Investigating the thermodynamic optimization of naturally convective flow in a corrugated enclosure: The influence of gap spacing and orientation of split baffles

The natural convection in cavities is frequently used in fluid mechanics and heat transfer engineering, such as heat exchangers, electronics, solar collectors, and growing crystals. However, the physics of natural convection flow and heat transfer in cavities with split baffles is least understood. The fundamental aim of this research is to investigate the impact of heated split baffles positioned at various locations on steady-state free convection within a sinusoidal corrugated star cavity. In this model configuration, the outer wavy enclosure is maintained at a constant temperature of Tc, while the inner split baffles are heated at a constant temperature of Th. The finite element method is employed to discretize and solve the governing equations describing the fluid flow and heat transfer within the enclosure. This numerical approach aimed to analyze the effects of baffle inclination angles, baffle spacing, Rayleigh number on the fluid dynamics and convective thermal transport characteristics. The variation in velocity and temperature profile is illustrated through the streamlines and isotherm contours. Moreover, the numerical result is displayed in term Nuavg of the heat transfer, which are analyzed for inside space of baffles and angles of the baffle (θ=00,450,900). The key finding demonstrates that increasing the Rayleigh numbers and the different positions (up, central, down) of inner vertical split baffles enhances the magnitude of the velocity by 88.1%, 85.9 and 89.6% respectively. Furthermore, for the inner rectangular split baffle angles of 0°,45°, and 90°, and within the Rayleigh number range of 104 to 106, the Nuavg exhibits significant variations, with maximum increases of 71.9% , 46.7% and a subsequent decrease of 45.9%.


