) shows the clockwise eddies that have been seen at the walls at the top, bottom, and upper left. But when there are several undulations in the cavity, which can impede fluid flow and produce a variety of vortex orientations. This undulation can be shown by the presence of buoyancy force and the significance of stream function. A clockwise vortex produces multiple vortexes due to the reduced undulation numbers.

Meanwhile, the plume-like isotherm lines seen at the hollow in Figure 16(Ψ) at N = 0, 1, 2, 3, 4. demonstrated that heat began to move from the left side of the crater. The isotherm contour illustrates in Figure 16(θ) that the thermal flow transport heated temperature to the entire cavity, and the inner obstacle also transfers heat. The undulation numbers on the bottom wall have little impact on the streamline and isotherms, except on the right side of the bottom wavy wall. As illustrated in Figure 16(Π), the heatline travels from the bottom wall via the left wall, and in the center of the inner obstruction in the hollow, there is a symmetric anticlockwise longitudinal line. Due to the increasing number of undulations, multiple vortexes are produced near the right corner of the block.

Furthermore, a counterclockwise vortex appeared at the bottom left of the cavity. The case N = 3 yields the best performance heat transport in the system. Undulations decrease the cavity area, and we discovered that the value N = 3 produces better fluid motions. The study is therefore assumed to be complete when N = 3.

6. Conclusions

This study explored the impact of a heated bottom wavy wall inside a lid-driven cavity on mixed convective flow and heat transfer for various dimensionless parameters (Re, Ri, Pr, and N). The velocity and temperature profiles are investigated to determine the most remarkable heat transmission of a lid-driven wavy cavity.

The following are a few of the study’s key conclusions:(1)Due to the increase in Re, the rate of heat transfer is augmented. The maximum top of the heat convection is primarily focused on both sides due to the motion of the top lid, which causes Nu_av to rise slowly.(2)The rate of increase in heat transfer with the increase in Re for the inner obstacle with D = 0.15 is better than that of any other size.(3)With low Ri, mixed convection is the dominant mode of heat transmission. On the other hand, natural convection dominates when the Richardson number is high.(4)Due to the upsurge of Re, Ri, and Pr, the overall Nu_av is augmented.(5)When the Pr is less than 1, thermal diffusivity predominates, and most of the heat transmission occurs via conduction. When the Pr is bigger than 1, it results in a convection approach with momentum diffusion. That means the highest values of the Pr dominate the convective of heat transport inside the wavy cavity.(6)The existence of undulations reduces the cavity area, where the value N = 3 is better fluid motions.(7)The wavy bottom lid-driven square cavity considerably improves the heat transfer performance by enhancing convection within two diamond-shaped obstacles.

Nomenclature

g:	Acceleration of the gravity (ms⁻²)
:	Average Nusselt number
B₀:	Magnetic induction (Wbm⁻²)
:	Temperature of cold wall (sink)
T_h:	Temperature of heated wall (source)
P:	Dimensional pressure (Nm⁻²)
u:	Dimensionless velocity along x-direction
v:	Dimensionless velocity along y-direction
k:	thermal conductivity of the fluid (Wm⁻¹ K⁻¹)
Gr:	Grashof number
D:	Diamond size
L:	Length of the enclosure
Pr:	Prandtl number
Ri:	Richardson number
Re:	Reynolds number
X:	Horizontal coordinate
Y:	Vertical coordinate
T:	Dimensional temperature (K)

Greek Symbol

θ:	Nondimensional temperature
α:	Thermal diffusivity (m² s⁻¹)
Ψ:	Streamlines
Π:	Heatlines
β:	Coefficient of thermal expansion (K⁻¹)
ν:	Kinematic viscosity (m² s⁻¹)
ρ:	Fluid density (kg m⁻³)
μ:	Dynamic viscosity of the fluid (kg m⁻¹ s⁻¹)

Subscripts

h:	Heated
c:	Cold
av:	Average.

Data Availability

The study was based on numerical technique, and no data were used in the findings of the study.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The authors like to express their gratitude to the Bangladesh University of Engineering and Technology (BUET), Bangladesh, for providing financial support.

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Copyright © 2023 Md. Yousuf Ali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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