Triangular Pin Fins Research Articles

Experimental and numerical investigation of hydrothermal performance of a microchannel heat sink with pin fins

The hydrothermal performance of the microchannel heat sinks with different pin fins (PF-MCHS) is studied experimentally and numerically. Five pin fins, namely rectangular pin fin (RPF), backward triangular pin fin (BTPF), forward triangular pin fin (FTPF), diamond pin fin (DPF) and ellipsoidal pin fin (EPR) are integrated in the microchannel for enhancing heat transfer. The results show that the PF-MCHSs possess 51.8–94.8 % higher average Nusselt number than the conventional microchannel (CMC) without pin fins, which indicates that these pin fins all can cause significant heat enhancement in the microchannels. Among all finned microchannels, the MC- RPF and MC-BTPF can offer the larger Nusselt number than the other microchannels. In addition to the improved thermal performance, the pin fins also result in the larger apparent friction factor. Furthermore, taking the MC-RPF and MC-BTPF as examples, three non-dimensional parameters α = P/L, β = wp/hc and γ = lp/hc are proposed for optimizing the global characteristics of microchannels. The rise of Nussle number and apparent friction factor is often accompanied by a decrease in α, or an increase in β and γ.

A novel microchannel-twisted pinfin hybrid heat sink for hotspot mitigation

Thermal hotspots cause excessive localized temperature rise, leading to significant temperature gradients across the microprocessor, which is the primary reason for its inadequate performance and early failure. This study proposes microchannel-pinfin hybrid heat sinks incorporating twisted and non-twisted pinfins of various cross-sectional shapes (hexagonal, pentagonal, square, and triangular) to demonstrate energy-efficient hotspot mitigation in a microprocessor with highly non-uniform power distribution. Microchannels and pinfins are positioned at low- and high-heat-flux zones, respectively, to reduce the temperature variations utilizing their unequal heat transfer capabilities. Here, high- and low-heat-flux zones represent the microprocessor-core area (hotspot) and remaining chip area (background zone), characterized by heat fluxes of 300 W/cm2 and 50 W/cm2, respectively. The pinfin twisting angle varies from 0° to 360° at a step of 45°. Conjugate heat transfer analyses are conducted through numerical solutions of the continuity, Navier-Stokes, and energy equations. The performance of the proposed hybrid heat sinks is compared with the non-hybrid (NH) and hybrid circular pinfins (HCP) heat sinks at Re = 120–440. The hybrid heat sink featuring triangular pinfins twisted at 225° angle (HTP-225) exhibits a remarkable reduction of 48.2 % in the total thermal resistance (Rth) and 58.4 % in the temperature non-uniformity (δT,bs) as compared to the NH heat sinks at Re = 440. Compared to the HCP design, the HTP-225 design shows 26.9 % and 35.8 % lower Rth and δT,bs, respectively. Moreover, the HTP-225 heat sink outperforms the NH heat sink with 46.0 % and 57.0 % lower Rth and δT,bs, respectively, at an equal pumping power of 18.6 mW. Furthermore, the HTP-225 heat sink demonstrates a 96.4 % and 38.5 % higher critical hotspot heat flux dissipating capacity than the NH and HCP heat sinks, respectively, making it a viable and effective solution for alleviating hotspots in high-power-density devices.

Numerical study about thermal performance evaluation of PCM and PCM/fins composite-based thermal control module at microgravity conditions

Satellite subsystems are becoming smaller and have extra power density. There are only two types of heat transport in space: conduction and radiation, making thermal management more difficult. For the thermal regulation of satellite subsystems, thermal energy storage materials are appropriate. In the present study, small satellite subsystems were controlled using a phase change material (PCM)-based heat sink. The design of the aluminium heat sink was according to the outside dimensions of the subsystem in a small satellite. The PCM material used in the work was RT 35. Integrated fins of various shapes were used to overcome PCM's poor thermal conductivity. Three fin geometries were investigated: parallel fins, cross fins, and pin fins. Three shapes of pin fins were evaluated: square pin, circular pin, and triangular pin fins. The heat sink was exposed to a thermal cycle with 80 min cooling and 10 min heating processes. The results reveal that pin fins have better thermal performance than cross and parallel fins. For pin fins, the triangular pin fin provides the best thermal performance among all cases. Maximum temperatures reported for triangular pin fin were 41.5 °C with a 10.8 % reduction. The results indicated a considerable improvement in thermal performance by increasing the number of pin fins.