Introduction
The phenomenon of natural convection thermal transport in the chamber has been investigated in recent decades, especially during * Corresponding author.
Contents lists available at ScienceDirect the rapidly developing electronic components industry.This natural convection setup is prevalent in various practical applications, including heat exchangers, electronics or LED cooling heat sinks, solar collectors, crystal growth, etc.The geometry with obstacles in the cavity is discussed by Mahdi et al. in Ref. [1].Roy and Bask [2] investigated free convection in a corrugated enclosure with a warmed thin rectangle plate.Atayilmaz and Teke [3] used finite elements to analyze free convection flows within a square cage featuring non-uniformly warmed walls.Reymond et al. [4] investigated natural flow around a heated horizontal surface through numerical simulation and experimental methods.Esam and Alawadhi [5] discussed that natural convection facilitates the transfer of heat between the two horizontally oriented cylinders.Bhowmik and Tou [6] presented the convectional flow in a horizontal ring with periodically fluctuating interior cylinders, which is investigated using Lagrangian and Eulerian kinematics.Bocu and Altac [7] investigated thermal transport and entropy generation in a chamber stuffed with nanofluid under the impact of a Hartmann field computed by neural networks.Heindel et al. [8] explored the experimental examination of the transient free convection heat transport from simulated electronic circuits.Khalili et al. [9] studied the effects of laminar unforced convection on thermal transport and airflow in three-dimensional rectangular cages with fixed arrays attached to the hot wall.Sheikhzadeh et al. [10] analyzed the conversion of the flow of air caused by free convection from several separate heat sources.Ho et al. [11] examined the free convection of an Al2O3 nanofluid between two horizontal cylinders bounded by a circle.Dai et al. [12] explored the effect of shape on magneto-convection in a square container with a low Prandtl number.Adlam [13] studied the convection caused by the atmosphere of the Earth within two horizontal containers having an adiabatic spherical boundary.Park and Change [14] discussed a cylinder container and free convection among both warm and cool microtubes.Fujii et al. [15] analyzed time-dependent free convection within a chamber containing interior bodies in a two-dimensional.Chowdhury et al. [16] investigated turbulent nanofluid flow in a channel with triangular vortex generators computed by using artificial neural networks.Saglam et al. [17] showed a computational analysis of the interaction of laminar free convection generated between a pair of vertically spaced horizontal containers.Altaee et al. [18] examined the natural air convection from a collection of vertical parallel plates with distinct and projecting heat sources.Oztop and Abu-Nada [19] investigated unforced convection in a permeable triangle cage with a circular obstruction under thermal generation.Radhwan et al. [20] studied free convection in a chamber with two separate heat sources.Yesiloz and Aydin [21] discussed the unforced convection inside of a square enclosure, which holds an equilateral triangle in various orientations.Al-Zuhairy et al. [22] conducted a numerical investigation on free convection in rectangular, substantially warmed, nanofluid-filled spaces.Al-jabair and Habeeb [23] analyzed laminar free convection in a square container with distinct perpendicular wall warming.Khalili et al. [24] investigated free convection in a quadrantal inclined chamber with adjacent walls heated and cooled.Santra et al. [25] explored a numerical simulation of the transfer of heat phenomena within a constrained square chamber.Elatar et al. [26] modeled free convection in concentric annuli, featuring an inclined square chamber on the outer side and a horizontal cylinder on the inner side.Nakhi and Chamka [27] studied a square cavity employed in an experiment to examine the distribution of nanocrystals in the free convection of Al2O3-water nanofluid.Shi et al. [28] used the L-shaped cavity to simulate the transport of the red blood cell by FEM.Sahib et al. [29] examined the use of a copper-water nanofluid to improve heat transmission in a square hole that is being heated differentially.Sheikhzadeh et al. [30] analyzed laminar free convection in a rectangular container with a single horizontal fin.Oztop et al. [31] studied the effect of a thin fin's width and tilt on free convection in a square container.Jabbar et al. [32] presented that a thin fin on the wall of a differentially warmed square chamber causes laminar unforced convection, which is the process by which heat is transferred.Sankar et al. [33] investigated the unforced convection process within a nanofluid-filled square chamber, taking into account the influence of interior entities.Nardini et al. [34] studied the nanofluid naturally convection in a hollow with partially active side walls.Bilgen [35] analyzed the influence of non-isothermal variation in temperature on free convection in nanofluid-filled cages and investigated it using computational methods.Bhattacharya and Das [36] used CFD to evaluate unforced convection in a square cavity with two narrow baffles of different lengths and placements on the hollow's vertical walls on opposing sides.Asif et al. [37] presented the impact of a thin baffle's size and placement on free convection in a vertical annular enclosure.Saha and Gu [38] studied free convection in a square hollow with two baffles on the vertical walls, which was investigated experimentally and numerically.Varol and Oztop [39] proposed natural convection in buildings with part-wall enclosures.Holtzman et al. [40] studied the constant natural convectional heat transfer in a square chamber for various Rayleigh and Nusselt number values.Kandaswamy et al. [41] analyzed the heat transfers within an enclosure that is rectangular and has baffles.Ghalambaz et al. [42] studied the analysis focusing on the unforced convection of a suspension containing nano-encapsulated phase change materials within a permeable medium.Mehryan et al. [43] discussed a numerical study employing the Arbitrary Lagrangian-Eulerian (ALE) approach to investigate the unsteady unforced convection occurring within an inclined square chamber divided by a flexible impermeable membrane.Ghalambaz et al. [44] examined the free convection phenomenon and studied the fluid-structure interaction within a square chamber partitioned by a flexible membrane and subjected to sinusoidal temperature heating.Zadeh et al. [45] investigated the natural convection induced by a warmed plate within a chamber, focusing on elucidating the impact of plate flexibility on fluid flow and thermal transport characteristics.Ghalambaz et al. [46] analyzed the convective thermal transport and creation of entropy within a chamber containing a suspension of nano-enhanced Phase Change Materials (NEPCM).Furthermore, comprehensive research in Refs.[47][48][49][50] aimed to simulate and analyze a nanofluid's free convection thermal transport within a quarter circle and a three-dimensional enclosure.They employed the lattice Boltzmann and mEDAM approaches, the graphical results validated the numerical simulations, and the obtained results were illustrated graphically.In this paper, the main objective is to analyze three instances of (Ra) involving a thermal transport issue within a star chamber with rectangular split baffles.The impacts of the split baffle with different angles and positions on the fluid flow characteristics and heat transfer rate are simulated.Further, this work determines the best way to install the plate arrays in the cavity to enhance free convection thermal transport and provides a practical reference for engineering applications.
Novelty: The novelty of the present work is to fill the research gap by analyzing natural convection within a star-corrugated enclosure with split baffles.The study focuses on exploring the influence of surface roughness on natural convection due to the A. Ali et al. unique configuration of the corrugated cavity and assessing the effectiveness of split baffles.It also investigates the novel aspect of the interior space of the baffles and the variation of angles ( θ = 0 0 − 90 0 ) within the enclosure, which could potentially impact convective heat transfer.The Finite Element Method (FEM) is employed for numerical calculations, and flow visualization results are offered as isotherms and streamlines contours.Additionally, average Nusselt numbers for the hot walls were calculated and examined numerically.
Applications: The mathematical model of a star corrugated cavity with split baffles has several physical applications (see Fig. 1).Here are some examples: Heat exchanger: The geometry of the star corrugated cavity with split baffles has practical applications in heat exchanger design.It can enhance convection to improve efficiency across various sectors, such as HVAC, automotive cooling, and industrial heat recovery.
Electronics cooling: The model has the potential to be applied to cooling systems of heat exchangers, electronics cooling, thermal management in buildings, and renewable energy systems.
Wave energy converter: Corrugated surfaces may be explored in wave energy conversion technology, utilizing the dynamic movement of water to generate electricity in a sustainable and renewable approach.
Solar Collectors: The design with star-shaped baffles can enhance solar collector performance by improving heat transfer and fluid flow, resulting in increased thermal efficiency.
The rest of the paper is distributed as follows: In section 2, we discussed the problem description.In section 3, we formulated the mathematical model of our physical problem.In section 4, we discretized the mathematical model by the finite element procedure.In section 5, we illustrated some numerical experiments to analyze our proposed study.In the last section, some conclusion remarks are presented to conclude the impacts of our research work.

