1. Introduction
Heat transfer is a mechanical engineering discipline that generates, utilizes, converts, and exchanges thermal energy (heat) through physical structures. Many thermal management or heat transmission problems have emerged in various industries due to technological advancements, including the cooling of high-power electronic devices [
1,
2], thermal management in engines [
3,
4], cooling of nuclear reactors [
5,
6,
7], biomimetic cylinders [
8], and biomimetic honeycomb fractal heat exchangers [
9]. However, the design and manufacture of electrical gadgets and solar energy converters encounter a severe obstacle in the capacity to expel or absorb heat in constrained environments. The increasing requirements concerning such equipment for heat absorption and distribution have been addressed in several investigations [
10,
11,
12,
13,
14]. Heat transmission enhancement strategies are critical for energy conservation and the use of appropriate energy sources. Effective heat transfer techniques have been used in various scientific domains, including chemical engineering, power generation, aircrafts, and refrigerants. The following describes the procedure for strengthening the efficiency of heat transfer systems. Two primary methods have been suggested to increase heat transfer in various contexts: passive approaches and active procedures. Active techniques such as mechanical mixing, rotation, vibration, and the incorporation of an external electrostatic or magnetic field are effectively employed to accelerate heat and mass transfer. This mechanism requires exterior force assistance to operate more quickly and efficiently. External effects may be provided to the system via a heated surface or the flow of fluids. However, in small spaces, external energy input is expensive and difficult. Conversely, passive methods can increase heat transmission by modifying the properties of the fluid and surface roughness, and mounting the objects to increase surface area. Among passive approaches, the use of nanofluids and surface modification are widely utilized and particularly effective at improving heat transmission in various engineering systems. According to many investigations, replacing conventional air cooling systems with liquid cooling systems is a viable way to meet the growing need for high heat flux expulsion while preventing temperature variations and wall overheating. Investigators have made more effort to increase the capacity of traditional fluids in heat transmission applications. In this regard, nanofluids that are finely dissipated metal or metal-oxide nanomaterials in a base liquid exhibit excellent thermal conductive properties. Moreover, the resultant nanofluid has substantially higher thermal characteristics than the base fluid. Nanofluids are used as coolants in nuclear reactors, thermal energy storage, automobile transmissions, solar power generation, electronic cooling systems, solar water heating systems, and radiators. The appealing outcomes that nanofluids yield in modern science and technology have inspired investigators to consider the thermophysical properties of nanofluids [
15,
16,
17,
18]. Many studies have been reported in the last few decades on heat transmission and nonliquid flow attributes while considering the various nanomaterials and geometries. Lu et al. [
19] considered a nanoliquid containing carbon nanotubes to examine its heat transmission and flow behavior past a thin film. Turkyilmazoglu [
20] probed the heat transfer rate of nanoliquid flow in a concentric annulus and concluded that the rate of heat transfer augments with the volume fraction of the nanoliquid. His study included different kinds of nanoparticles, namely Copper (Cu), Copper oxide (CuO), Silver (Ag), Alumina (Al
2O
3), and Titanium Oxide (TiO
2). The effect of a chemical reaction in a stream of water-based nanofluid containing Ag was explored by Suleman et al. [
21]. Haq et al. [
22] discussed the thermal radiative heat transmission and flow of a nanoliquid (Cu-Al
2O
3–water) past an exponentially stretchy sheet. The chemical reactive flow of a nanoliquid containing CuO-Al
2O
3 particles was examined by Ramzan et al. [
23]. The impact of heat sink/source in the stream of a titania–ethylene–glycol-based nanofluid over a stretchable cylinder was scrutinized by Alsulami et al. [
24]. Alharbi et al. [
25] elucidated the magnetohydrodynamic flow of a nanofluid past an elastic stretching surface. The significance of a nanoliquid (Ag-Al
2O
3-TiO
2–water) in the mass and heat transference mechanism of a ternary nanoliquid was examined by Nagaraja et al. [
26], with the consideration of thermal radiation. Adnan et al. [
27] explained the thermal enhancement in a Cu–kerosene oil-based nanofluid stream across plates with the impact of radiation and magnetic force.