Three-dimensional Lattice Boltzmann study on structure optimization and heat dissipation performance of pin-fin heat sink integrated with phase change material

Phase change material (PCM) cooling is an excellent approach for reducing the excessive temperature of electronic devices. However, the heat transfer capacity of a heat sink is diminished by the low thermal conductivity of a PCM. Although this issue can be ameliorated by using extended pin-fins and nanoparticles, the latent heat storage capability of a PCM is decreased. To optimize the heat transfer efficiency of PCM heat sink with pin-fins, in this study, the effects of pin-fin shapes (circle, triangle, square, pentagon, hexagon, and octagon), novel arrangements with triangular fins, and the volume fraction of nanoparticles are investigated using the 3D enthalpy-based multi-relaxation time lattice Boltzmann method. The results showed that the PCM heat sink with triangular pin-fins exhibited optimal thermal performance due to the largest heat transmission area between the PCM and pin-fins. After conducting optimization research on triangular pin-fin arrangements, the full melt time was shortened by 14.3 % and the heat dissipation power was increased by up to 15.2 %, when compared with the PCM heat sink with triangular pin-fins. Furthermore, nanoparticles with a volume fraction of <0.1 were beneficial for balancing the elevated heat dissipation capacity and reducing the latent heat duration of the nano-enhanced PCM.

Cooling performance in a minichannel heat sink with different triangular pin-fins configurations

With the continuous progress of automotive new energy technology, the motor has become an important part of the power system, and the heat dissipation of insulated-gate bipolar transistors (IGBT) determines the reliability of the power system. Minichannel structure can be added to the thermal management system of new energy vehicles to improve the heat transfer capacity. Due to the growth of the boundary layer in the smooth minichannel flow channel, the cooling performance improvement was limited. Pin-fins and rib structures were used to break the boundary layer and increased the heat transfer area to enhance the heat transfer capacity. In this study, a numerical simulation model of minichannel with triangular pin-fins with different rotation angles was established and calculated using the SST k-omega method. The temperature field, velocity field, pressure, and vortex distribution under different configurations were discussed in detail. The jet area formed by the prism wall and the side wall of the minichannel would impact the wall and reduce the growth of the boundary layer. However, the stagnation area generated in the center and corner will reduce the improvement of heat transfer capacity. The thermo-hydraulic characteristics of different configurations at different Reynolds numbers (Re), such as Nusselt number (Nu), Darcy friction resistance coefficient (f), and performance evaluation criterion (PEC), were analyzed. As Re increased, the best and worst configurations changed, the best configuration changed from the 90°–120° structure to the 120°–120° structure, and the worst configuration changed from the 75°–60° to the 60°–60° structure. When the Re = 663, the influence of the front and rear rotation angle on the cooling performance was explored. When the rotation angle was closer to 60°, the cooling performance of the minichannel was better. And the closer the rotation angle was to 120°, the cooling performance was better. This has a reference effect on the design of minichannel heat sinks.

Experimental Analysis of Nano-Enhanced Phase-Change Material with Different Configurations of Heat Sinks.

The demand for high-performance and compact electronic devices has been increasing day by day. Due to their compactness, excessive heat is generated, causing a decrease in efficiency and life. Thermal management of electronic components is crucial for maintaining excessive heat within the limit. This experimental research focuses on the combined effect of nano-enhanced phase-change material (NePCM) with different configurations of heat sinks for cooling electronic devices. Multi-walled carbon nanotubes (MWCNTs) are used as nanoparticles with concentrations of 3 wt% and 6 wt%, RT-42 as the phase-change material (PCM), and aluminum as the pin fin heat sink material. Different configurations of the heat sink, such as circular, square, and triangular pin fins, are used against the fixed volume fraction of the fins. It is found that the square configuration has the highest heat transfer with and without PCM. A maximum base temperature reduction of 24.01% was observed in square pin fins with RT-42 as PCM. At 6 wt% of NePCM, the maximum base temperature lessened by 25.83% in the case of a circular pin fin. It is concluded from the results that a circular pin fin with NePCM is effective for base temperature reduction, and all fin configurations with NePCM collectively reduce the heat sink base temperature.