Problem description
In this problem, we discussed the natural heat convection in a star-shaped corrugated cavity with rectangular split baffle.The split baffle is heated with temperature (T h ), whereas the enclosure's exterior walls are set to be cold with temperature (T c ).The boundary conditions for velocity on its surface are considered to be non-slip.The fluid with Prandtl number (Pr = 7.0) is considered in the star  corrugated enclosure.We assume that the fluid has constant density (i.e., the fluid is incompressible).The fluid in the aforementioned cavity dependent on temperature and can compute the changes in temperature and the fluid is independent of pressure changes.In this work, we insert the rectangular split baffle in the positions as up, center, and down in the cavity.The Rayleigh number parameter is presented (10 4 − 10 6 ) for the solution of the proposed partial differential equations.The problem is assumed to be in a steady state with laminar flow.The Boussinesq approximation is used to formulate the mathematical model which induces the natural convection term in the flow.The physical description of the anticipated physical domain of the star corrugated enclosure having inner split baffle is presented in Fig. 2.

Mathematical formulation
In the current mathematical model, the thermo physical properties, density fluctuations, and body forces are presented in the term of momentum equation.The Boussinesq approximation is employed to describe fluid characteristics, establishing a relationship between density changes with temperature and the coupling of the temperature field to the flow field.The governing equations for the steady state free convection flow employing energy, momentum, and mass equations are as follows [53,54]: (1) The associated boundary conditions for (1) − ( 4) are: Where the x and y are the lengths evaluated horizontally and vertically, respectively.The velocity ingredients along the x and y directions are indicated as u and v, respectively.T represents the temperature; v and α represent kinematic resistance and thermal conductivity, respectively; p and ρ represent pressure respectively.The T h and T c are the temperatures at the hot and cold walls, respectively.
Using the following non-dimensional variables [55,56]: Using the non-dimensional parameters defined in equation ( 6), the dimensional governing equations ( 1)-( 5) can be converted into their respective dimensionless representations [53,54]: With the non-dimensional boundary conditions, Dimensionless coordinates X and Y fluctuate along the horizontal and vertical axes.U and V depicts dimensionless velocity ingredients in the X and Y directions; while θ represents temperature; P is stand for pressure; and Ra and Pr are Rayleigh and Prandtl numbers, respectively.The transfer of heat coefficient is described in terms of the local Nusselt number (Nu Local ) and the mean Nusselt number (Nu Avg ), as follows: where n represents the normal direction on the plate.

Galerkin procedure
The Galerkin finite element procedure is used to solve the equations (8 − 10) of the momentum and energy equations.The continuity equation ( 7) is utilized as a constraint to generate the pressure distribution due to the mass conservation [2].We utilized the penalty finite element method to solve equations (9) − (11), where the pressure P is reduced by an extra parameter and the incompressibility constraints specified by equation (7) (see Reddy [2]) which generates as follows, The continuity equation ( 7) is obviously valid for the big values of γ.The prevalent values of γ produce a reliable result is 10 7 [2].By employing Eq. ( 13), the momentum dimensionless equations ( 9) and ( 10) are reduced as follows,

