Pin Fin Research Articles

Experimental analysis of double layer microchannel heat sink with distinct fin configurations in upper and lower layers

In the present experimental study, two distinct configurations of double layer microchannel heat sinks (DL MCHS) are proposed. It consists of rectangular parallel channels in the bottom layer and an array of square pin fins in the upper layer. Pin fin height (Hf) in the first configuration is equals to the channel height (Hc) (i.e. Hf/Hc=1). However, in the second configuration, pin fin height is equivalent to 75 % of Hc such that Hf/Hc=0.75. The proposed modified DL MCHS configurations are then compared with the conventional double layer microchannel heat sink (CDL MCHS). Hence, the idea of the current work is to develop a novel DL MCHS with improved heat transfer capabilities and reduced pressure penalties. Heat dissipation rate, pressure data and coolant flow behaviour are carefully measured and analyzed. Findings reveal that thermal performance of the modified heat sink with Hf/Hc=1 is not appreciable because it delivers almost similar to conventional configuration. Whereas, modified heat sink of Hf/Hc=0.75 has consistently exhibited better heat transfer rate and thermal performance factor. As compared to CDL MCHS, thermal performance factor was found ≈38 % higher in this case. Overall thermal and hydraulic performance of the DL MCHS is significantly influenced by the flow pattern of the coolant, which is a result of the novel channel design.

Effect of Trenched Hemispherical Pin Fins on Cooling Performance of Heat Sink

Effect of Trenched Hemispherical Pin Fins on Cooling Performance of Heat Sink

Investigation on flow characteristics and its effect on heat transfer enhancement in a wedge channel with combination of circular, oblong, teardrop, and pencil pin fins

Abstract Gas turbine engines are used extensively in a variety of industries, including power generation, aviation, and marine propulsion. One of the most difficult issues in developing gas turbine engines is dealing with the high temperatures. Internal cooling is a typical strategy for keeping important components, such as turbine blades, at a safe working temperature. Pin-fin cooling is a significant technology used in gas turbine blades to manage severe operating temperatures. This research paper investigates the impact of a new geometry combining two pin fins in cooling channels in gas turbine blades. The study involved testing seven different pin-fin arrays over a Reynolds number varying from 10,000 to 80,000 and a constant heat flux of 3280 W/m2 applied to all the surfaces. The findings indicate that the use of pencil pin fins leads to a notable enhancement in cooling efficiency owing to the existence of a low-pressure drop, 5.2 % compared to pencil and tear drop pin fins and by 1.6 % compared to pencil and oblong pin fins, and it is 1.7 % less than pencil and circular fins.

Experimental and numerical investigation on turbulent convection enhancement in minichannel heat sink with staggered V-shaped pin fins

With the continuous advancements in new energy vehicle technology, the insulated gate bipolar transistor (IGBT) thermal properties have a direct impact on power system reliability. In this article, a minichannel heat sink with staggered V-shaped pin fins (SVPF) is investigated through both experimental and numerical approaches. Initially, the heat transfer performance of SVPF and conventional minichannel heat sink was analyzed using the CFD numerical simulation method. Subsequently, numerical and experimental validation was carried out by assessing the Nusselt number and turbulence characteristics of SVPF. Finally, an in-depth analysis was conducted to investigate the effects of SVPF geometric parameters on the turbulent characteristics and heat transfer performance of the minichannel heat sink. The results demonstrate that SVPF exhibits superior hydrothermal performance, which could maintain better heat transfer performance while simultaneously reducing the friction factor of minichannels. These findings provide valuable insights for the design of three-dimensional pin fins minichannels heat sink.

A comprehensive study on passive cooling of a PV device using PCM and various fin configurations: Pin, spring, and Y-shaped fins

This study addresses the need for effective passive cooling strategies in compact photovoltaic (PV) modules by exploring three distinct fin shapes—pin fin, Y-shaped fin, and spring fin—utilizing both numerical simulations and experiments. The objective is to enhance heat transfer rates in PV devices through extended surfaces and phase-change material (PCM). Departing from conventional approaches like metal foams and plate fins that contribute to increased weight and system complexity, the research employs the finite volume method in computational fluid dynamics for numerical simulations, validated with experimental data. Comparative scenarios include fins with the same cross-sectional area and the same volume, revealing that the pin fin configuration outperforms others significantly. An experimental focus on pin fin numbers and lengths demonstrates a remarkable 9 °C temperature reduction with fully saturated pin fins, translating to a 4 % increase in efficiency and a noteworthy 0.8 V enhancement in open-circuit voltage. The findings underscore the potential of this proposed PV-PCM passive cooling approach for achieving performance enhancements while being easily constructed at a lower cost, providing a cost-efficient solution with clear quantitative results indicating temperature reduction, efficiency improvement, and enhanced voltage.

