Number Of Fins Research Articles

Solidification acceleration of phase change material in a horizontal latent heat thermal energy storage system by using spiral fins

One important solution for societies to overcome the energy crisis is to manage the production and storage of energy. In this regard, the latent heat energy storage systems have recently gained a remarkable attention. Hence, this work is devoted to enhance performance of a latent heat tube-shell storage system by using novel spiral fins with different geometrical characteristics. Different number of vanes have been employed on the fins with constant twisting pitch. The different cases studied include the cases with single-fin, double-fin, triple-fin and quadruple-fin. These fins have been employed to augment heat transfer from a low temperature fluid to the PCM inside the shell container during the solidification process. To model the phase change, the enthalpy-porosity technique has been adopted. Various parameters have been used to assess the functionality of the system including the Nusselt number, total solidification time, temperature, solid fraction evolution, solid fraction contours, temperature contours and etc. The results demonstrated that the triple-fin and double-fin cases took the advantage in heat transfer augmentation and discharging process while the case with single-fin showed the worst performance. The results indicated that fin number is not the only influencing factor and fin length also has a dominant role.

Performance enhancement of latent heat thermal energy storage system by using spiral fins in phase change material solidification process

Latent heat thermal energy storage systems (LHTESS) have recently gained attention due to the critical demand for clean energy production and storage. The influence of spiral fins on the performance augmentation of a vertical tube-shell LHTESS in the solidification process was studied numerically. Different formation of fins which includes the quadruple, triple, double and single fins were studied. Amount of phase change material (PCM) mass inside the PCM enclosure was preserved equal in all cases and the length of the fins were adjusted for different fin numbers to keep the surface of heat transfer constant to find the optimized fin number. The phase change process was simulated by adopting the enthalpy-porosity technique. It was observed that the triple fin case outperformed other cases and the single fin case showed the least enhancement. When comparing the different cases while the heat transfer surface was kept constant, the triple fin case shows better performance in terms of time averaged Nusselt number and total solidification time respectively. It was revealed that the performance enhancement was not directly proportional with the number of fins and there was a trade-off between fin number and length of each fin.

Effect of novel concentric annular fins on the melting and solidification process of stearic acid in thermal energy storage devices

The latent heat thermal energy storage device provides an alternative solution to the problem of imbalance between energy supply and demand. To enhance heat transfer, a series of latent heat thermal energy storage devices with novel concentric annular fins are proposed, as the design accelerates the melting and solidification processes of stearic acid. Based on the finite volume method, the enthalpy-porosity approach is employed to numerical simulation the charging/discharging process. Effects of the number and arrangement of concentric annular fins on the liquid fraction, melting and solidification front, melting uniformity, temperature uniformity, velocity uniformity and total melting and solidification time during melting and solidification are studied. Results showed that the melting and solidification rate increases with increasing fin number. The total melting and solidification times were reduced by 72.83% and 86.39%, respectively, for the case with 9 concentric annular fins compared to the bare tube. Both melting performance and temperature uniformity were improved. Further, the effect of fin arrangement on the melting and solidification performance was investigated with the same total volume of fins. Results revealed that the heat transfer performance of progressively shorter fin structures < uniformly distributed fins < progressively longer fins < performance of non-uniformly distributed fin arrangement. The non-uniform fin arrangement reduces the total melting and solidification time of stearic acid by 85.46% and 90.11%, respectively, compared to bare tube. This work provides new insights into the understandings of the transient phase change process and the strategies for guiding the design for thermal energy storage devices using annular fins.

Metal fins efficacy on stepped solar still performance: An experimental study

In recent years, significant attention has been paid to the investigation of parameters associated with the absorber surface of stepped solar stills, aiming to enhance their performance. In this study, metal fins have been employed on the absorber surface to increase the absorption of radiant energy. The experiment's input variables included the inlet flow rate (100, 150, and 200 ml/min), number of fins (1, 2, and 3 fins on each step), angle of fins (−30°, 0°, and +30°), height of fins (1, 2, and 3 fins on each step), and material of the fins (copper, aluminum, and galvanized steel). 27 main experiments were designed with the help of design of experiments. Results showed that productivity decreased and increased with increasing inlet flow rates and fin numbers, respectively. In addition, the +30° fin had the best results compared to other angles, and freshwater productivity decreased with increasing fin height. Also, copper fins performed better than other fins. Finally, compared to the stepped solar still without fins, a 171 % increase in efficiency was seen in the optimal mode, which had three copper fins with a height of 3 cm, an angle of +30°, and an inlet flow rate of 100 ml/min.