Cooling a plate lithium-ion battery using a thermoelectric system and evaluating the geometrical impact on the performance of heatsink connected to the system

In this paper, the cooling process of a plate lithium-ion battery cell using thermoelectric is simulated. The cold part of the thermoelectric is placed on the battery and a heatsink with a number of pin fins is mounted on the hot part of the thermoelectric. Pin fins have elliptical, circular, triangular, and trapezoidal shapes. They are placed in a channel saturated with alumina nanofluids (NFs). By changing the Reynolds number (Re) of NFs flow between 300 and 600 for different types of pin-fins, the values of battery and heatsink temperature, NFs output temperature, and pressure drop (DP) are examined. The battery cooling system is modeled using COMSOL Multiphysics software. The findings show that utilizing triangular pin-fins creates the greatest DP in the channel, and the output NFs temperature is greater than using other pin-fins. The oval pin fin leads to the minimum DP and NFs temperature drop in the channel. The use of a triangular pin-fins results in the minimum temperature on the battery and the heatsink, while the elliptical pin-fins cause the maximum temperature (Tm) on the battery and the heatsink. As the Re enhances from 300 to 600, the DP is enhanced 4.85 and 7.67 times for the elliptical and triangular pin fins, respectively.

Thermal management of Electronics: Numerical investigation of triangular finned heat sink

The micro pin fin heat sink is an innovative method to enhance heat dissipation from the electronic system. The various geometrical configuration of the triangular micro pin fin heat sink (TMPFHS) for the fluid and heat transfer characteristics is numerically investigated in the present work. Finally, the best configuration is proposed. Three different configurations of triangular pin fin have been considered (i) uniformly varying the fin height ranging 0.25 mm-0.75 mm. (ii) Orientation of fin both in the clockwise and counter-clockwise direction (30°, 40°, 50o, and 60°) (iii) Change in the direction of fins facing upstream fluid from forward triangular to backward triangular between two successive rows and vice versa. A 3-Dimensional numerical simulation is carried out for a triangular finned heat sink arranged staggered manner subjected to 10 W/cm2. A single-phase laminar flow is considered for Reynolds numbers ranging from 100 to 900 using coolant water. Results reveal that the heat dissipation rate for all the configurations increases substantially with the rise in pressure drop. A Non-dimensional parameter thermal performance index (TPI) is employed to access the superior heat sink in maximum dissipation and minimum pressure drop. The TPI with alternate forward and backward arrangement outperforms all other configurations of the range 1.01–1.44.

Experimental Investigation of Innovative Cooling Schemes on an Additively Manufactured Engine Scale Turbine Nozzle Guide Vane

Abstract This study includes the design, validation, and fabrication via direct metal laser sintering (DMLS) of a gas turbine nozzle guide vanes (NGV) that incorporates three innovative cooling schemes specifically enabled by additive manufacturing. The novel NGV design is the culmination of an extensive research and development effort over a period of 4 years that included low- and high-speed cascade testing coupled with unsteady computational fluid dynamics for numerous candidate innovative cooling architectures. The final vane design (SJ-vane) consists of sweeping jet (SJ) film cooling holes on the suction surface (SS), sweeping jet impingement holes at the leading edge and double-wall partial length triangular pin-fin with impinging jet at the trailing edge. For comparison purposes, a second DMLS enabled vane (777-vane) was designed and fabricated with prototypical cooling circuits to serve as a baseline. This vane consists of a shaped film cooling holes on the suction surface, circular impingement holes at the leading edge, and full-length cylindrical pin-fins at the trailing edge. Experiments with the two DMLS enabled vanes were performed at the Ohio State University Turbine Reacting Flow Rig (TuRFR) at engine-relevant temperature (1375 K) and Mach number conditions. Infrared (IR) thermography was utilized to measure the wall temperature of the pressure and suction surface at several coolant mass flowrates to estimate the overall cooling effectiveness (ϕ). Results showed improved cooling performance for the advanced cooling schemes (sweeping jet film cooling, impingement cooling, and triangular pin-fin cooling) compared with the baseline cooling schemes.