U
∂V ∂X The velocity ingredients (U, V) and temperature (θ) are expressed by employing basis set {∅ k } N k=1 as follows: The nonlinear residual equations for Eq. ( 14), ( 15), (16), and (10) were generated by the Galerkin finite element method at the nodes within the internal domain.Ω: The integrals in the residual equations are evaluated by using Gaussian quadrature for the three-point bi-quadratic basis functions.The second term carrying the penalty parameter (γ) is assessed with two points in Eqs. ( 17) and (18).Eq. ( 18)− ( 19) are residuals which are represented in the matrix-vector representation by finite element procedure as follows: K 1 , K 2 are the matrices derived from the Jacobian of the residuals where an indicates the indeterminate vector.The constraint equation is well satisfied, as γ occurs to a significant plenty (∼ 10 7 ).The result of the extension of the K 1 is negligible (use Eq. ( 20)) when compared to γK 2 .
This means that as γ approaches infinity, the governing equations are reduced to just the constraint condition, which is the continuity equation.Furthermore, because K 2 is nonsingular for large γ, the solution obtained from Eq. ( 21) is trivial.To achieve nontrivial solutions for large γ (∼ 10 7 ), K 2 must be a singular matrix.This is accomplished by applying two-point Gaussian quadrature for K 2 and three-point Gaussian quadrature for K 1 .
The Newton-Raphson method is applied for solving the nonlinear residual equation ( 17) − (19) in order to ascertain the expansion coefficient in Eq. ( 16).The linear (3 N × 3 N) system is illustrated at each iteration.
where n denotes the number of iterations index.The Jacobian matrix element J(a n ) contains the velocity component derivatives of the residual equations, and the residual vector is represented by R(a n ).Convergence criteria are used to determine the point at which the iterative process should end The iso-parametric mapping technique uses a nine-node bi-quadratic element in the two-dimensional X − Y plane.It is based on a unit square domain in the ξ − η plane and incorporates nine-node bi-quadratic basis functions to enhance the analysis of internal domain features in the residual equations.
The local bi-quadratic basis functions Φ i (η, ξ) are defined over the ξ − η domain.The integrals in Eqs. ( 17)-( 19) can be computed within this domain using the following relationships: Where ⃒ .The local Nusselt number on a surface (Nu Local ), defined in Eq. ( 12), utilizes the bi-quadratic basis set in the ξ − η domain for evaluating the normal derivative using Eqs.( 23) and (24).

Evaluation of stream function
The flow potential ψ are created from the velocity ingredients V and U, which is employed to convey the flow dynamic.For the two-   dimensional flow, the connection between flow potential, ψ and velocity ingredients are as follows [57]: That produce a singular equation [57]: According to the description of the stream function given above, the positive sign of ψ indicates anti-clockwise circulation, while a negative value of ψ signifies clockwise circulation.The Galerkin finite element approach produces the subsequent linear residual equation for Eq. ( 26) through the expansion of the stream function (ψ) with the basis set , and the incorporating the relationship for U, V from Eq. ( 16).

Table 2
Comparing present results with Afsana et al. [52] for MHD effects on Nu avg where P r = 0.733..  A. Ali et al.

Ra
Since there is no cross flow and the no-slip criteria holds true at all boundaries, ψ = 0 is employed as the residual equation at the boundary nodes.The bi-quadratic basis function is employed to compute the integrals in Eq. ( 27), and the temperatures ψ's are determined by solving the N linear residual equations given in Eq. ( 27).

Table 3
The numerical variation in Nu avg against Ra for the up horizontal splitting baffle in a star cavity.

Validity of mesh generation
Grid independence testing is a crucial component of numerical experiments employing the finite element technique.The goal of grid independence testing is to identify the mesh size for a particular problem at which mesh refinement has little to no impact on the solution.To demonstrate the reliability of the capitalized computational system, the average Nusselt number is calculated using Pr = 0.71 and Ra = 10 6 .Table 1 displays the statistics from this grid convergence test.Fig. 3. Shows a more compact computational grid with triangular inside and rectangular edges.While the number of elements and degree of freedom at various levels of refinement are shown in Table 1.

Validation of code
To assess the reliability of the simulations conducted using COMSOL software, a verification test was conducted, wherein the results of the current study were compared to those of a previous study with certain limitations imposed.A comparison between the current isotherms and streamlines with the previous work computational results of Mansour et al. [51] at Ra = 10 5 and Pr = 6.87 is shown in Fig. 4. The current outcomes and those obtained by Mansour et al. [51] are in good agreement.
Additionally, Table 2 provides a comparison of the Nu avg for the case of the Hartmann field's impact on free convection in a corrugated enclosure filled with nanofluid.The number of Prandtl is fixed at 0.733, and the numbers of Rayleigh (Ra = Gr × Pr) are 1.466 × 10 4 and 1.466 × 10 5 , respectively.The obtained outcomes for the Nu avg show good agreement with the results obtained by Afsana et al. [52], in which authors used the finite volume method (FVM) to solve the Navier-Stokes and energy equations.

