Enhancing Engine Cylinder Heat Dissipation Capacity Through Direct Optimization (DO) Techniques

Abstract

Internal combustion (IC) engines are used widely as the primary power source for automobiles of all types, cars, motorcycles, and trucks. Because of the high combustion temperatures involved in the operation, the excess heat is removed by means of extended fins that increase the surface area for adequate cooling. Significant improvement in the heat dissipation characteristics of the engine cylinder can be achieved by optimizing the design of these fins. The aim of this study is to evaluate the thermal performance of engine cylinder fins using an analytical system of finite element analysis (ANSYS FEA) software, using a direct optimization (DO) approach to identify optimal fin design. Analysis shows that fin length and width play critical roles in improving cooling efficiency, lowering the maximum temperature within the cylinder to 549.46 K and enhancing total heat flux to 7225.31 W/m², which is a 25.87% increase from the generic design, capable of heating removal of 5740.22 W/m². The current fin design is effective but could be improved in heat dissipation, mainly at fin tips. To optimize thermal performance while minimizing material costs, a balanced fin dimension is recommended. Alternative materials, transient heating analysis, and experimental verification may be examined in the future to achieve a total understanding of fin geometry and behavior under real operating conditions. These insights lay a foundation to accelerate cooling systems development in the automotive, aerospace, and heavy equipment industries, where efficient heat transfer is key for performance and long-term durability.

1. Introduction

Internal combustion (IC) engines are indispensable components of a variety of applications including automobiles and industrial equipment [1]. The cylinder block is at the core of fuel combustion, producing high temperatures because of fuel combustion [2]. In extreme cases, the temperature can be as high as 2500 °C (or 4500 °F) during the combustion process [3]. That kind of intense heat can break down the lubricating oil layer that is needed to offset friction in moving parts. Lack of adequate thermal management results in a real risk of mechanical failure, for example, with components seizing, or welding closed, due to overheating [4]. Maintaining engine performance and durability, and preventing thermal-induced damage, requires efficient heat dissipation. Thermal loads beyond the limits of the engine can cause thermal stresses that reduce efficiency, increase the wear of engine components, and, in extreme cases, result in catastrophic engine failure [5]. Thus, improved cooling solutions should be developed to enable IC engines to run reliably under a long duration and at high stress. An effective method of enhancement of heat dissipation is the use of fins, i.e., extended surfaces that exponentially increase the area available for heat transfer [6]. The fins attached to the engine cylinder improve the heat transfer capability by improving convection and radiation heat removal more effectively, as shown in Figure 1.

The overall effectiveness of the cooling depends critically on the design of these fins including their geometry, material composition, and arrangement. Fin structures are important, though, because they not only offer a low-cost solution but confer substantial thermal performance without introducing large amounts of production complexity or cost [8]. Fins have been used as a widely adopted solution for heat dissipation in internal combustion engines; nonetheless, the design optimization of fins to specific application requirements constitutes a difficult engineering problem [9]. The reason for this challenge lies in the need to balance a number of objectives, including maximizing thermal efficiency, manufacturability, and production cost control. To address this complex question, this research uses direct optimization (DO) techniques [10] to systematically tune fin geometry and other key design parameters. The goal is to improve the thermal dissipation capability of the engine cylinder within practical manufacturing constraints.

The comprehensive thermal performance of various fin designs is assessed with the use of the advanced capabilities of the ANSYS FEA platform. The study focuses on investigating the insights generated in the different configurations to identify those that lead to the best heat dispersal efficiency design. The findings should address not only increasing the cooling efficiency of internal combustion engines but also serve as a valuable resource for guiding continued innovation in engine design for the automotive, aerospace, and heavy machinery industries. The present study takes a step further and optimizes the thermal performance of the engine cylinder fins on the basis of this foundation. Previous research has investigated many different fin designs and cooling strategies for internal combustion engines, but many studies have either looked at generalized configurations or focused on specific cases without a comprehensive optimization approach. Systematic refinement of the fin design parameters, geometry, and material properties through advanced simulations still offers a large margin for improving fin cooling efficiency. This study aims to fill these gaps by leveraging computational methods such as direct optimization (DO) in combination with finite element analysis (FEA) to push the boundary of heat dissipation capabilities in IC engines. In the following literature review, we examine the current literature dealing with engine cylinder fins and what has been achieved technically to bring us to this point. It will also identify unresolved challenges and future work areas and broadly frame the objectives and contributions of this current study. Babu et al. [11] carried out extensive simulation studies on the thermal behavior of engine cylinder fins based on the ANSYS finite element analysis (FEA) simulation package. To predict the transient thermal performance of a cylinder with fins they used parametric models that have variable fin thickness and geometry including curved, circular, and rectangular designs. Pro/Engineer was used for 3D modeling and the thermal properties of aluminum alloy 204 have been evaluated, which has a thermal conductivity range of 110–150 W/m·K. The findings also highlight the enhanced heat transfer capability of the cylinder block with different fin configurations and set forth the first foundational ideas on how the fin geometry affects thermal performance.