Orientation effects on mixed convective performance of twisted pin fin heat sink: Experimental investigation

In the current work, an experimental study is carried out to examine the heat transfer performance and friction effects on a pin fin matrix of a heat sink for different design variables and operating conditions. This examination aims to assess the thermo-hydraulic performance of the heat sink with three orientations (90°, 180°, and 270°). In the presence of three heat loads (66 W, 91 W, and 121 W), each of these orientations is tested with three twisting angles (30°, 60°, and 90°) for different pin fins cross-sections of square and hexagonal at various ranges of air Reynolds number (Re) (3182 to 9971). The downward position of a heat sink achieves a higher Nusselt number (Nu) than the sideward and upward positions. The fin pin with a twisting angle 30° has superior efficiency for three orientation angles and hexagonal and square cross sections. Square pin fin records the lower thermal performance at Re = 3182, orientation angle (β) = 270˚, and pin twist angle (θ) = 30°, and the best at Re = 9971, β = 180°, and θ = 90°. Compared to 60˚ and 90˚, the pin fins had a reduced pressure loss at a twisting angle of 30°.

Performance enhancement of a battery thermal management system using novel liquid cold plates with micro-channel featuring pin fins

The battery thermal management system (BTMS) with liquid cold plates has been proven to be effective in temperature control and heat transfer. In this work, a novel liquid cold plate featuring pin fins for the cooling of prismatic lithium-ion batteries is proposed. The performances of BTMS with liquid cold plates are numerically investigated by using a three-dimensional CFD model and compared under different coolant inlet velocities, pin fins' heights, and arrangements. The efficiency index (EI) is employed to evaluate the comprehensive performances of cold plates by considering heat transfer and liquid flow. The results indicate that the introduction of pin fins contributes to improving the heat transfer performance and thus reducing the maximum battery temperature rise (ΔTrise) and temperature difference (ΔTdiff). Besides, both the ΔTrise and ΔTdiff increase as the pin fins’ height (PFH) decreases. However, the cooling micro-channel with pin fins featuring a dimensionless height (Hd) of 1/4 provides the best thermo-hydraulic performance and the lowest power consumption under the same battery thermal performance. In addition, the cooling micro-channel with pin fins placed on two opposite heat transfer walls exhibits better heat transfer performance and thus better battery thermal performance, compared with the cooling micro-channel with pin fins placed on the single heat transfer wall. When the coolant inlet velocity of 0.4 m/s at a 3C discharge rate the ΔTrise and ΔTdiff of the cold plates with pin fins staggered arrangement in stream-wise direction for the opposite walls on both top and bottom walls are reduced by 4.045K and 3.122K, respectively, compared with the cold plates without pin fins.

Multi‐objective optimization of a Fibonacci phyllotaxis micro pin‐fin heat sink

AbstractThere are still significant technical challenges associated with thermal management of electronic devices such as microprocessors. To improve heat dissipation performance of integrated circuits, a new Fibonacci phyllotaxis design of circular micropin fin heat sinks has been developed. To minimize both chip temperature and pumping power, a multi‐objective optimization technique was employed. The effect of design parameters such as phyllotaxis coefficient, pin fin diameter, and pin fin height on response parameters was numerically investigated using the full factorial design of the experiment. Artificial neural network was coupled with MO‐Jaya, to arrive at a Pareto frontier of optimal compromise solutions. The optimal set of design variables were found to be a height of 300 μm, a diameter of 122.6 μm, and a phyllotaxis coefficient of 130 μm with an inlet velocity of coolant 2.263 m/s. The selected optimum design was then investigated numerically, and the outcomes were compared to those predicted by the MO‐Jaya algorithm. The final confirmed response variables were a maximum temperature of 51.6°C and a pumping power of 0.191 W. The results show that the Fibonacci phyllotaxis structure of the micro pin fin heat sink has better heat‐dissipating performance.

