Single Fin Research Articles

Numerical analysis of the combined influence of fin shape and location on constrained melting of phase change materials in a spherical capsule with double fins

AbstractThis study presents a novel approach to investigating the combined influence of fin position and shape on the constrained melting behavior of phase change material (PCM) within a spherical capsule (S.C.) through numerical analysis. Unlike previous research, which predominantly focused on single fin shapes or positions, this work uniquely explores the impact of double, simple, and easily manufacturable fin shapes. A two‐dimensional computational model employing the enthalpy–porosity method assesses melting behavior, temperature distribution, and PCM flow. Numerous fin shapes, namely rectangular, trapezoidal converging, trapezoidal diverging stepped, inverse stepped, and triangular, are considered in the analysis. The study reports the influence of the location of two identically shaped fins on the thermal performance. The fins' cross‐sectional area and base thickness are kept equal in all cases. The thermal performance of an S.C.‐integrated fin system is evaluated by analyzing various attributes such as total saving in the duration of melting, enhancement ratio, and Nusselt number. The results indicate that the position of the fins has a more significant impact on melting performance than the fin shape. The best performance is achieved when fins are placed in the lower half of the capsule, followed by the center and upper halves, regardless of fin shape. For rectangular fins, shifting the position of the fin from the bottom half to the center increases the melting time by 24.7% and the top half by 68.3%. The shortest melting time of 93 min is observed for lower‐half rectangular fins, followed by center‐placed triangular fins (94 min). This study offers a theoretical foundation for optimizing the performance of different technologies using latent heat thermal energy storage systems such as packed‐bed, cascaded thermal energy storage systems.

Comprehensive analysis of thermal performance and low-grade energy charging efficiency of pipe-embedded building envelopes enhanced with single-level tree-shaped fin structures

Pipe-embedded walls (CnPWs) are structural and energy composite building components that can resist external disturbances by forming stealth thermal shielding layers. To tackle the mismatch between the heat charging rate and heat diffusion rate during energy charging processes, as well as the unsatisfactory robustness of stealth thermal shielding layers, the single-level tree-shaped metal finnd pipe-embedded walls (TfPWs) are proposed. To verify the effectiveness of TfPWs and obtain dynamic performances, a simulation study is conducted on 8 risk variables in 4 pairs through the validated numerical model. Results showed that the improved design was effective in obtaining more robust thermal shielding layers in auxiliary energy supply mode, the effect gained prominence as both the injection temperature and pipe spacing were augmented. In room heat load reduction mode, favorable benefits arise when pipe spacing exceeds 400 mm. The maximum increase rate of total injected energy under different reduction ratios of external insulation layer was 11.83%–31.91 %, while the maximum extra total heat loss was 5.33 %. Secondly, the trunk fins and branch fins played different roles in minimizing the excessive heat accumulation surrounding pipes, and the vertical and horizontal sizes of heat accumulation region mainly increased with the increase in trunk fin size and branch fin size respectively. Meanwhile, the utilization efficiency of fin material was higher when trunk fin size was smaller, and parameter combinations with trunk fin size of 0.2b and branch fin size of 0.4a/0.6a could achieve a better balance between material input and performance increase. Thirdly, the improvement effect of single left branch fin schemes was close to that of double branch fin schemes and significantly better than that of single right branch fin schemes. It was recommended to use single left branch fin schemes with an inclination angle of 60°. Finally, even if the reduction ratio of external insulation layer in different cities increased to 80 %, the inside surface temperature of TfPWs was still greater than room air. Taking CnPWs with standard external insulation layer as references, the TfPWs applied in Harbin, Beijing, and Shanghai could achieve similar or better results even when the reduction ratio of external insulation layer increased to 60 %, while TfPWs applied in Guangzhou could exhibit better performance even when the reduction ratio of external insulation layer increases to 80 %.

Influence of the foam-fin structure on the thermal performance of a coupled phase change liquid cooling module

Effective thermal management is key to ensuring the reliable operation of high power electronic equipment. In this study, the strategy of phase transition and liquid cooling coupling applied to transient high power electronic equipment has been examined. In order to improve the performance of the phase changing material (PCM) in temperature control, the effects of the coupling structure have been addressed with a consideration of fin, copper foam (CF), graphite foam (GF), fin-copper foam (FCF) and fin-graphite foam (FGF) structures in heat dissipation. In this study, pure paraffin wax (PPW) was used as phase change material to prepare heat sinks based on the above five structures. The experimental study investigates the impact of different thermal conductivity strategies on temperature control characteristics, with a focus on cold capacity recovery and the combined phase change and liquid cooling, using pure paraffin wax module as a reference. The results have revealed that the fin-foam coupling structure delivers a better PCM performance than the single fin or foam structure. Operating at a heating power of 10 W, 15 W and 20 W, the temperature control time of the FGF structure was increased by 13.6 %∼14.6 % relative to the GF structure. At 15 °C with flow rates of 1 L/min, 1.5 L/min, 2 L/min liquid cooling conditions, the cooling capacity recovery time was reduced by 18.8 %, 17.2 %, 19.7 %, respectively. In the phase-change liquid-cooling coupling temperature control experiment, the final temperature increase in the FGF system was 11.7 °C -15.2 °C lower than that of the GF system under the same water temperature and volume flow for a 50 W heat source. The incorporation of fins also enhanced the thermal conductivity strengthening capability of the copper foam and reduced the cold recovery time. Based on the comprehensive evaluation, the FGF structure demonstrates superior temperature control performance and cold recovery characteristics of PCM, making it an optimal strengthening method. Following closely are the FCF, GF, Fin and CF structures. Compared to pure paraffin modules, these five modules exhibit varying degrees of improvement in temperature control and cold capacity recovery efficiency. This study provides guidance for optimizing heat sink design based on PCM in electronic applications.