K. Angamuthu et al. [12] also studied alternative materials like magnesium alloy 6061 that have comparatively good thermal conductivity, and potentially better heat dissipation properties. This research underscored the value of material selection for maximum thermal efficiency in engine components, important information for our study. Mahek et al. [13] compared the thermal analysis of a Stirling engine with and without fins using ANSYS software. After examining a range of fin geometries and thicknesses, they found that rectangular fins yielded the best thermal performance, a result that is fully in line with our research topic. In the study by Avinash et al. [14], they studied thermal distribution and heat flux to thermal strains of the BAJAJ 150CC engine block, over different fin designs, using ANSYS. After developing a 3D computer-aided design (CAD) model with SolidWorks, they concluded with an optimized square-shaped fin with filleted edges and superior thermal characteristics, justifying their goal of optimizing fin geometry for maximum thermal efficiency. The cooling potential of stator lamination fins in radial permanent magnet motors was investigated by Dobzhanskyi et al. [15]. Their study maximized heat transfer by using computational fluid dynamics (CFD) and finite element modeling to identify optimal fin count and thickness. Their methodological approach to fin design has insight that rings true to our optimization efforts as exploring the interactions of fin design and thermal performance. The thermal performance of pin fins versus plate fins was analyzed by Saxena et al. [16] using ANSYS with particular attention to the role of surface perforations on the rate of heat transfer. Innovative fin configurations were found to be critical for improving thermal efficiency, a principle that our research is also focused on.

By varying the cylinder geometry, material, and profile, S.K. Mohammad Shareef et al. [17] quantified the thermal properties of engine cylinders using ANSYS Work Bench. Angular profiled fins were shown to produce the highest heat flux and lowest temperatures, indicating that fin profile optimization can significantly increase thermal performance. The effect of engine cylinder fin shape on heat transfer characteristics under forced convection conditions was studied by Agarwal et al. [18]. A consistently observed relationship with all shapes investigated was identified in regions of high heat transfer rates, located at diametrically opposite positions. The results show that the heat transfer coefficient and heat flux are significantly influenced by the flow patterns. The importance of understanding fluid dynamics for the design and optimization of the engine cylinder fins is highlighted by this research. Khan et al. [19] examined engine cylinder variations in fin thickness and material using ANSYS FEA simulations for a detailed analysis. The results reveal that conventional aluminum alloy fins heated up to 15.3% more than the magnesium alloy fins. This focus on both material and geometric variation in their study supports our research emphasis on material and geometric optimization of critical factors.

Chaitanya et al. [20] performed a thermal analysis of cylinder fins via ANSYS workbench, applying transient thermal behavior variables such as fin shape, material, and thickness. Aluminum alloy 6061 is found to have a higher heat dissipation capacity compared with aluminum alloy 204 by 5.4%, a result which is consistent with the material evaluations conducted in the study. Sandeep Gupta et al. [21] looked at different fin shapes ranging from convex and tapered to triangular or rectangular types in 3D modeling using SolidWorks and steady-state thermal analysis in ANSYS. The results show that convex cylinder fins provided improved heat transfer characteristics of 8.2%, highlighting how innovative fin shapes can enhance thermal performance, which is the aim of our study.

Kumaravelu et al. [22] studied the effect of different fin geometries (circular, pin, rectangular) on Stirling engine efficiency. The numerical analysis provided against previous studies was validated and revealed that fins had a positive impact on heat transfer rates as well as overall engine performance. Rectangular fins were proven to have the highest efficiency among fin types with 19.03% efficiency, mainly resulting from their large surface area and superior thermal properties. This research demonstrates the fundamental role of fin design in achieving thermal performance optimization in engine applications. Paweł Ocłoń et al. [23] conducted a detailed study of computational fluid dynamics (CFD) on the flow distribution in the tubes of a fin and tube heat exchanger. In addition, their structural analysis based on ANSYS was used to quantify the thermal stresses in the system. In particular, the introduction of a novel design for the heat exchanger manifolds contributed to a reduction in the tube wall temperature from 185 °C to 134 °C. This innovative design also resulted in a remarkable fivefold decrease in compressive stresses within the heat exchanger construction from 105 MPa to 23 MPa in the fin-and-tube heat exchanger manifolds, when compared with traditional fin-and-tube heat exchanger manifolds. These results demonstrate that advanced design approaches hold promise to improve the thermal performance and structural integrity of heat exchangers, and are relevant to our optimization objectives.

Sharon Z. Varghese et al. [24] performed an analytical study on a conventional circular type of fin array, where heat dissipation and material selection were focused upon. A non-dominated sorting genetic algorithm II (NSGA-II) was used to generate a set of optimal, Pareto-efficient designs for a 100 cc engine cylinder fin array subject to maximum heat transfer. Genetic algorithms combined with CFD analysis in this research are effectively combined to produce a robust optimization framework. The outcomes indicate that the proposed method is both efficient and reliable, and the proposed method has good potential to substantially improve the engine fin array optimization process. These findings are complementary to our research objectives, particularly the need for advanced optimization techniques to enhance the thermal management of engine components.