Computational analysis of microchannel heat sinks with constant circular pin fins: Performance evaluation and optimization

This research entails a comprehensive computational simulation aimed at comparing the performance of microchannel heat sinks (MCHS) featuring 55-pin fins, characterized by constant circular pins with a diameter of 15µm, uniform spacing of 50µm, and variable heights ranging from 60 to 35µm. The primary objective was to assess the performance of these models with a reference Mini channel. Mesh independence validation was meticulously executed on MCHS with pin fins to ascertain the accuracy of the computational findings. The simulation encompassed seven Reynolds numbers within the range of 500–1500. The performance evaluation incorporated hydraulic and thermal factors, specifically pressure drop, Nusselt number, and the thermal performance factor (TPF). A holistic assessment of overall performance was achieved through the establishment of a heat sink thermal performance factor, accounting for both hydraulic and thermal aspects. The optimal geometry was determined based on this factor, and corresponding visual representations were generated to illustrate these findings.

Investigation on the thermal and hydraulic characteristics of the micro heat sinks with grooves and pin fins by Taguchi-based sensitivity analysis

The heat dissipation issue of the micro electronic devices seriously restricts their application in the aerospace, national defense, communication, etc. The novel heat sinks with trapezoidal grooves and rectangular pin fins are proposed to meet the cooling requirement of the high-power devices. The cooling effect, thermohydraulic characteristics, total efficiency and thermodynamic performance of the heat sinks are studied by three-dimensional numerical simulation. Firstly, the influence of the relative position between the grooves and the pin fins on the thermohydraulic performance is explored in detail. Secondly, Taguchi optimization and analysis of variance are adopted to quantitatively analyze the impact degree of the pin fin width, length and height on the Nusselt number, friction factor and total performance index. The optimal structures are obtained for different objectives. Lastly, the temperature performance, total performance and the irreversibility of the optimal structures are compared thoroughly. New findings include that: the best arrangement of the grooves and pin fins is obtained, which enhances the Nusselt number by 1.5 times compared to the smooth heat sink. The fin width is the most critical factor for the heat transfer and flow, while the fin length shows the greatest importance in the overall performance. The optimized heat sink with the fin width of 50 μm, length of 60 μm and height of 150 μm reduces the peak temperature by 12.3 ℃ compared to the smooth heat sink for Reynolds number of 303. This heat sink yields the highest total performance index with 1.43 for Reynolds number of 368 and significantly reduces the irreversible loss. Moreover, the optimized heat sink with the fin width of 10 μm, length of 60 μm and height of 100 μm reduces the friction factor by 61.39 % compared to the original structure for Reynolds number of 635, which is beneficial to reduce the energy consumption. The quantitative analysis of the parameter sensitivity for novel heat sinks reveals the mechanism of the heat transfer enhancement by modifying the geometric parameters and provides an effective solution for thermal management of the high-power devices.

Topological and multi-objective optimization of single-phase heat transfer and energy efficiency using manifold micro-channels for high-power electrics cooling

To achieve energy-efficient cooling of high-power electrics, present work demonstrates combined methods using topological design and multi-objective optimization to reconstruct manifold micro-channels (MMC). The micro-channel domain is first topologized by density-based method under pressure drop and energy dissipation constraints. The multi-objective optimization is subsequently applied to optimize structure and operating parameters of reconstructed MMC using kriging model and genetic algorithm. The simulation results show that favorable thermal performance is obtained in the topological MMC with branch-channels, pin fins and root-channels, increasing average heat transfer coefficient by 19.4 % compared to conventional MMC. For the optimal flow rate, the lowest total thermal resistance (Rtotal) of 0.17 KW−1 is obtained for the optimized-topological MMC at a pumping power (Pp) of 9.53 mW, meanwhile the maximum temperature-rise is decreased by 15.2K. Furthermore, an extensive benchmark of different single-phase micro-fluidic cooling technologies is performed. For an extremely low Rtotal of 0.2 KW−1, present optimized-topological MMC only requires Pp of 3 mW, which is 11.7 times, 26.7 times and 70 times lower than that of conventional MMC, pin-fin and strip-fin micro-fluidic systems. This superior hydro-thermal performance successfully manages the heat flux of 100 W/cm2 to 400 W/cm2 with cooling coefficient of 104 to 107, significantly outperforming other micro-fluidic cooling technologies.