Conjugate Heat Transfer Study of Innovative Pin-Fin Cooling Configuration

The Paper involves experimental and numerical heat transfer analyses of four pin-fin cooling configurations in a rectangular channel. Two design concepts were studied with two separate pin-fin (cylindrical and triangular) geometries. The first design includes a single-wall pin-fin configuration where the coolant flows through an array of full-length cylindrical (PF) and triangular pin fins (TF). The second configuration involves a double-wall pin-fin–jet configuration where the coolant jet impinges on the target wall, then flows through the array of partial-length cylindrical pin fins with jets (PFC) and partial-length triangular pin fins with jets (TFC). IR thermography was used to measure the steady state wall temperature of the target surface to estimate the overall cooling effectiveness . A transient heat transfer experiment was conducted to evaluate the internal heat transfer coefficient from the transient wall temperature. It is found that the double-wall pin-fin–jet (PFC and TFC) configurations show higher cooling effectiveness compared to the single-wall pin-fin (PF and TF) designs and the triangular pin fin (TF and TFC) showed a higher heat transfer augmentation compared to the cylindrical pin fin (PF and PFC) design. Numerical study later confirmed that the triangular pin fin creates a pair of streamwise vortices that augments the local heat transfer. The presence of the pin fin in the double-wall configuration prevents the development of a strong crossflow that negatively affects the heat transfer of the impinging jet. In addition, the triangular pin fin not only prevents the strong crossflow but redirects the coolant in the lateral direction that eventually contributes to the formation of a counterrotating vortex pair in the streamwise direction and thus augments local heat transfer and improves overall cooling effectiveness. Pressure drop measurement showed that the full-length triangular pin fin has a higher-pressure loss but the partial-length pin fin can lower the pressure loss considerably without compromising additional cooling performance.

Numerical investigation of thermo-hydrodynamic performance of triangular pin fin heat sink using nano-fluids

Cooling of miniaturized electronic components is of greater need to enhance the reliability, performance and life of the electronic component. Miniaturized devices with fins is an advanced cooling method used to maintain the surface temperature of the component by providing additional surface area for heat dissipation, Different geometries of extended surfaces and different cooling fluids are studied to enhance the thermal- hydro performance. This paper presents a numerical study of flow and heat transfer characteristics of three- dimensional heat sink with triangular pin fin using water and ethylene glycol (EG) as base fluid. Later the base fluid mixed with diamond powder (DM), aluminum oxide powder (Al2O3) and copper powder (Cu) nanoparticles with 2% and 4% volume concentration is considered. The study is carried out for Reynolds number ranging 100–900 subjected to constant heat flux 10 W/cm2. A non-dimensional parameter thermal performance index is used to access the heat transfer characteristics of a heat sink. Results indicate heat dissipation rate of the finned heat sink was enhanced employing nanofluids, however, the performance index of nanofluids was slightly affected compared to base fluids. Pressure drop for water-based copper nanoparticles for 4% volume concentration is 9.4% greater compared to pure water. The heat dissipation rate enhances by 20.31% for ethylene glycol-based nanofluids and by 6.54% for water-based nanofluids. The conservative equations for fluid and solid domain are solved using FLUENT 16.2.

Subcooled flow boiling in an expanding microgap with a hybrid microstructured surface

Flow boiling in microgap is attracting increasingly wide attention in heat transfer community due to its promising application potential for thermal management of electronic devices. In this study, an expanding microgap with a hybrid microstructured surface is proposed. It consists of a roughened inlet region followed by an array of staggered micro triangular pin-fins machined downstream. Subcooled flow boiling tests were conducted using distilled water as the working fluid with the inlet subcooling between 20 °C and 40 °C at different flow rates ranging from 80 to 480 mL/min over a heat flux range of 100.0–651.7 W/cm2. High-speed visualization was performed to explore the flow pattern transitions and the effects of operating conditions on heat transfer and pressure drop characteristics. A new flow pattern was observed in which the bubbles blanket the surface over both roughened upstream surface and the micro pin-fins downstream surface at higher flow rates and higher heat flux conditions. Combination of the increased bubble nucleation site density on the roughened surface and suppression of local dryout from the micro pin-fins due to their capillary effect jointly led to the high heat transfer performance in the bubble blanket pattern. In addition, the expanding configuration provides additional space downstream to facilitate bubble growth and two-phase flow in the direction of expansion with reduced resistance, resulting in a relatively low pressure drop in the present system.