Heat transfer from various systems, such as electronic components, bio-medical functions, vehicle radiators, and heat sinks is significant. However, traditional heat transfer strategies are inefficient due to the small size, shape, and weight of the various systems. The advancement of technology necessitated the development of efficient heat transmission systems. Operating compact and smaller electronic devices that generate an exceedingly large quantity of heat, and fail to provide sufficient surface area for transferring this heat, demands the requirement for a highly effective cooling strategy. Thus, extended surfaces or fins of different shapes are used to increase surface area and thereby improve the rate of heat transmission. Fins are frequently employed in many thermal engineering applications to accelerate the rate of heat transfer from heated surfaces. Fins are useful in removing heat from other electrical components, such as computer CPUs, heat evaporators, compressors, and internal combustion engines [
28,
29,
30,
31,
32]. Also, wet extended surfaces are widely implemented in refrigeration and air conditioning, where heat transfer necessitates simultaneously chilling and dehumidifying humid air at room temperature. The surface of the fin becomes wet when the actual temperature on the fin surface drops below the dew point temperature of the ambient air. In view of this context, Kundu and Lee [
33] studied the heat transmission mechanism in rectangular, triangular, convex, and exponential fins by considering wetted conditions. Turkyilmazoglu [
34] explored the mass and heat transmission in a fully wetted permeable fin. Das and Kundu [
35] discussed the consequence of wetness on the convective heat transmission of rectangular and concave profiled fins. Hazarika et al. [
36] investigated the mass and heat dissipation enhancement of a fin under wet conditions. Gamaoun et al. [
37] described the mechanism of heat dissipation in a rectangular fin wetted by a zinc oxide-Society of Automotive Engineers 50 nanolubricant. Abdulrahman et al. [
38] considered a nanoliquid to analyze the heat transmission in a wetted exponential fin with radiation impact.
Geometrical modifications are one of the primary methods used to increase heat transfer rates under various problem conditions. The performance of the heat transfer rate of equipment may be improved by using this simpler and most affordable technique. In this regard, a wavy-designed system is the most important model for analyzing heat and mass transmission efficiency. This kind of design is also used in cooling towers, microchips, and heat exchangers. On the other hand, compact heat exchangers with wavy fins are utilized in thermal equipment for construction, agricultural, and industrial purposes. Optimizing the air side fin arrangement is the most effective way to improve the performance of fin-and-tube heat exchangers. Employing wavy fins is the conventional method for increasing air side heat transfer. Several experimental studies have examined the efficiency of wavy fin-and-tube heat exchangers for air side heat transfer. Wavy fins have become a preferred alternative to flat fins for heat pump air conditioners. Xiao et al. [
39] discussed the heat transfer enhancement in a wavy-finned flat tube bundle using water spay cooling. Wen et al. [
40] studied the performance of wavy fins in plate-fin heat exchangers with the consideration of a fluid–structure interaction. Chu et al. [
41] explained the air side functioning of fin-and-tube heat exchangers with sinusoidal wavy fin geometry. The study also experimentally compared heat transfer performance in round and oval tube configurations. Zhang et al. [
42] studied the heat transfer of a herringbone wavy fin, applicable in the analysis of heat exchangers. Erdinc [
43] examined heat transfer in circular wavy fin-and-tube heat exchangers and elliptical fin-and-tube heat exchangers.