Nahum Y. Godi [25] investigated the impacts of geometric variations and hybridization on micro heat exchangers with cylindrical fins in order to improve thermal conductance. The study shows that half-hollow fins have 16.4% greater thermal conductance than solid fins, and only 0.14% higher than hollow fins in parallel flow. Half-hollow fins in counterflow can achieve 5% higher thermal performance than solid fins and 0.5% higher than hollow fins, giving insight into fin design optimization. Thus, considerable research has been conducted on the thermal performance of engine cylinder fins, but only limited work has been carried out to systematically optimize fin designs using advanced computational techniques. Previously, most studies have focused on analyzing the fin shapes and materials separately and ignored the convergence of multiple design parameters. In addition, existing research typically does not provide a complete evaluation of the effect of the design variation on heat dissipation characteristics in the context of real-world operating conditions. Thus, this study attempts to close this gap through the use of direct optimization (DO) methods to improve the design of engine cylinder fins to enhance their heat dissipation potential. The optimization of engine cylinder fin designs using direct optimization techniques is expected to offer a significant improvement in heat dissipation characteristics of internal combustion engines.

In particular, it is hypothesized that the optimized fin configurations will have higher thermal performance than conventional fin designs and ultimately provide an increased engine efficiency and longevity. It follows that the main research questions we are discussing are:

• How do different fin geometries and thicknesses influence the thermal performance of engine cylinder fins in internal combustion engines?
• What is the impact of various materials on the heat dissipation characteristics of optimized fin designs?
• How can direct optimization techniques be effectively applied to enhance the thermal efficiency of engine cylinder fins?
• What are the optimal design parameters (geometry, thickness, and material) that yield the maximum heat dissipation for engine cylinder fins?

Thermal management of the engine cylinder fins plays a key role in the performance of the internal combustion engine, as its ability to dissipate heat has a dramatic impact on the engine’s performance. Existing research attests to a higher heat dissipation introduced by fin configurations, yet extensive studies that utilize advanced computational methods, including direct optimization (DO), are severely lacking from the literature on the effects of fin configurations in enhancing the heat dissipation characteristics of engine cylinder fins. A significant gap that this research attempts to fill is by systematically evaluating and optimizing the fin designs using the ANSYS FEA simulation package. The objective is to estimate the best fin configuration that maximizes heat dissipation and, therefore, improves the overall engine performance and reliability.

2. Materials and Methods

In this study, the thermal performance of fins attached to a single-cylinder, 4-stroke, air-cooled internal combustion engine is analyzed. This type of engine is commonly used in smaller motorcycles and automobiles. The engine operates in an ideal mode at 1000 RPM, representing a low-speed condition with reduced fuel consumption and heat generation [26]. During this mode, the vehicle remains stationary, resulting in minimal airflow over the fins. As such, heat dissipation occurs primarily through natural convection, as is typical for idle conditions in such engines [27,28]. This section provides the approach used in this study to assess the thermal performance of the engine cylinder fins with the help of ANSYS workbench simulation software. The approach comprises several critical steps: formation of a 3D solid model, generation of the meshing, application of thermal boundary conditions, and configuration of solver setting [29]. All the steps are crucial to obtain maximum confidence in the simulation results, which is critical to making sound assessments of fin performance.

2.1. Development of the 3D Model

The first step is to build a precise 3D model of the engine cylinder with the integrated fin structures. The design modeler in ANSYS is used to create this model due to the robust interface needed to design complex geometries. The process captures the physical dimensions and configuration of the engine cylinder and its fins very accurately in terms of sketching and extruding techniques. This detailed representation of the geometry is necessary because even small variations in geometry can have a big impact on thermal performance. To ensure that the fin configuration matches industry standards, dimensions are drawn from the existing literature [30]. The importance of this approach comes from its ability to validate the model against real-world data, which increases the relevance of the results. The pattern tool is used to produce multiple fins, which facilitates the efficient replication of fin design based on the given parameters.

The design intricacies of the engine cylinder with fins are shown in Figure 2, which illustrates the CAD model. The importance of accurate geometry lies in its direct effect on thermal performance, because fin shape, size, and arrangement can noticeably influence heat transfer characteristics.

The specifications of the engine block are outlined in

Table 1. Engine block specification [17].

Parameter	Value
Stroke	49.5 mm
Bore	50 mm
No. of fins	6
Fin pitch (mm)	7
Fin thickness (mm)	3
Fin material	Cast iron

, which include stroke, bore, number of fins, fin pitch, thickness, and material. Cast iron is chosen as the fin material on the basis of its superior thermal conductivity and mechanical properties that optimally favor heat dissipation in the internal combustion engines [21].