Thermal performance enhancement of multiple tubes latent heat thermal energy storage system using sinusoidal wavy fins and tubes geometry modification

In this paper, performance enhancement of a shell and multiple tube latent heat thermal energy storage system (LHTESS) is numerically investigated by implementing sinusoidal wavy fins and different geometrical designs of heat transfer tubes. The annular space of the shell is filled with the paraffin wax RT35 as phase change material (PCM) and absorbs heat from hot water through the multiple tubes. With the constant total cross-section area of all tubes and fins as the constraint condition, the effect of tube number and tube shape incorporated with the proposed fins on the heat transfer properties of PCM during the melting process is evaluated. The computational results demonstrate that the sinusoidal wavy fins can improve the phase change efficiency compared to the conventional straight fins. The double-pitch sinusoidal wavy fins decrease the total melting time by 9.5% compared to the straight fins for the single-tube case. As the number of HTF tubes increased from one to four, the complete PCM melting time decreased by 38.3%. Geometrical design alterations of heat transfer tubes from circular to petal-shaped are proposed to further improve the thermal performance of multiple tubes LHTESS. The melting rate of PCM is accelerated with an increase in the number of petals. The petal tubes with nine petals can save the charging time up to 24 % in comparison with the circular tubes in a four-tube case with double-pitch sinusoidal wavy fins, and up to 57% compared to the base case with a single circular HTF tube and straight fins.

Three-dimensional numerical simulation of heat transfer enhancement of electronic devices by single crystal diamond rhombus-shaped pin fin microchannel heat sink

Pin fin microchannel heat sink is an excellent solution for enhancing the thermal dissipation for electronic devices with high integration and high-power density. The effect of the single crystal diamond (SCD) rhombus-shaped pin fin microchannel (RPFMC) heat sink with single-phase laminar fluid on the device heat transfer is investigated by three-dimensional numerical simulation, and geometrical parameters of the RPFMC heat sink are optimized and evaluated according to the performance evaluation criterion. The simulation results indicate that the thermal resistance of the device gets reduced by up to 81.6 % through using a SCD RPFMC heat sink instead of a silicon RPFMC heat sink with the same design, due to the superior thermal conductivity of SCD. Hotspot heat fluxes are evaluated to explore the tolerance of the SCD RPFMC heat sink which could withstand a heat flux of 2000 W/cm2 with the temperature increased by only 17.3 K. Geometric design evaluation suggests that the SCD RPFMC heat sink with the rhombus-shaped pin fin angle of 75° and duty ratio of 0.4 has the optimal overall thermal performance.

Heat transfer simulation and performance optimization of plate-type phase change energy storage unit

As the core of the phase change energy storage technology, the heat transfer performance of the phase change energy storage unit has an important impact on the operating efficiency of the energy storage system. In this study, a three-dimensional CFD model of the plate-type phase change energy storage unit is established to simulate the melting process of paraffin wax. Three types of plate-type phase change energy storage unit models are established, without fins, single fin, and double fins. The influence of cylindrical fin on natural convection melting process of paraffin is studied, which provides the basis for the design and performance optimization of plate-type phase change energy storage unit, and improve its application value. The results show that the melting time of paraffin in the energy storage unit without fins is 858 s, and the melting time is shortened to 827 ~ 842 s after adding single fin. The melting time of paraffin wax with single fin is lower than that with double fins. For the plate-type phase change energy storage unit, adding fins at the central section can effectively improve the melting rate of phase change material. The single fin A located at the lower part of the central section has the greatest promotion effect on paraffin melting. The key to enhance the phase change heat transfer process in plate-type phase change energy storage unit is the paraffin in the lower half of the symmetry plane.