Table 5
The numerical variation in Nu avg against Ra for the down horizontal splitting baffle in a star cavity.

Numerical experiments
In this section, we will compute several experiments to support our proposed study that how the heat is transferred naturally within a star enclosure with inner heated baffle via convection characterized by corrugated walls.Our main objective is to explore that how we can correlate the parameters to the impact of the temperature distributions and the intensity of streamlines.Additionally, we present viscous and thermal contour plots to facilitate a visual understanding of the natural convection patterns influenced by various factors.We employed a broad range of parameter variations, spanning from Ra = 10 4 to Ra = 10 6 , while holding Pr constant at 0.71, to clarify the particular changes in associated profiles.

Table 9
The numerical variation in Nu avg against for the Up inclined with angle 45 0 splitting baffle in a star cavity.that with an increase in Ra from 10 4 − 10 6 , the impact of buoyancy forces becomes more prominent, leading to significant changes in the isotherm patterns.Combining the baffles and higher Rayleigh numbers results in complex and intricate temperature distributions, indicating enhanced convective heat transfer and thermal mixing.The change in heat flux co-efficient versus deviation in (Ra) and (S) is envisioned in Table 3 wide range of (Ra) varying from 10 4 to 10 6 is selected.The different cases of splitting are discussed in organized manner.In this table the result of splitting baffles is enumerated in comparative manner with no splitting (S = 0) and with splitting space (S 1 − S 3 = 0.23 − 0.31).It is noticed that by increasing the (Ra) and (S), the Nu avg will up 17.231 and 33.632.In view of impact of splitting of baffles will be enhanced the Nu avg will be escalate 48% to 75% for the Up, Central and Down split baffle as shown in the Tables 3-5 in details.

Effect of Ra on streamlines and isotherms with vertical split baffles (UP, central, down)
Figs. 7 and 8 depicts the streamlines and isotherms at Ra = 10 4 − 10 6 , θ = 90 0 , and for different positions of split baffle (up, central, down).The heat transfer within the star cavity can be improved by the existence of vertically split baffle.By creating the vertical split baffle enhance the effective surface area available for the heat transmission and support the convective heat transfer.This result shows the better cavity cooling and heat dissipation phenomena.Moreover, the variation of the Rayleigh number effects the expanding of the vertical baffle spaces on the stream function and isothermal lines.The heat transfer rates and buoyancy-driven flows are high for the higher Rayleigh numbers.The effect of the split baffle on the flow and temperature distribution within the cavity become more noticeable as the Rayleigh number enhances as shown in the Figure 7 and 8.The Tables 6-8 show that when the vertical splitting of baffle (up, central and down) is increasing then the Nu avg is decreasing significantly.inner rectangular split baffles (up, central, down).For Ra = 10 4 − 10 6 , the velocity magnitude increases by 92.4%, 84.2%, and 69.8% for the up, central, and down positions of the inclined split baffles, respectively.The inclined split baffles disturb the flow pattern, which helps to create turbulence and better mixing.When the Rayleigh numbers are higher, buoyancy forces become more dominant, strengthening the convective currents.As a result, the combination of inclined split baffles and increased Rayleigh numbers leads to clearer and more defined temperature differences shown by the isotherms within the corrugated enclosure.
For the inclined split baffle, the details are shown in the Tables 9-11 the splitting of baffles increases, and then the average Nusselt number is enhanced.) and different spaces of vertical split baffle (up, central, down) on the Nu avg .As the baffle spacing increases (0.215 to 0.225), it leads to larger gaps between the baffles, allowing for more fluid flow and reduced obstruction.This results in decreased fluid mixing and reduced convective heat transfer, decline the Nu avg .Conversely, there is a significant escalate in the values of Nu avg .when Ra enhance from 10 4 , to 10 6 .Fig. 13 comprehensively compares different values of inclined split baffle spaces and their corresponding Nu avg ., plotted against a range of Rayleigh numbers.As the inner inclined split baffle spacing increases from 0.155 to 0.211, fluid circulation is enhanced, convective heat transfer is increased, and the Nu avg is raised.