2.2. Meshing the Model

After setting the geometry, the next important step is the discretization of the model through meshing. Hexahedral elements are chosen due to their efficiency in capturing complex geometries and maintaining numerical stability, where the model is discretized. Unlike tetrahedral elements, hexahedral elements enable better performance in thermal analysis, with superior accuracy and faster convergence properties. Standard thermal analysis requirements apply to the meshing process. For the accurate thermogradients capture, a mesh growth rate of 1.4 with normal inflation is used, which helps in preserving the mesh size near the boundaries in a gradual manner.

Furthermore, the transition ratio of 0.275 provides a smooth transition between different mesh regions and six layers of inflation improve resolution at critical boundary interfaces where heat transfer takes place. Figure 3 shows that the discretization leads to 84,569 elements and 100,259 nodes. High resolution in this fine mesh is critical to the analysis of temperature distribution and heat flux [31,32], both indicators of thermal engine cylinder fin performance.

2.3. Application of Thermal Boundary Conditions

Since the model is meshed successfully, steady-state thermal boundary conditions are applied for accurate simulation of internal combustion engine operating conditions. The thermal loading applied to the engine cylinder is demonstrated in Figure 4. The red-colored zone represents the temperature of 311.85 °C being imposed by the inner wall of the cylinder. This temperature was chosen based on values from the literature and real-world engine data, which corresponds to conditions in typical internal combustion engine conditions during peak operating. This temperature is used to maintain a realistic simulation of actual engine operation in order to assess the heat dissipation capabilities of the fins under high thermal loads.

An ambient temperature of 295 K and a convection coefficient of 5 W/m² are applied to the fins [33]. Modeling the heat transfer processes between the fins and the surroundings requires these boundary conditions, which are critical for modeling the thermal performance and cooling efficiency of the engine fins. The convection boundary condition is depicted by the yellow-colored zone in Figure 3, emphasizing the interaction between the fins and the ambient air, which significantly affects overall heat dissipation.

2.4. Heat Balance and Thermal Management

In the heat balance of an engine, the thermal energy generated during combustion is distributed across various components. This distribution includes useful work, heat rejected through the cooling system, heat lost via exhaust gases, and other miscellaneous losses. The cooling system’s efficiency, crucial to maintaining the engine’s overall thermal balance, is directly affected by the design and optimization of fins. Enhancing fin geometry, material, and surface area can improve the cooling system’s ability to reject heat, thereby boosting engine performance and reducing thermal losses. The major heat balance components include heat generated by combustion Q_combustion, useful work Q_work, heat rejected by cooling system Q_cooling, and heat loss to exhaust gases Q_exhaust. The total heat balance equation is expressed as follows [34]:

Q_combustion = Q_work + Q_cooling + Q_exhaust + Q_misc

(1)

In this context, Q_cooling represents the heat removed by the cooling system and is the primary focus of this study regarding fin design optimization.

2.5. Solver Settings

Thermal boundary conditions are established, and appropriate solver settings are defined to analyze. This study chooses a conjugate gradient (CG) solver [35] type as it is efficient in solving large-scale thermal problems, especially for problems where sparse matrices were generated while meshing. The CG solver is well suited to thermal analysis because it is also fast to converge even in complex geometries, resulting in increased efficiency in computation. The reason for the choice of solver is due to the fact that this study involves a large number of elements and nodes. An efficient solver is used to ensure that the simulation produces reliable results with minimal computational delay, thus making it possible to explore multiple design iterations during optimization [36].

The methodology used in this study is applied to study the thermal characteristics of engine cylinder fins. The research utilizes advanced simulation techniques to ensure simulation accuracy and application relevance, by leveraging the capabilities of the ANSYS workbench simulation platform. It is important for capturing heat transfer complexities in real-world scenarios to detail the attention to geometric representation and thermal boundary conditions. Additionally, the combination of direct optimization techniques permits a thoughtful study of how design variables affect thermal performance. This structured approach helps establish, prior to further analysis, other actionable insights on how to optimize fin designs for improved engine efficiency. The results are presented in the following sections and discussed in terms of their implications for engine thermal management.

3. Results

3.1. Thermal Distribution Across Engine Cylinder Fins

Figure 5 illustrates the temperature distribution across the engine cylinder and its fins to provide critical insights into the thermal performance of the system. The cylinder’s highest temperature is reached by the inner wall at 311.85 °C, which is considered the maximum expected temperature for engines operated under high-performance conditions with high-intensity combustion processes. The high temperature shown in this result implies that the engine cylinder is generating heat efficiently. The fins are then subjected to an ambient temperature of 301 K and convection coefficient of 5 W/m²K, to simulate the heat transfer to the surrounding air.

3.2. Grid Independence and Validation

The model’s obtained temperature distribution closely agrees with the previous literature [8,9,10], verifying the accuracy of the model. From the analysis, the maximum temperature is found to be 307.8 °C (consistent with previous studies [21]). Such validation is critical for ensuring that the simulation results correspond to the actual environment, adding support to the strength of the methodology used. A grid independence test was conducted in order to ensure the accuracy of the results, as shown in

Table 2. Grid independence test.