Analysis of the Heat Transfer in Electronic Radiator Filled with Metal Foam

The performance of an electronic radiator filled with metal foam with a porosity of 96% was studied. The effect of the factors including the flow rates, the pores per linear inch (PPI) and the numbers of fins was analyzed. The results show that the electronic radiator with metal foam reflects a stronger ability of the heat transfer compared to the electronic radiator without metal foam. With the increase in the flow rate between 10 L/h and 60 L/h, the heat transfer coefficient of both of the two electronic radiators will be improved, but it is also dependent on the number of fins. In this study, we find that the heat transfer coefficient first increases and then decreases with the number of fins. The optimum number is three. As for the effect of the PPI, the higher the PPI, the larger the heat transfer coefficient, while the pressure drop always increases with the flow rates’ increase, the pores per linear inch (PPI) and the numbers of fins.

Exploring the feasibility of next-generation CO2-based adsorption cooling systems using different adsorbent reactor configurations

The present investigation expounds on the effects of the reactor geometry, cycle time and heating/cooling fluid temperatures on the performance of a 4-bed CO2 adsorption cooling system. Cylindrical adsorbent reactors of varying aspect ratios (AR) with an optimum number of internal longitudinal fins and non-finned reactors are compared. The study confirms the substantial effect of reactor configuration on the system COP, specific cooling effect (SCE) and power, energy interactions during various processes and the total cycle time (TCT), which the equilibrium or lumped system analysis fails to predict. An increment of 98 % and 189 % in system COP and SCE is attained by varying the aspect ratio of the reactor with fins under subcritical operations. In continuation, a reduction of 41 % in TCT is observed. The study confirms the optimum adsorption/desorption time for which the COP and SCE are maximum, especially for higher AR reactors. It is noteworthy that proper selection of reactor aspect ratio results in a better system COP, even at lower heating fluid temperatures. During the transcritical operations, an increment of 23 % in COP and 6 % in SCE is achieved for a gas cooler exit temperature of 35 °C. Moreover, the reactor configuration also affects the optimum gas cooler pressure for the transcritical cycle, like the gas cooler exit temperature. One of the crucial observations is that, for a given combination of reactor configuration, heating/cooling fluid temperatures, and operating pressures, there exists a minimum cycle time below which a cyclic steady-state condition is impossible to achieve. During the subcritical and transcritical operations, a maximum COP of 0.1 and 0.052 is achieved for the proposed adsorption chiller configuration, respectively.

Optimization of the Cooling Performance of Symmetric Battery Thermal Management Systems at High Discharge Rates

An air cooling battery thermal management system (BTMS) is widely used in electric vehicles (EVs). In this work, numerical simulation is used to provide a greater understanding of the system efficiency of T-type symmetric air cooling BTMS (T-BTMS) and its coupled systems. For T-BTMS, the method of the coefficient of variation (MCV) is applied to evaluate the schemes with different inlet flow rates and battery clearances. It is found that optimum cooling performance and energy consumption are achieved at an internal clearance of 3 mm and an inlet air velocity of 6 m·s–1. Further improvements in cooling performance can be realized by introducing heat transfer fins into the module. Increasing the number of fins can improve cooling performance but results in higher energy consumption. To further improve the cooling performance at high battery discharge rates, a coupled system with air cooling and liquid cooling is proposed. It is found that, at high discharge rates, the coupled system gives better cooling performance and lower energy consumption compared to uncoupled systems. When the battery module is fully discharged at the rate of 4 C, the maximum temperature of the coupled system is below the critical value of 45 °C and the maximum temperature difference is less than 5 °C.

Development and Analysis of a Three-Fin Trigate Q-FinFET for a 3 nm Technology Node with a Strained-Silicon Channel System.