Experimental optimization of conical solar distillers using graphite pin fins as sensible heat storage materials: Energy, exergy, and exergo-economic approach

Fresh water and energy are essential for the development and prosperity of societies. Solar stills are easy to build, operate, and maintain, but their disadvantage is low daily productivity. This work aims to optimize and enhance the performance of conical solar stills by integrating innovative graphite pin fins that function as extended surfaces and sensible energy storage in the distillation basin. Graphite is inexpensive, available locally, natural properties, and has good thermal characteristics and heat capacity. Four different alternates spacing between the graphite pin fins ranging from 10 to 70 mm have been investigated and optimized to achieve maximum daily water production. Three identical conical solar distillers were designed, manufactured, and tested, under the same weather conditions in El Oued city, Algeria (33.3676◦ N and 6.8516◦ E). Energy, economy, exergy, and exergo-economics approach were performed to evaluate the economic feasibility of modified conical distillers. The results showed that reducing the distance between the pin fins leads to a decrease in the productivity of the distiller due to the increase in the shadow area. Among the pin fin distances evaluated, the 50 mm distance achieved the highest daily water production with reasonable economic feasibility. Adding graphite pin fins to conical distiller basin increases daily productivity and thermal efficiency by 52.16–90.78% and 33.44–63%, respectively. The production cost and payback time of the modified conical distillers with pin fins are reduced by 35.49–79.72% and 35.48–79.72%, respectively compared to the traditional conical stiller.

A conjugate heat transfer investigation of outer-wall cooling performance in double-wall vane pressure side

Double wall cooling has significant potential for high-pressure turbine vane cooling technology. Geometric parameters of the double-wall vane play a crucial role in determining the cooling performance. This paper presents a double-wall cooling model with five outer wall thicknesses and three injection angles, using the curvature of the actual pressure side of the engine as a reference. The overall cooling effectiveness is investigated over the range of blowing ratio from 0.5 to 2.5. Results indicate that, at injection angles of 20° and 30°, an outer-wall thickness of 1.5D f maximizes the combined benefits of film cooling and thermal conductivity in solid domains. At an injection angle of 40°, the blowing ratio becomes a determining factor in selecting the optimal outer wall thickness. Additionally, a reasonable arrangement of pin fins promotes a more uniform outer wall temperature distribution. A thinner outer wall at higher blowing ratios provides optimum overall cooling effectiveness.

An approach for topology optimization of heat sinks for two-phase flow boiling: Part 2 – Model calibration and experimental validation

Flow boiling offers increased heat transfer coefficients and effective heat capacity rates that can be leveraged by topology optimization (TO) to generate high-performance microchannel heat sinks. Topology optimization of heat sinks having two-phase flows can be accomplished using the homogenization approach wherein designs are represented as spatially varying distributions of microstructures, as demonstrated in Part 1 of this two-part study. Flow and heat transfer within the microstructures are captured using a two-phase mixture model featuring an effective porous medium formulation. However, closure of these governing equations requires empirical correlations for pressure drop and heat transfer that are specific to the operating conditions, geometry, and surface finish. Therefore, it must be demonstrated these available correlations can be successfully calibrated over a range of microstructural variations present within the homogenization framework, so as to attain the required prediction generality and accuracy needed to ensure the resulting designs achieve Pareto-optimality. This Part 2 of our study successfully demonstrates a comprehensive end-to-end process for two-phase flow model calibration, topology optimized design generation, and experimental validation of optimized performance for flow boiling heat sinks. To this end, a TO algorithm with the homogenization approach and a two-phase mixture model is implemented using available flow boiling correlations for microchannels. A set of uniform pin fin calibration samples are additively manufactured and experimentally tested under flow boiling at various flow rates and heat inputs for model calibration. All of the unknown/free coefficients in the adopted correlations are determined by minimizing the error between the model predictions and the experimental measurements using gradient-based optimization. The calibrated topology optimization algorithm is then used to generate a Pareto-optimal set of heat sinks optimized for minimum pressure drop and thermal resistance during flow boiling. Experimental characterization of these additively manufactured heat sinks, unseen during the model coefficient calibration process, reveals that the measured Pareto optimality curve matches that predicted by the topology optimization algorithm. Lastly, a heat sink design is generated for a design space involving multiple hot spots and background heating to showcase the capability of the experimentally calibrated two-phase topology optimization algorithm at handling complex boundary conditions. The optimized heat sink intelligently distributes an adequate amount of coolant flow to each of the heated regions to avoid local dry-out. This work demonstrates a complete framework for two-phase topology optimization of heat sinks through experimental calibration of flow boiling correlations to the porous medium used by the homogenization approach.