Number of Elements	Temperature (K)
81,546	305.1
82,145	306.4
83,549	306.5
84,256	307.8
84,569	307.8

. This test analyzed the influence of mesh density on the temperature outcome, and, hence, reliability of the computational model. The results indicate that with an increasing number of elements, temperatures stabilize, reaching values between 305.1 K and 307.8 K. The stabilization indicates that this size of mesh can give reliable results, which confirms that the model can accurately represent the thermal behavior of the engine cylinder.

The findings from this grid independence test corroborate more strongly the model validation with the experimental results of previous studies, thus ensuring the overall validity of all the analyses.

3.3. Total Heat Flux Distribution in Engine Cylinder

The total heat flux distribution across the engine cylinder and fins is shown in Figure 6 with the highest heat transfer locations. The plot shows that the heat flux values are higher at the base of the fins linking to the cylinder blocks representing the main heat generating zone. This observation supports the principle that heat flow rates are higher in areas where the temperature gradient is steepest, resulting in a more efficient heat transfer process [37,38].

As the heat conducts along the fins, the heat flux decreases towards the tips, highlighting a significant reduction in thermal effectiveness in these regions. This decline in heat flux can be attributed to the decreasing temperature difference between the fin surfaces and the surrounding air at the fin tips, which suggests that the current fin design may not optimize heat dissipation effectively.

Figure 7 further illustrates this phenomenon through a vector plot of heat flux, where arrows represent the direction of heat flow and their thickness indicates the density of heat flux on the engine components. The heat flux vectors are notably directed toward the base of the fins, which signifies the most efficient heat transfer zones. As illustrated in Figure 7, the lengths of these vectors diminish towards the tips of the fins, indicating reduced thermal conductivity in these areas [39,40].

3.4. Optimization Results

This study aims to enhance the thermal dissipation efficiency of engine fins by systematically optimizing key geometric parameters: fin length (L) and fin width (W). The optimization objective is twofold: (1) to minimize the maximum temperature (T_max) on the fin surface to eliminate thermal hotspots; and (2) to maximize the total heat flux (q), i.e., the fin’s overall heat dissipation capability. The direct optimization (DO) method simultaneously optimizes multiple parameters to find optimal configurations that meet both thermal performance criteria. The optimization is governed by an objective function f that combines these goals through weighted terms for temperature reduction and heat dissipation [41,42]:

$$\mathrm{f}=\propto \left({\displaystyle \frac{{\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{{\mathrm{T}}_{\mathrm{r}\mathrm{e}\mathrm{f}}}}\right)+\mathsf{\beta }\left({\displaystyle \frac{\mathrm{q}}{{\mathrm{q}}_{\mathrm{r}\mathrm{e}\mathrm{f}}}}\right)$$

(2)

A design variable space is explored through the optimization process shown in

Table 3. Direct optimization definition.

Optimization Study
Minimize P1; P1 <= 549 k	Goal, minimize P1 (default importance); strict constraint, P1 values less than or equals to 549 K (default importance)
Minimize P2; P2 <= 5300 W/m2	Goal, minimize P2 (default importance); strict constraint, P2 values less than or equals to 5300 W/m2 (default importance)
Maximize P3	Goal, maximize P3 (default importance)
Maximize P4	Goal, maximize P4 (default importance)

and

Table 4. Optimization points generated.