Multi-gate field effect transistors (FETs) such as FinFETs are severely affected by short-channel effects (SCEs) below 14 nm technology nodes, with even taller fins incurring fringing capacitances. This leads to performance degradation of the devices, which inhibits further scaling of nanoFETs, deterring the progress of semiconductor industries. Therefore, research has not kept pace with the technological requirements of the International Roadmap for Devices and Systems (IRDS). Thus, the development of newer devices with superior performances in terms of higher ON currents, acceptable leakage currents and improved SCEs is needed to enable the continuance of integrated circuit (IC) technologies. The literature has advocated integration of strained-silicon technology in existing FinFETs, which is highly effective in enhancing ON currents through the strain effect. However, the ON currents can also be amplified by intensifying the number of fins in trigate (TG) FinFETs. Thus, three-fin TG quantum (Q)-FinFETs, using a novel tri-layered strained-silicon channel, are deployed here at 10 nm and 8 nm channel lengths. Threshold voltage is calculated analytically to validate the designs. The electrical parameters and quantum effects of both devices are explored, analysed and compared with respect to existing heterostructure-on-insulator (HOI) FinFETs and the proposed existing standard requirement of IRDS 2022 for a 3 nm technology node. The comparisons demonstrated a significant increase in the drive currents upon employing three fins of the same dimensions (8 nm gate length) and specifications in a device-based system. The performance is augmented in contrast to the 3 nm technology node device of IRDS 2022, with SCEs within the limits. Thus, employing a tri-layered strained-silicon channel system in each fin allowed for forming a three-fin Q-FinFET that, in our opinion, is the technique for consolidating the performance of the devices and enabling future generation device for faster switching operation in a sub-nano regime.

External shading and its effect on the energy efficiency of Tehran's office buildings

AbstractModern office building designers tend to propose highly glazed façades that provide occupants with a view and daylight; however, the use of such façades has consequences, like glare and high energy consumption, especially in warm climates. Shadings affect energy usage for cooling, heating, and artificial lighting, defined as the objectives and output in the optimizer algorithm. The input variables are shading type, WWR, the depth of the shading, the distance between the shading and the window, the distance between fins, the number of fins in shading, and the distance from the top of the window. This research aims to comprehensively study external shadings and window‐to‐wall ratios to reduce the high energy consumption in modern office buildings in Tehran and cities in locations with a similar climate. The results can benefit all scientists researching building science, architects, instructors, and those wanting to buy a low‐energy consumption office. Energy consumption was calculated in Ladybug–Honeybee; the best objectives were obtained for each shading with the optimization process by the Octopus plugin in Grasshopper. Results were analyzed and rated compared with a window without shading. The best scenario was obtained for Egg‐crate with a 14.86% reduction in cooling energy and a 20.04% increase in useful daylight illuminance.

Optimal Design of Wearable Micro Thermoelectric Generator Working in a Height-Confined Space

With the increasing development of self-powered wearable electronic devices, there is a growing interest in thermoelectric generators (TEGs). To achieve more comprehensive and reliable functionality of wearable devices, improving the power generation performance of thermoelectric devices will be the key. It has been shown that integrating a heat sink at the cold end of the TEG increases the effective temperature difference and, thus, maximizes the power output of the thermoelectric device. However, the space left for the power supply is often limited. How to optimize the integrated system of micro-thermoelectric generators and heat sinks in a height-confined space has become the key. In this study, we have established a corresponding model using a numerical calculation method, systematically studied the influence of TEG geometric size on the number of fins and fin height, and determined the optimal number of fins for the highest equivalent convective heat transfer coefficient corresponding to different fin heights. We also conducted the co-design of TEG and fin topological structure to study the effects of the ratio of leg height to fin height (l/H), the width of legs (w), and the number of thermoelectric leg pairs (N) on the maximum output power density per unit area (Pm1) and the maximum output power density per unit mass (Pm2) of the device. When N = 16, w = 0.3 mm, l/H = 2.5 (that is, l = 3.57 mm, H = 1.43 mm), and Pm1 reaches the maximum value of 30.5 μW/cm2; When N = 2, l/H = 0.25 and w = 0.3 mm, and Pm2 reaches a maximum value of 5.12 mW/g. The measured values of the open-circuit voltages of fabricated micro-TEGs with different thermoelectric leg heights (l = 0.49 mm, l = 1.38 mm, and l = 1.88 mm) are basically consistent with the simulated values. When N = 2, l = 0.49 mm, H = 3.74 mm, and w = 0.85 mm, and Pm2 reaches 0.44 mW/g. The results provide insights into the optimal design of wearable micro thermoelectric generator working in a height-confined space and highlight the importance of co-designing TEGs and fin topological structures for optimizing their performance.