CFD analysis of employing a novel ecofriendly nanofluid in a miniature pin fin heat sink for cooling of electronic components: Effect of different configurations

This research aims to study the thermal and hydraulic attributes as well as energy efficiency of a new ecofriendly nanofluid including functionalized graphene nanoplatelets in a mini heat sink with three different pin fins. The circular, triangular and drop-shaped pin fins are investigated and compared with each other. The effects of nanoparticle fraction and flow velocity on the thermal resistance, temperature uniformity, convective heat transfer coefficient, maximum surface temperature, average surface temperature, pressure loss and pumping power are assessed. Increasing the concentration or velocity reduces the temperature on the heated wall, and also improves the temperature distribution uniformity. At both constant velocity and invariant pumping power, the heat sink fitted with the circular pin fins leads to the best performance while that equipped with the triangular pin fins results in the worst efficiency. In addition, the Figure of Merit (FoM) is greater than 1 for all conditions, which proves that the nanoparticle suspension possesses a greater merit to be employed as the coolant in the heat sinks compared to the base fluid.

Pin-fin shape-dependent heat transfer and fluid flow characteristics of water- and nanofluid-cooled micropin-fin heat sinks: Square, circular and triangular fin cross-sections

The combined influence of pin-fin shape variation and utilisation of nanofluid coolants on heat transfer and fluid flow characteristics of a heat sink are investigated through the Lagrangian-Eulerian approach. The staggered arrangement of the square, circular and triangular cross-sectioned micropin-fins is evaluated for the parametric pressure range of 570 Pa ≤ ΔP ≤ 2760 Pa. The thermal performance of an aqueous-based alumina nanofluid is probed for a nanoparticle volume fraction and an average diameter of 0.5% and 20 nm, respectively. The heat transfer attributes are analysed in terms of thermal resistance (Rth), thermal contours, local (Nus) and average Nusselt number (Nuavg), whereas flow streamlines and velocity contours elaborate flow distribution across the heat sinks with variable pin-fin configurations. The results illustrate that utilising the nanofluid enhanced the heat exchange capacity of the heat sink regardless of the pin-fin configuration. However, an appropriate pin-fin shape can supersede the advantage of employing nanofluid coolants at the studied particle concentration. At the highest pressure drop, the nanofluid-cooled circular, square and triangular pin-fins demonstrated a maximum Nuavg enhancement of 23.1%, 16.5% and 8%, respectively, compared with water-cooled triangular pin-fins. While the Nuavgof water-cooled circular and square fins was noted to be 12.2% and 6% higher respectively, than that of the water-cooled triangular pin-fins.

Thermal performance enhancement in a miniature channel using different passive methods

In the present work, different passive methods have been numerically investigated to improve the thermal performance in a miniature channel. The heat transfer and pressure drop of 1 vol% Al2O3–H2O nanofluid inside triangular longitudinal pin fin miniature channel and 0.5 vol% SWCNT–H2O nanofluid inside miniature channel with wavy vortex generator with different angles have been numerically investigated. The angles of wavy vortex generator have been considered to be 0°, − 60° and 60°. The nanofluid flow has been simulated by mixture two-phase model. The results show that the thermal performance of Al2O3–H2O nanofluid is increased about 40% compared to that of pure water in miniature channel, while the pressure drop is slightly changed. The overall performance has been improved by the triangular pin fin and wavy vortex generator in miniature channel. The highest value of the overall performance has been observed for Al2O3–H2O nanofluid in triangular longitudinal pin fin miniature channel; the increase rate is about 83% than that of pure water in miniature channel. Also, in all different angles of wavy vortex generators, the thermal and frictional performances have been increased by adding the SWCNT nanoparticles. But, the effect of nanoparticles on the frictional performance was negligible. Also, the heat transfer and pressure drop have been increased when the angle of the wavy vortex generator was 0°. The highest and least values of the overall performance are observed for angles of 60° and − 60°, respectively.