Design Point	P3-Length (mm)	P4-Width (mm)	P1-Temperature Probe Maximum Temperature (K)	P2-Heat Flux Probe Minimum Total (W/m2)
1	117.13	121.635	567.0899719	5740.224301
2	117.39	135.135	557.2738098	6969.619151
3	117.65	128.385	562.361853	6390.156727
4	117.91	141.885	551.3477539	7233.406658
5	118.17	125.01	564.4932312	5962.532627
6	118.43	138.51	554.1000427	7005.728446
7	118.69	131.76	559.4509338	6529.746769
8	118.95	145.26	547.9578308	7225.314662
9	119.21	123.3225	565.1445068	5606.025618
10	119.47	136.8225	555.1293396	6765.61932
11	119.73	130.0725	560.2942566	6224.146702
12	119.99	143.5725	549.1270508	7028.968602
13	120.25	126.6975	562.4623474	5810.567217
14	120.51	140.1975	551.8947205	6819.6902
15	120.77	133.4475	557.3109802	6353.461488
16	121.03	146.9475	545.6858887	7018.54887
17	121.29	122.47875	564.7088989	5182.492672
18	121.55	135.97875	554.9860596	6431.141529
19	121.81	129.22875	559.9961304	5837.584318
20	122.07	142.72875	549.0932373	6736.400213
21	122.33	125.85375	562.0661377	5409.426697
22	122.59	139.35375	551.7786926	6498.572212
23	122.85	132.60375	557.0473389	5990.671368
24	123.11	146.10375	545.6727966	6734.215435
25	123.37	124.16625	562.6366333	5070.445399
26	123.63	137.66625	552.7248596	6242.656236
27	123.89	130.91625	557.807959	5696.35007
28	124.15	144.41625	546.7604431	6541.721514
29	124.41	127.54125	559.91297	5294.350943
30	124.67	141.04125	549.459967	6319.591139
31	124.93	134.29125	554.7904724	5833.608594
32	125.19	147.79125	543.292395	6550.565582
33	125.45	122.05687	562.8096985	4523.352965
34	125.71	135.55687	553.4365601	5824.17605
35	125.97	128.80687	558.2475952	5195.91973
36	126.23	142.30687	547.678717	6188.668439
37	126.49	125.43187	560.1883606	4772.796432
38	126.75	138.93187	550.2454895	5922.780754
39	127.01	132.18187	555.3192505	5362.855782
40	127.27	145.68187	544.2703308	6218.651307
41	127.53	123.74437	560.6398682	4437.160012
42	127.79	137.24437	551.0786804	5666.833954
43	128.05	130.49437	555.9632935	5077.768478
44	128.31	143.99437	545.2502197	6024.683051
45	128.57	127.11937	557.939978	4665.187214
46	128.83	140.61937	547.8320679	5772.503137
47	129.09	133.86937	552.9684204	5246.437272
48	129.35	147.36937	541.7963623	6066.769987
49	129.61	122.90062	559.8994202	4064.157068
50	129.87	136.40062	550.6368164	5351.727535
51	130.13	129.65062	555.3633179	4730.951224
52	130.39	143.15062	544.9259399	5736.147703
53	130.65	126.27562	557.2427734	4312.210891
54	130.91	139.77562	547.423407	5467.564964
55	131.17	133.02562	552.4074463	4906.922827
56	131.43	146.52562	541.4994873	5786.779727
57	131.69	124.58812	557.6198792	4012.067467
58	131.95	138.08812	548.1778015	5222.592291
59	132.21	131.33812	552.9744934	4621.83869
60	132.47	144.83812	542.4005493	5587.637089
61	132.73	127.96312	554.8890747	4242.300543
62	132.99	141.46312	544.9122375	5330.447908
63	133.25	134.71312	549.9561829	4802.859318
64	133.51	148.21312	538.9321655	5642.574958
65	133.77	121.8459	557.8023438	3473.322464
66	134.03	135.3459	549.0212158	4764.084053
67	134.29	128.5959	553.4863953	4120.3156
68	134.55	142.0959	543.5063843	5189.862581
69	134.81	125.2209	555.2061218	3723.137789
70	135.07	138.7209	545.8576111	4896.003902
71	135.33	131.9709	550.5871948	4317.732674
72	135.59	145.4709	540.1228699	5267.76048
73	135.85	123.5334	555.4531006	3439.519901
74	136.11	137.0334	546.4879822	4657.310405
75	136.37	130.2834	551.026709	4053.495899
76	136.63	143.7834	540.9054932	5072.047784
77	136.89	126.9084	552.7838806	3674.591077
78	137.15	140.4084	543.2735046	4793.554788
79	137.41	133.6584	548.065802	4233.895729
80	137.67	147.1584	537.4812378	5150.085797
81	137.93	122.6896	554.4274658	3145.558231
82	138.19	136.1896	545.7613892	4361.00811
83	138.45	129.4396	550.1418518	3757.250785
84	138.71	142.9396	540.3026489	4787.572671
85	138.97	126.0646	551.8049683	3383.136113
86	139.23	139.5646	542.5856384	4512.958036
87	139.49	132.8146	547.2244934	3947.428553
88	139.75	146.3146	536.9121765	4883.55314
89	140.01	124.3771	551.986853	3114.801354
90	140.27	137.8771	543.1440491	4270.544368
91	140.53	131.1271	547.5952515	3698.249939
92	140.79	144.6271	537.6216187	4682.196593
93	141.05	127.7521	549.2950806	3345.591707
94	141.31	141.2521	539.9206299	4407.400711
95	141.57	134.5021	544.6202454	3875.893848
96	141.83	148.0021	534.1936707	4766.812185
97	142.09	122.26781	551.5043091	2748.905208
98	142.35	135.76781	543.194281	3911.140046
99	142.61	129.01781	547.374762	3316.911719
100	142.87	142.5178	537.8911194	4339.659693

, seeking design improvements in the heat dissipation performance of the engine cylinder. Two critical geometrical parameters were optimized. The fin length and width were chosen, to minimize the extreme temperature while keeping the total heat flux constant. The study employed the direct optimization definition shown in Figure 8, which shows the parameters and constraints used for the optimization process.

The results of optimization show large variations in maximum temperature and heat flux over the design points, indicating the significant influence of fin geometry on thermal properties.

These optimizations led to maximum temperatures between 545.68 K and 567.09 K and total heat fluxes of between 3145.56 W/m² and 7233.41 W/m². The results highlight the strong dependence of thermal performance on fin geometry. In particular, fins that are longer and wider, and, thus, have a greater amount of surface area, have lower maximum temperature because of their superior surface area, which enhances heat dissipation.