Heat Transfer Augmentation Using Duplex and Triplex Tube Phase Change Material (PCM) Heat Exchanger Configurations

The significance of latent heat thermal energy storage is more substantial when compared to sensible energy storage due to its higher energy storage capability. In this paper, heat transfer enhancement techniques for melting (charging) and solidification (discharging) by using external fins and internal–external fins for a phase change material (PCM) in duplex and triplex tube heat exchangers (DTHX and TTHX) are investigated numerically. A two-dimensional analysis is carried out using ANSYS Fluent for various configurations. Moreover, the effect of different critical parameters, number of fins, fin length, fin thickness, and the heat exchanger tube material are evaluated in terms of the total time of complete phase change of the PCM. Four cases are investigated; cases 1 and 2 are based upon a DTHX while cases 3 and 4 are TTHXs. By considering case 1 as a reference case, it is found that case 2 and case 3 reduce the total melting time by 48.76% and 90.12%, respectively. Case 4 achieves the shortest time for complete melting of the PCM, and the total melting time is decreased by 92%. Solidification behaviour for all four cases is also investigated. The novel configurations increase (doubled) the supply of heat transfer fluid (HTF) while at the same time significantly enhance the melting/solidification characteristics for all the cases without disrupting the convectional currents during phase change of the PCM. Tube materials with different thermophysical properties are also investigated with the heat transfer rate and melting time significantly improved with a high thermal diffusivity material. Moreover, the heat transfer is found to increase with fin length and fin thickness.

Evaluation of the solidification process in a double‐tube latent heat storage unit equipped with circular fins with optimum fin spacing

AbstractIn this study, the effect of fin number and size on the solidification output of a double‐tube container filled with phase change material (PCM) was analyzed numerically. By altering the fins' dimensions, the PCM's heat transfer performance is examined and compared to finless scenarios. To attain optimal performance, multiple inline configurations are explored. In addition, the initial conditions of the heat transfer fluid (HTF), including temperature and Reynolds number, are considered in the analysis. The research results show a significant impact of longer fins with higher numbers on improving the solidification rate of PCM. The solidification rate increases by 67%, 170%, 308%, and 370% for cases with 4, 9, 15, and 19 fins, respectively, all with the same fin length and initial HTF boundary condition. The best case results in a solidification time that is 4.45 times shorter compared to other fin number and dimension scenarios. The study also found that moving from Reynolds numbers 500 to 1000 and 2000 reduced discharging times by 12.9% and 22%, respectively, and increased heat recovery rates by 14.4% and 27.9%. When the HTF entrance temperature was 10°C and 15°C, the coolant temperature showed that the entire discharging time decreased by 37.5% and 23.1% relative to the solidification time when the initial temperature was 20°C. Generally, this work highlights that increasing the length and number of fins enhances thermal efficiency and the phase change process.

Investigation of the impact of fin number and length attached to an enclosure subjected to a magnetic field

In the current study, the heat transfer and entropy generation of an Al2O3CuO/water hybrid nanofluid in a square enclosure with a constant magnetic field is investigated and optimized after sensitivity analysis. Varying lengths of fins, three different configurations of single, double, and triple fins attached on the left hot wall of the enclosure are compared. The right wall is kept at a lower temperature, while the top and bottom walls are insulated. The configuration is taken into account as a categorical factor and the length of the fins is used as a numerical factor in the regression modeling. The d-optimal method is then used in sensitivity analysis and optimization. A two-objective optimization was conducted to minimize the entropy generation and maximize the heat transfer rate, at the same time. The findings indicate that using more fins, even if they are not long, can result in a 30% increase in heat transfer. Furthermore, with fewer fins yer longer, the heat transfer enhancement can still be achieved. Additionally, attaching more fins decreases the entropy generated by viscous dissipation.