Thermal management of electronics: An experimental analysis of triangular, rectangular and circular pin-fin heat sinks for various PCMs

This study implies experimental investigation for optimization of heat transfer in electronic integrated circuits using close packed phase change materials (PCMs) filled pin-fin heat sinks. The aim of this study is to find the most efficient pin-fin configuration filled with optimum PCM to extend the operating range of electronic circuits. The experimental methodology is based upon variation of pin-fin configurations in rectangular, round and triangular cross-sections. Each configuration is allowed a pin-fin volumetric percentage of 9%. For analysis using PCM a volume fraction of 90% is maintained and six PCMs with different thermo-physical properties (varying melting temperatures, latent heats and heat capacities) are selected. These include paraffin wax, RT-54, RT-44, RT-35HC, SP-31 and n-eicosane. Moreover, the power levels mimicking heat input range between 5 W and 8 W. The resulting information is analyzed for the performance of a heat sink with and without PCM. Besides that, PCM ascendency is manipulated in terms of operational time, enhancement ratios, Stefan number and storage ratio. The outcomes suggest that triangular pin-fins are found to be the most effective pin-fin configuration for heat transfer both with and without PCM.

New correlations to predict the thermal and hydraulic performance of different longitudinal pin fins as vortex generator in miniature channel: Utilizing MWCNT-water and Al2O3-water nanofluids

In this paper, a parameter as area modification factor is defined for the cross section shape of pin fins. The effect of this parameter on the thermal and hydraulic performance of different coolant fluids inside pin fin miniature channel is numerically investigated. This parameter amount is 90°, 82°, 75°, 68° and 59° that lead to the rectangular, trapezoidal of type (3), (4) and (5) and triangular fin. The MWCNT-water and Al2O3-water nanofluids are working fluids which are simulated by mixture two-phase model. The range of the Reynolds number and nanoparticles volume concentration are 300–2100 and 0–3vol.%, respectively. The results show that the thermal performance is enhanced much folds by using the nanofluid compared to that for the pure water inside the miniature channel with a slight increase in pressure drop penalty. The water flow and 1vol.% Al2O3-water nanofluid has the highest overall performance in the triangular pin fin miniature channel but MWCNT-water nanofluid has the highest and least overall performance in the trapezoidal pin fin of type (3) and triangular pin fin, respectively. New correlations are also suggested to predict the Nu number and friction factor of the different pin fin miniature channels.

Influence of Shape, Number, and Position of Horizontal Minifins on Thermal-Hydraulic Performance of Minichannel Heat Sink Using Nanofluid

ABSTRACTIn the first part of present study, an experimental setup with constant heat flux is used to investigate the thermal performance of the water inside a horizontal triangular pin fin channel. For the sake of validation of the computational fluid dynamics (CFD) study, a simulation is conducted according to the geometry and operating conditions of the experimental work. The numerical model consists of a study that has been established based on the geometrical parameters and operating conditions similar to the experimental work. The influence of four different cross sections of minifins (shaped as square, trapezoidal, triangular, and sinusoidal) and of number of triangular minifins (1, 3, 5, 7, and 9) and their positions (in the regions of entrance, central, and terminal) on the heat transfer rate and pressure drop in a minifin minichannel heat sink are numerically investigated by a two-dimensional CFD model. The coolant is Cu–water nanofluid at a volumetric concentration of 2%. The results demonstrated that the sinusoidal minifin minichannel heat sink has the highest convective heat transfer coefficient in comparison with other shapes, while the trapezoidal minifin minichannel showed the highest thermal resistance. The highest pressure drop was observed for the triangular minifin inside minichannel. By increasing the number of fins, thermal resistance considerably decreased. Likewise, at the central and entrance positions, respectively, the highest Nusselt number and friction factor inside the minichannel was observed. This study can provide useful guidelines for the design of the cooling devices.

Mathematical Extrapolating of Highly Efficient Fin Systems

Different high‐performance fins are mathematically analyzed in this work. Initially, three types are considered: (i) exponential, (ii) parabolic, and (iii) triangular fins. Analytical solutions are obtained. Accordingly, the effective thermal efficiency and the effective volumetric heat dissipation rate are calculated. The analytical results were validated against numerical solutions. It is found that the triangular fin has the maximum effective thermal length. In addition, the exponential pin fin is found to have the largest effective thermal efficiency. However, the effective efficiency for the straight one is the maximum when its effective thermal length based on profile area is greater than 1.4. Furthermore, the exponential straight fin is found to have effective volumetric heat dissipation that can be 440% and 580% above the parabolic and triangular straight fins, respectively. In contrast, the exponential pin fin is found to possess effective volumetric heat dissipation that can be 120% and 132% above the parabolic and triangular pin fins, respectively. Finally, new high performance fins are mathematically generated that can have effective volumetric heat dissipation of 24% and 12% above those of exponential pin and straight fins, respectively.