3.4.1. Optimal Design Point

This study identified the optimal design point for the fins to have a length of 124.67 mm and a width of 141.04 mm with a maximum temperature of approximately 549.46 K and a total heat flux of 6319.59 W/m². This is because the size of the fin length and width provides a good balance of cooling the engine and the amount of material that one needs to use on the fins. Figure 8 is a ‘samples chart’ where candidate designs generated in the optimization process are shown. Each path (colored lines) represents candidate designs. This path represents a specific combination of fin length and width, which enables us to evaluate the influence of fin geometry on T_max (maximum temperature) and total heat flux. The most effective candidate design is the one that exhibits lower maximum temperature (P1) and higher heat flux (P2). From the chart, it is also evident that T_max reduces with an increase in fin length and fin width up to the threshold limit. An optimal balance exists for a certain range of fin length and fin with dimensions. Beyond this range, the cooling performance is suboptimal with lower heat flux (heat dissipation) or high temperature. The candidate points taken for further analysis, as shown in Figure 9, are based on their performance metrics. The candidate points chart represents an optimized design (represented by curves) for the engine fin geometry, which is efficient and offers superior performance as compared to the rest of the candidate points. Each curve represents a specific set of values for the length and width of the fin for which the optimal thermal efficiency of the engine fin is attained.

From the candidate points chart, there are three candidate points as represented by three curves. As shown in Figure 10, the first candidate point has a length of 141.83 mm, a width of 148 mm, a maximum temperature of 534.19 K, and a total heat flux of 4766.8 W/m². The second candidate point has a length of 142.87 mm, a width of 142.52 mm, a maximum temperature of 537.89 K, and a total heat flux of 4339.7 W/m². The third candidate point has a length of 140.79 mm, a width of 144.63 mm, a maximum temperature of 537.62 K, and a total heat flux of 4682.8 W/m².

3.4.2. Trade-Off Analysis

Nevertheless, beyond a threshold fin size, no additional benefit was observed from further increases in fin size, indicative of the necessity for careful fin dimension optimization. This balance is illustrated by the trade-off analysis shown in Figure 11, which shows that some designs have lower maximum temperatures, but at the expense of more heat flux. Although the design point with the lowest T_max, 545.68 K, had a total heat flux of 5145.56 W/m², a higher heat flux of 6319.59 W/m² was reached, having a slightly higher T_max of 549.46 K. This trade-off shows that the fin geometries must be optimized to meet the overall thermal efficiency without compromising the material costs involved.

3.4.3. Sensitivity Analysis

Figure 12 shows the sensitivity analysis of the thermal performance trends of engine cylinders with respect to changes in fin length and width. The results indicate that fin length, rather than fin width, is the dominant factor in heat dissipation. This insight is especially valuable for future designs aimed at enhanced thermal efficiency and suggests that during the design, to meet thermal performance objectives, designers should focus on optimizing the fin length and adjust the width accordingly.

3.5. Critical Factors Influencing Performance

3.5.1. Mesh Quality and Element Selection

The thermal interactions within the model are accurately captured by the quality of the mesh. The cylinder model was discretized using 84,569 hexahedral elements and 100,259 nodes. With a growth rate of 1.4 and a transition ratio of 0.275, this configuration was sufficient to allow the mesh to accurately reflect the thermal gradients especially close to the internal walls of the cylinder and the bases of the fins. The current mesh proved to be reliable, but refining mesh around fin edges could improve precision in thermal characteristics in future studies.

3.5.2. Material Considerations

The choice of the fin material, cast iron, is based on its great thermal conductivity and durability. Nevertheless, its weight could be a disadvantage for this material. An approach with better thermal performance, yet reduced weight, can be found in alternatives such as aluminum alloys or lightweight composites [43]. The future research could optimize these materials for improved heat transfer while reducing weight.

3.5.3. Boundary Conditions

The boundary conditions applied in this study simulated typical engine operating conditions, where the inner cylinder surface experiences elevated temperatures due to combustion, while the fins undergo convective heat transfer to the atmosphere. Although these conditions provide valuable insights, real engine scenarios may involve more dynamic and transient conditions. Subsequent studies should incorporate transient thermal testing to better reflect practical usage.

3.5.4. Design and Manufacturing Constraints

While the current fin design demonstrates effective heat dissipation, it is crucial to consider manufacturing feasibility. Complex geometries may lead to increased production costs and challenges in maintaining structural integrity [44]. Future designs should optimize thermal performance while considering manufacturability and robustness, potentially utilizing multi-objective optimization strategies to achieve this balance. Figure 13 provides a summary of the key results, including the modeling errors and variations from the reference.