Numerical investigations into the influence of geometric configurations on hydrodynamic characteristics of torpedo anchors

Torpedo anchors are an innovative and cost-effective technology in marine foundation engineering; however, there is a lack of systematic and comprehensive studies on the influence of torpedo anchor geometry on its hydrodynamic characteristics, especially the effect of anchor fin configuration on the hydrodynamic characteristics is rarely reported in the existing literature. Therefore, this study investigates the influence of geometric characteristics of both finless and finned torpedo anchors on their terminal velocity, drag coefficient and installation directional stability in water through CFD numerical analysis in a systematical manner. The considered geometric characteristics include the center of gravity position, shape and angle of anchor tip, shaft and fin aspect ratio, fin number, fin thickness, fin shape, fin position and fin area. Based on the obtained numerical results, some practical design recommendations and impact weighting charts of different anchor geometric factors are provided, which enables a quick qualitative and quantitative assessment of torpedo anchors. In addition, a simple weight-based approach for estimation of terminal velocity and drag coefficient of torpedo anchors considering multiple geometric configuration factors is proposed, which may provide some reference and scientific guidance for experimental and engineering design of torpedo anchors.

Convective condensation of R134a and R1234ze(E) inside microfin tube

Environmental concerns are forcing the replacement of the commonly used refrigerants and finding new fluids is a top priority. The hydro-fluoro-olefin (HFO) R1234ze(E), because of its smaller global warming potential (GWP) and shorter atmospheric lifetime, replaced R134a. Accordingly, for HVAC systems design, a detailed knowledge of the thermo-fluid-dynamic characteristics of the fluids and reliable predictive models are required. To improve the understanding, R134a and R1234ze(E) were employed in convective condensation experiments (saturation temperature Tsat = 35°C, mean quality xm = 0.1~0.9, quality changes Δx = 0.05~0.6, mass flux G = 43~444 kg·m−2s−1) inside a microfin tube (outer diameter D = 9.52 mm, fin number n = 60, fin height H = 0.2 mm). The results were used for two goals: the former is the comparison of the heat transfer features of the two fluids, while the latter aims at testing the performance of prediction models available in the open literature. At the saturation temperature T = 35°C, the two fluids show small differences in the thermal properties so that, as expected, the experiments highlighted a very similar behavior in the typical operating conditions of HVAC systems. In fact, for all the operating conditions marginal differences were observed in the pressure drop, the heat transfer coefficient and the flow pattern maps. The issue of prediction reliability, however, is still open. Actually, not all the models achieving good results for R134a show the same performance for R1234ze(E), especially for the pressure drop.

Investigation on the thermal management performance of a non-contact flow boiling cooling system for prismatic batteries

It is a great challenge to control the temperature of high energy-density lithium-ion batteries within an appropriate working range during rapid charging and discharging with a battery thermal management system (BTMS). As a hot topic in current BTMS research, boiling cooling technology with high heat transfer efficiency is a reliable way to solve these thermal management problems. In this study, a novel thermal management system for prismatic batteries based on cooling by non-contact flow boiling is proposed, and various cold-plate structures are considered with different numbers and locations of coolant inlets and outlets inside the cold plate cavity, and with different numbers and arrangements of ribs and fins. A three-dimensional transient model was conducted to investigate the effect on the cooling performance of the boiling BTMS of several variables — notably inner-channel design schemes, the number of ribs or fins in the cold plate, coolant inlet temperatures, and inlet Reynolds numbers. The results indicate that among the six design schemes that were considered, the best comprehensive heat transfer performance is achieved with two pairs of inlets and outlets, a vertical fin arrangement, and fin height equal to 3/4 of the inner channel dimension. With an increase in the number of fins, the maximum temperature and maximum temperature difference of the structures that were considered decrease by no <0.8 °C and 0.2 °C, respectively. Also, the temperature uniformity of the battery pack can be improved by appropriately increasing the coolant inlet temperatures and reducing the inlet coolant flow rate. When the number of fins is 19, the inlet temperature is 29 °C, and the inlet Reynolds number is 893, the preferred BTMS is always able to maintain its maximum temperature below 35.67 °Cand the maximum temperature difference to below 4.47 °C, at 3C high discharge rate.