Heat transfer optimisation using novel biomorphic pin-fin heat sinks: An integrated approach via design for manufacturing, numerical simulation, and machine learning

With the availability of advanced manufacturing techniques, non-conventional shapes and bio-inspired/biomorphic designs have shown to provide more efficient heat transfer. Consequently, this research investigates the heat transfer performance and fluid flow characteristics of novel biomorphic scutoid pin fins with varying volumes and top geometries. Numerical simulations were conducted using four hybrid designs for Reynolds Number 5500–13500. The impact of pin fin 'top' geometrical features on the heat transfer coefficient (HTC) was evaluated by combining computational fluid dynamics (CFD), experimental data, and machine learning. The results highlighted that the new pin fins saved 6.3 % to 14.3 % volume/material usage but produced around 1.5 to 1.7 times more heat transfer than conventional square/rectangular fins. Also, manipulating pin fins via the top geometrical properties can lead to more uniform velocity and temperature distributions while demonstrating the potential for increased thermal efficiency with reduced thermal resistance. Furthermore, six machine learning models accurately predict HTC using volume and surface area as key variables, achieving less than 5 % mean absolute percentage error (MAPE). Overall, this research introduces innovative biomorphic designs with unconventional geometries, emphasising resource optimisation and efficient HTC prediction using machine learning. It simplifies design processes, supports agile product development, calls for re-evaluation of conventional heat sink geometries, and provides promising directions for future research.

Numerical study of heat transfer enhancement by using protrusions in curved pin-fin arrays

The trailing edge of a turbine blade constantly faces the harshest conditions, and pin fin is usually equipped for internal cooling channel of trailing edge to augment heat transfer. The present study aims to explore the impact of various protrusion positions on the heat transfer efficiency of a hybrid channel, incorporating protrusions and curved pin fins, under both stationary and rotational conditions. Three protrusion positions (front, middle, and behind) are studied for the range of Ro from 0 to 0.5. The baseline of the curved pin fins channel without protrusions is considered. This study is based on the numerical method of the realizable k-ε turbulence model for calculation. Numerical calculations reveal that arranging protrusions within the curved pin-fin channel can significantly enhance the overall heat transfer performance. Protrusions of front get the best improvement 15.47% in thermal performance factors under stationary condition. Under rotating condition, the arrangement of protrusions also brings improvement of the Nu number on endwalls from 5.32% to 10.74%.

CFD simulation and geometric optimization of a novel baffle heat sink for power electronics cooling

The electric drivetrain of an electric vehicle typically has two fluid circuits: an oil circuit for lubrication and a water-glycol circuit for cooling. Eliminating the water-glycol circuit can result in a more compact and lighter drivetrain. However, this requires the drivetrain components to be cooled with oil as coolant, which has inferior heat transfer properties compared to water-glycol mixtures. This is particularly challenging for the power modules in the power electronics unit, which exhibit some of the highest heat fluxes in the drivetrain. This study focusses on the design and optimization of a novel type of heat sink for laminar flows with baffles to guide the flow in four different directions. This has two main advantages: the baffles act as fins and increase the heat transfer area and they introduce a swirling motion in the oil thereby disturbing the boundary layers continuously. Computational fluid dynamics simulations using Ansys Fluent are performed to evaluate the thermohydraulic performance of the heat sink. The influence of design parameters such as the height and thickness of both fins and baffles and the baffle spacing in horizontal, upward and downward direction was evaluated by simulations with several combinations of the design space, considering manufacturing constraints. The optimization of the design showed that the fin thickness, horizontal baffle spacing and baffle length should be as small as possible, while there were optimal values for fin height, upward and downward baffle spacing, streamwise baffle spacing and baffle thickness. The simulations show that the thermal resistance of the baffle heat sink can be 19% lower than that of a benchmark pin fin heat sink at equal pumping power.