These “Variation from Reference” columns summarize deviations of measured values from the optimal reference values. It maintains adequate heat flux with minor adjustments to the model as geometric change takes place. The minimal errors indicate that precision-critical applications require continuous monitoring, while the optimization balances dimensional constraints and performance. Fin design can be changed slightly to improve or degrade heat dissipation without much effect on temperature. Candidate 1 is most balanced, with the closest match to reference values for applications that are most concerned with thermal efficiency and design adherence. Candidates 2 and 3 show slightly larger maximum temperatures, which indicates that small design variations affect thermal performance and highlight the sensitivity of the design to the best performance.

3.6. Comparative Analysis

The findings of this study corroborate previous research on finned heat exchangers, which emphasizes the significant influence of fin length and area on heat removal efficiency. This alignment with the existing literature enhances the credibility of the results. Comparative analysis with the work of Sonawane et al. [45] illustrates that variations in fin pitch and thickness also impact thermal characteristics. The quantitative variations in heat flux and temperature distribution reflect the differences in material properties and simulation parameters used in this study. The research produced two design prototypes: a generic design with dimensions of 117.13 mm in length and 121.635 mm in width, yielding a heat flux of 5740.22 W/m²; and an optimized design, which measures 118.95 mm in length and 145.26 mm in width, with a resulting heat flux of 7225.31 W/m².

Table 5. Design type comparative analysis.

Design Genetic	Length (mm)	Width (mm)	Heat Flux (W/m2)
Generic design	117.13	121.635	5740.2243
Optimized design (mathematical model)	118.95	145.26	7225.31 W/m2

illustrates the potential for significant improvements in thermal performance in terms of optimized fin geometry.

4. Discussion

Results from the engine cylinder fin optimization were in good agreement with the initial hypothesis and expectations. The substantiation of the premise that systematic optimization can afford large thermal benefits is supported by the substantial increase in the heat dissipation capacity, especially the 25.87% improvement observed in the optimized fin design. The careful fin dimensioning and the use of advanced computational techniques permitted more efficient design than methods used prior to this enhancement. The findings of the heat dissipation distribution, specifically the lower heat transfer at fin tips, were anticipated and point to additional refinement in the areas. These results maintain consistency with previous studies, lending support for utilizing direct optimization techniques in the pursuit of enhancing thermal performance in engine applications.

5. Conclusions

The comprehensive finite element analysis (FEA) in this study successfully validates our initial hypothesis that heat dissipation efficiency in the engine cooling system can be improved significantly by optimizing fin geometry. Key questions underlying the research were the influence of fin design on thermal performance and potential trade-offs associated with increasing heat transfer rates and decreasing temperatures inside the engine cylinder. The findings revealed several critical insights:

• Optimization of fin geometry: The optimization process demonstrated a clear correlation between fin dimensions—specifically length and width—and thermal performance metrics such as maximum temperature and total heat flux. The optimized design measured 118.95 mm in length and 145.26 mm in width and had a capacity for heat dissipation of 7225.31 W/m², which is 25.87% higher than the capacity of the generic design, 5740.22 W/m². This enhancement underscores the potential for significant improvements in engine cooling efficiency through targeted geometric modifications.
• Heat transfer characteristics: The analysis indicates that while the fins effectively dissipated heat, the heat flux was notably lower near the fin tips. These findings suggest further refinement of fin geometry or study of alternative materials having better thermal conductivity to realize higher heat flux density overall.
• Importance of material selection: The study used cast iron, which has good thermal properties and the work demonstrated the feasibility of lighter materials or high-conductivity alloys to obtain improved performance. This consideration is particularly relevant to automotive and aerospace applications owing to weight reduction constraints while maintaining thermal efficiency.
• Despite these substantial findings, certain limitations were recognized in the study:
• The reliance on steady-state thermal analysis presents a limitation, as it does not account for the transient heat transfer characteristics inherent in real engine operations under varying loads. This factor may affect fin performance differently depending on changes in engine temperatures during operation, which are not considered in the steady-state model presented here. The potential modeling errors may arise due to assumptions in material properties, boundary conditions, and simplified geometries. Variations in the mesh resolution and external environmental factors may also influence the accuracy of the results.
• The FEA results provide useful information but also indicate the significance of experimental validation. Additional dynamics of fin performance could be found in real-world conditions (such as workflow variations, manufacturing defects, and material behavior under operational stress). In the future, transient heat analysis and experimental studies should be incorporated into research to more fully understand the fin efficiency in engine cooling systems.

Although the present fin design can be effective at heat dissipation, additional optimization is required for improved performance, especially at fin tip locations that have less effective heat transfer. Designs for future projects should pursue fin dimensions where an appropriate balance exists between thermal optimum properties and material cost efficiency. The present fin design is suitable for effective heat dissipation; however, optimization is necessary to enhance performance, particularly in regions such as fin tips where heat transfer is less efficient. These results provide a robust starting point for the application of these designs and efficiencies for cooling systems in automotive, aerospace, and heavy machinery applications that rely heavily on efficient heat transfer for keeping systems operating and performing. This research contributes to a growing field of knowledge aimed at improving engine performance and sustainability by continuing to uncover the complexities of fin design and thermal management.