Metaheuristic algorithms have developed effective methods for handling complicated real-world problems in various disciplines. The interaction of intensification and diversity, inspired by natural and physical processes, is vital to their problem-solving abilities [
44]. These algorithms use a natural selection-like process in which viable solutions evolve over numerous generations, adapting and improving through selection, crossover, and mutation operations. Genetic algorithms (GAs) investigate a solution space by maintaining a population of potential solutions, encouraging diversity, and gradually converging on optimal or near-optimal solutions. Also, biological evolution principles inspire the GA, one of the most well-known metaheuristic algorithms [
45]. GAs have been shown to be quite effective in handling a wide range of optimization and search difficulties. Improving energy efficiency in smart cities is a significant requirement; thus, Le et al. [
46] proposed a unique GA-ANN model to analyze the heat load of buildings. In this work, the GA-ANN outperforms other techniques in terms of performance. These models can anticipate characteristics that are important in optimizing building design for energy efficiency and can be integrated into smart homes and municipal planning. Albadr et al. [
47] proposed a GA-based natural selection technique to improve exploitation and exploration control. The proposed method surpasses the traditional GA and other optimization approaches in various tests, providing a better balance of exploration and exploitation through chromosomal selection refinement and introducing a mean-based evaluation. In the developing field of wind power, Zhang et al. [
48] studied the improvement of wind speed prediction accuracy for reliable grid operation and energy delivery. The model improves prediction accuracy by applying hierarchical clustering, and optimizing artificial neural networks with evolutionary algorithms. Hamdia et al. [
49] present a robust optimization strategy for machine learning models that uses evolutionary algorithms to optimize the architecture and feature configurations of the ANN model. This study was conducted in computational material design and validated the approach by boosting prediction accuracy for fracture energy in polymer–nanoparticle composites. The optimized ANN outperforms traditional models, with fewer generations in the evolutionary process. Let et al. [
50] investigated the bed expansion in a binary particle combination within Newtonian liquid in circular columns. The findings reveal that bed expansion increases with increasing liquid velocity and decreases with increasing particle diameter. The combination of GA and neural networks improves the accuracy of bed height forecasts, providing valuable tools for future research in this area. Sharifi et al. [
51] presented an ANN that outperforms semi-empirical correlations in estimating heat transfer rates and friction coefficients for heat exchangers with coiled wire within input variable ranges. The application of the GA in conjunction with ANNs in the study determines the ideal spiral wire structure for the highest overall efficiency enhancement in heat exchangers, offering valuable insights for heat exchanger design and optimization. Wen et al. [
52] inspected the ZnO–water nanofluid’s thermal and flow properties in multiport mini-channels. Heat transfer performance is predicted in this study using an ANN-based genetic approach. Cui et al. [
53] examined the impact of a metal foam–fin hybrid structure and inclination angle on the heat transfer performance of a phase change material. The implemented GA-ANN model effectively predicts liquid fractions and Nusselt numbers during the phase change.
The typical approach for enhancing air side heat transfer involves using a wavy extended surface. In the aforementioned literature, it is noted that several researchers investigated heat transmission in a wavy profiled fin. However, heat transport in a wet wavy fin with temperature-dependent thermal conductivity has not yet been studied. On the other hand, optimization strategies, which are a subset of intelligence techniques, can be used for analyzing mathematical models. A genetic algorithm is a prominent evolutionary method for achieving this objective. Thus, the current study focuses on analyzing heat transmission of a wet wavy fin with variable thermal conductivity using an optimization algorithm. Also, the heat transport behavior of the wet wavy fin is studied by employing a genetic algorithm-enhanced neural network (GA-ENN). Further, the consequence of different constraints on the thermal profile of the wavy fin is exhibited with the help of graphs. Numerous investigations on the thermal characteristics of various fin designs have been reported in the literature. For a more comprehensive understanding,
Table 1 provides recent studies on fin structure while considering the wet conditions.
It is evident from
Table 1 that the thermal features of wavy fins have been given less importance. The pioneering of the present research over previous investigations can be described as follows:
Presenting a mathematical model for thermal transfer in a wetted wavy fin with convection and radiation mechanisms to inspect the heat transport features of the fin.
Analyzing the impact of radiation and surface wetness on the thermal performance of the wavy fin.
An artificial intelligence-based genetic algorithm is used to examine the heat transfer rate of the wavy fin. Implementing this sophisticated optimization method and better computing technology has enabled an estimation of the thermal characteristics of the wetted wavy fin.
Comparing the thermal variation attributes of dry and wet wavy fins under the influence of convection and radiation.
The current investigation has been organized according to the following:
Section 2 describes the mathematical model of the problem, including an explanation of the physical illustration of the wavy fin, the fundamental governing equations, the appropriate boundary conditions, and the applied dimensionless variables.
Section 3 discusses the general procedures of genetic algorithm-enhanced neural networks. Tables and graphs are used to explore the results, which are reported in
Section 4.
Section 5 contains the conclusions, which provide an overview of the major results.