Numerical and experimental investigations on melting heat transfer performance of PCM in finned cold thermal energy storage

Cold thermal energy storage (CTES) is of great importance for the enduring decrease in fossil fuel energy consumption. Moreover, CTES with phase change materials (PCMs) can be an effective measure to accumulate the heat or cooling energy for overcoming the mismatch between the supply and demand of air conditioning loads, augmenting system dependability and flexibility in operations of power grids. This paper numerically and experimentally examines the melting characteristics of PCM inside a CTES tank with the installation of interior fins. The computational fluid dynamics (CFD) software ANSYS/Fluent® is applied to predict the time sequences of liquid fraction contours and temperatures in comparison with the photographed images of ice-liquid water interface and measurement data in the CTES tank to verify the accuracy of CFD predictions. The simulations by the validated CFD model are extended to evaluate the influences of fin height and total number of longitudinal fins on the heat transfer outcomes in the storage tank. The present study further proposes a novel design adopting stratified fins to enhance the melting performance of the CTES device. The estimated mean power with the new stratified fin design is notably greater than that without fins by 156.3%, achieving the effectively liquefaction enhancement of ice for guiding the development of finned cold thermal energy storage.

Design and Optimization of a Spiral-Tube Instantaneous Water Heater Using Response Surface Methodology

In this paper, the fabrication and optimization of a spiral-tube heat exchanger (STHE) were considered for improving the heat transfer rate and efficiency of traditional instantaneous water heaters. The large number of instantaneous water heaters exported from the customers of the “Garman Gas Toos” company, which was mainly due to corrosion and leakage, imposed a lot of cost and credit reduction for this company. The high energy consumption was the second reason that justified working on a new STHE. The main innovation of this research is the design and construction of a new heat exchanger with a smaller size and higher efficiency with the help of identifying the factors affecting its efficiency and heat transfer rate. In order to optimize the responses, three variables were considered, including fin number (per unit area), exhaust outlet diameter, and water flow rate. Implementing face-centered central composite design (CCD), the proposed levels of factors and the corresponding response variables were measured in the “Garman Gas Toos” laboratory. Using the design of experiments (DoE), the effects of the three factors and their mutual interaction effects were evaluated. Response surface methodology (RSM) was devised to build a prediction model and obtain the values of the factors for which the responses were optimal. Based on the results, optimum conditions for the STHE were found to be an exhaust diameter of 4 cm and a water flow rate of 6 L/min coupled with six fins. At this optimal point, the values of efficiency and heat transfer rate, as response variables, were obtained as 85% and 8480 W, respectively.

Improving the ability of thermoelectric generators to absorb industrial waste heat through three-dimensional structure optimization

A large amount of waste heat in the industrial sector is lost to the environment in the form of radiant heat, causing serious energy loss. In this study, thermoelectric conversion technology is used to recover industrial radiant heat, and the ability of the thermoelectric generator (TEG) to absorb radiant heat is effectively improved by optimizing the heat collector's structure. In order to reduce the research cost, the heat transfer process between the industrial environment and TEG is analyzed by a numerical calculation method. According to the numerical calculation results, the influence of the heat collector's structure on the power generation performance is analyzed, and the optimal structure scheme is determined. Finally, the accuracy of the research results is verified by industrial experiments. This study makes up for the need for related research through many industrial experiments. The results show that increasing the height and number of heat collecting fins will increase the hot end temperature of the heat collector. When the number of fins is 19, and the height is 8 cm, TEG's total heat absorption and output power are the largest. The total heat absorption is 1.0 kW, and the output power is 38.4 W. The longer the length of the heat collector, the more pronounced the temperature inhomogeneity, leading to an increase in the number of the low-efficiency thermoelectric module (TEM). The number of low-efficiency TEM is the least when L = 50 cm, so the conversion efficiency of the TEG is the largest, and the conversion efficiency is 3.76 %.

Design and Optimization of a Helix Finned Tube Heat Exchanger for 2 K Superfluid Helium Vertical Test Stand

Abstract A 2 K heat exchanger is essential for 2 K superfluid helium cryogenic systems, as it increases cooling capacity and improves overall system efficiency. The thermal performance of a 2 K heat exchanger is affected by many factors, such as fluid properties, operating conditions, and geometric parameters. The segmented effectiveness-NTU method approach is used to design the heat exchanger because the physical prosperities of helium vary significantly in the heat exchanger's working temperature, which greatly influences heat transfer characteristics. Meanwhile, the response surface methodology (RSM) is used to optimize the heat exchanger. The optimum combination of geometry parameters is found based on thermal performance and fabrication. According to analyses of single and multiple geometric characteristics by RSM, the tube diameter and fin number have the most significant impact on the heat exchanger performance. Finally, the performance of the heat exchanger is verified experimentally. The experimental results are in good agreement with the present design and optimization model.