Conclusion
In this research, we studied the effect of the interior space of plates and the variation of the angles of the baffles on heat transfer in a corrugated star cavity.We also investigated the correlations between the Nusselt number and Rayleigh number in different baffle positions.The findings can be addressed to draw a conclusion and make remarks for our proposed study.

Table 10
The numerical variation in Nu avg against for the central inclined with angle 45 0 splitting baffle in a star cavity.A. Ali et al.

Fig. 1 .
Fig. 1.Physical application of the star corrugated cavity in the form of Solar Collector and Heat exchanger devices.

Fig. 4 .
Fig. 4. Comparison of streamlines and isotherms of current work with previous computational results of Mansour et al. [51].

5. 1 .Fig. 7 .
Figs.5 and 6illustrates the impact of horizontal split baffles (up, central, down) and Rayleigh numbers (Ra) on the streamlines and isotherms.For = 10 4 − 10 6 , the maximum velocity magnitudes for horizontal split baffles (up, central, and down) are (1.1, 3.89, 16.38), (2.8, 6.02, 18.42) and (3.02, 13.85, 49.52) respectively.The presence of these baffles is evident in their disruption of the flow pattern and creation of additional flow paths, which in turn induce flow separation and reattachment.This disruption facilitates improved mixing and convective heat transfer.With increasing Rayleigh numbers, buoyancy forces become dominant, resulting in intensified convective currents and higher fluid velocities.The combination of these baffles and higher Rayleigh numbers synergistically enhances fluid motion, leading to an overall amplification in the velocity magnitude within the system.Fig.6 depicted

Fig. 11
Fig.11illustrates the influence of different spaces of horizontal split baffle (up, central and down) on the average Nusselt number against Ra with a fixed Pr = 0.71.As the Rayleigh number (Ra) upsurge from Ra = 10 4 to 10 6 , there is a notable growth in the values of the Nu avg .Additionally, when the baffle spacing increases from 0.23 to o.31, the Nu avg concurrently increases, and indicating a stronger convective thermal transport effect.Fig.12represents the impact of number of Rayleigh ( Ra = 10 4 , 10 5 , 10 6 ) and different spaces of vertical split baffle (up, central, down) on the Nu avg .As the baffle spacing increases (0.215 to 0.225), it leads to larger gaps between the baffles, allowing for more fluid flow and reduced obstruction.This results in decreased fluid mixing and reduced convective heat transfer, decline the Nu avg .Conversely, there is a significant escalate in the values of Nu avg .when Ra enhance from 10 4 , to 10 6 .Fig.13comprehensively compares different values of inclined split baffle spaces and their corresponding Nu avg ., plotted against a range of Rayleigh numbers.As the inner inclined split baffle spacing increases from 0.155 to 0.211, fluid circulation is enhanced, convective heat transfer is increased, and the Nu avg is raised.

•
Increasing the number of Rayleigh and different position of split baffles (θ = 0 o − 90 o ) enhances the strength of the fluid flow.• The heat transfer mode of convection will be dominant when the Rayleigh numbers increase.• The average Nusselt number (Nu avg ) for various spaces of the inner horizontal split baffle increases by 67.4% when S 1 = 0.23, 71.9% when S 2 = 0.27, and 82.5.4% when S 3 = 0.31, at Rayleigh numbers (Ra) from 10 4 to 10 6 .• The Nu avg is directly proportional to the Ra and inversely proportional to the vertical increase in split baffle spaces.• The average Nusselt number (Nu avg ) progressively increases when the baffles are in inclined positions (center, up, and down) for the baffles spacing rises from 0.155 to 0.211..

Fig. 11 .
Fig. 11.Variation of Nu avg for different space of horizontal split baffles (UP, Central, Down) against Ra.

Fig. 12 .
Fig. 12. Variation of Nu avg for different space of vertical split baffles (UP, Central, Down) against Ra.

Table 1
Variation in Nu avg against different refinement levels.

Table 4
The numerical variation in Nu avg against Ra for the central horizontal splitting baffle in a star cavity.
A.Ali et al.

Table 6
The numerical Variation in Nu avg against Ra for the up vertical splitting baffles in a star cavity.

Table 7
The numerical variation in Nu avg against Ra for the central vertical splitting baffle in a star cavity.

Table 8
The numerical variation in Nu avg against Ra for the down vertical splitting baffle in a star cavity.

Table 11
The numerical variation in Nu avg against Ra for the down inclined with angle 45 0 split baffle in a star cavity.
A.Ali et al.