Thermal performance of pin fin heat sinks with phase change material for electronic devices thermal management

In the present paper, an experimental and numerical study is conducted to analyze various factors affecting the thermal performance of a heat sink with phase change material (HS-PCM). In order to maintain the chip below the limit temperature of 80 °C, ZDJN-35 with a phase change temperature of 37 ∼ 45 °C is selected as the energy storage material. Under different PCM filling volume fractions, heat fluxes, and operation modes, the study evaluates the thermal performance of the HS using chip temperature and the effective time extension coefficient. The volume fractions of PCM are 0 vol%, 30 vol%, 60 vol%, and 90 vol%. Under heat fluxes of 4000 ∼ 14000 W/m2, the results indicate that under continuous operation, the HS without PCM reaches the limit temperature within 18 min at heat flux of 8000 W/m2. In contrast, the time to reach the limit temperature for HS with 30 vol% PCM, 60 vol% PCM, and 90 vol% PCM extends by 12 min, 19 min, and 26 min, respectively. Compared to the HS without PCM, the peak temperatures reduce by 4.8 %, 10.5 %, and 12.8 % for the HS with 30 vol% PCM, 60 vol% PCM, and 90 vol% PCM under intermittent operation. Moreover, under intermittent operation, temperature fluctuations decrease by 27.3 %, 36.0 %, and 37.3 %, respectively. Finally, the numerical results show that the optimization of pin fin diameter is opposite for passive and active cooling modes, and a heat dissipation unit height of 25.5 mm is recommended.

Numerical investigation of thermal and hydraulic characteristics in porous pin fin heat sinks using single phase nanofluids

This study aims to numerically investigate the thermal performance of porous square pin-fin heat sinks, considering three different configurations: inline, staggered, and 45° inline. Six different nanofluids, comprising CuO, Al2O3, and TiO2 nanoparticles dispersed in water and water–ethylene glycol mixtures at two volume fractions (φ = 0.5 % and 2 %), are employed as coolants. The impact of porosity on the thermal and fluidic behavior is also examined for the CuO–Water nanofluid (φ = 2 %) at porosity values of 40 %, 50 %, and 60 %. The commercial CFD code: Ansys Fluent 2020R1 is utilized for this numerical analysis and the results are compared to relevant experimental works for validation. The effects of heat sink geometry, nanofluid type, and porosity on heat transfer performance are systematically analyzed. The results show that the 45° inline configuration of the square pin-fin heat sink exhibits superior heat transfer enhancement compared to both the inline and staggered configurations. The use of nanofluids as coolants significantly improves the thermal performance compared to conventional fluids, with CuO–Water nanofluid demonstrating the most promising results. This comprehensive analysis provides valuable insights for the design optimization of high-performance cooling systems for electronic devices.

Fluid flow and heat transfer characteristics of a microstructured microchannel heat sink under flow boiling condition

A microchannel heat sink (MCHS) is known as a heat dissipation device from the miniaturized electronic components and devices due to its capability to dissipate high heat flux from smaller surface area. However, the higher pressure drop and the uneven heat removal along the channel length are the noticeable disadvantages of MCHS. Though there are attempts to address these shortcomings, no existing study has been found to study the effect of positions of microstructures (micro-pin fin and blind holes) and combined effect of micro-pin fins and blind holes under flow boiling condition. Therefore, in the present study, an attempt has been made to logically explain the effect of various arrangements and positions of pin fins and blind holes in the selected twenty-four uniformly distributed stations on the thermohydraulic performance of MCHS through numerically predicted results. The objectives of the study have been attained using the following three analyses, flow boiling, (i) with saturated fluid inlet conditions (inlet Re = 500), (ii) with different inlet subcooling (20, 40, and 60 °C), and (iii) with different heat flux conditions (100, 150, 200 and 250 W/cm2). From the study, it is observed that the pin fin enhances heat transfer in single-phase flow and delays the phase change by disturbing the flow. The blind holes act as nucleation sites and help phase change heat transfer. It is also observed that the ratio of single-phase and two-phase length and arrangement of microstructures in these two regions predominately dominate the heat transfer and fluid flow characteristics of the microchannel heat sink. The optimum performance (maximum heat transfer coefficient and minimum pressure drop) is achieved when twelve pin fins are placed in the upstream half and twelve blind holes are located at the downstream half of the channel. However, design improvement is possible through more computational and experimental analysis.