NUMERICAL STUDY OF THERMAL MANAGEMENT FOR A CYLINDRICAL HEAT SOURCE BY PCM COMBINED WITH ANNULAR FINS

In the study, annular fins are used to improve the thermal management performance of the phase change material (PCM) towards a cylindrical heat source. A two-dimensional axisymmetric model is established and the influence of fins on the temperature of the heat source is studied in conjunction with the melting process of PCM. The effects of the positions of a single annular fin are investigated. Results show that the lower the individual fin is in the PCM, the faster the melting rate and the lower the temperature, which is because the PCM above the fins can absorb more heat from the upper surface of the fin through natural convection. Maintaining a constant total volume of fins, the effect of multiple annular fins is studied. The results show that multiple annular fins have larger heat transfer areas and more uniform fin distribution, resulting in lower temperature and temperature difference of the heat source surface. Furthermore, the use of multiple fins of unequal height, with bottom fins being higher, is found to be more effective. The best improvement in the thermal management performance of the system is achieved when the height of the fins is 4, 8, and 11 mm from top to bottom, respectively.

Enhanced Total Ionizing Dose Response of 16 nm n-FinFETs With a Single Fin

Enhanced Total Ionizing Dose Response of 16 nm n-FinFETs With a Single Fin

Heat transfer enhancement and temperature uniformity improvement of microchannel heat sinks with twisted blade-like fins

To enhance heat and fluid exchange between main flow and near-wall flow in microchannels, a twisted blade-like fin with an advantage in stimulating both spanwise and normalwise secondary flow is proposed. The cross sections of the fin are low-drag airfoils in different orientations. The flow and heat transfer performances of microchannels with fins are numerically investigated at Re = 50–700. The results show that the twisted blade-like fin improves heat transfer process significantly, especially wall temperature uniformity, and reduces the flow separation region behind the fin, resulting in an obvious small pressure penalty. At small inflow (Re = 50), the best heat transfer and lowest pressure penalty are obtained in the microchannel with a single fin. When Re > 150, better heat transfer is obtained in the microchannel with three fins, and the highest comprehensive thermal performance (TP) reaches 3.58. The twisted direction of fins has a significant effect on heat transfer but less on flow drag. Due to the twisted fins, left and right walls experience an overall decline in temperature, and the temperature uniformity of top and bottom walls is improved. Compared with a smooth microchannel, the average and maximum temperature of the investigated microchannels are reduced by 48.1 K and 49.0 K at most respectively.

Surface Properties of Double-Fin Generated Shock-Wave/Boundary-Layer Interactions

Shock-Wave/Boundary-Layer Interaction (SBLI) is ubiquitous in high-speed air vehicles. SBLI surface flowfield properties of crossing shocks induced by symmetric Double-Fins (DFs) at fin angles of 8° and 10° at Mach 2 are experimentally investigated; a 10° Single-Fin (SF) is also explored as a comparison. Surface visualization is used to capture distinct flowfield structures such as separation and upstream influence. Steady and unsteady Pressure-Sensitive Paints (PSPs) are used to obtain global surface pressure fields. Characteristics of DF-SBLI surface topology are discussed by comparing the corresponding SF-SBLI. The effect of fin angle on DF-SBLI is characterized, and unsteady dynamics of the pressure field are examined. Spectral Proper Orthogonal Decomposition (SPOD) is performed on unsteady PSP, and traveling surface pressure waves and their frequency-dependent behavior are discussed. Dispersion relation of surface pressure waves is revealed by performing two-dimensional space–time Fourier transform on unsteady PSP, and the results are compared with the phase velocity distributions obtained from SPOD. Accompanying group velocity behavior is examined for distinct SBLI regions wherein wave propagation is found dependent on its frequency. Steady surface pressures along the centerline are compared with previous experimental data. Fin-tip spacing is found to be an essential parameter for scaling of upstream influence length.

Effects of circumferential fin on cooling performance improvement of forced air-cooled battery pack

In demand for clean energy sources, batteries have a vital role to play. Batteries are the heart of many electrical energy storage systems, as in electric vehicles (EVs). The high internal heat generation from a battery is the main hindrance to battery performance and safety. The high-temperature environment impacts performance; therefore, maintaining the battery temperature within desired limits is essential. In this work, we focus on the increasing effectivity of forced air cooling for high-capacity batteries at high discharge rates, decreasing auxiliary power consumption without compromising the compactness of the battery pack. The novelty of this work is that we have developed a hybrid BTMS consisting of circumferential fins and forced air cooling. Using a circumferential fin clad to the cell body has the advantage of increasing the surface area of the battery pack so that the ability of air to extract heat from the battery pack is improved and the auxiliary power consumption is reduced. The experiments use thin circumferential fins of 0.5 mm thickness mounted on cell bodies and discharged at various rates. The numerical model has been developed and tested using ANSYS FLUENT software. Using a single circumferential fin (Model 1) improves cooling performance by 3.14 %, and using three circumferential fins (Model 2) improves cooling performance by 7.32 % in the natural convection mode compared to the uncooled model. The improvement achieved in forced air cooling with a velocity of 2 m/s and three circumferential fins cooling performance is improved by 18.71 %. It is observed that using fins, the overall increase in weight of the system is by 3.58 %.

Hydrodynamics of Butterfly-Mode Flapping Propulsion of Dolphin Pectoral Fins with Elliptical Trajectories.

This article aims to numerically study the hydrodynamic performance of the bionic dolphin equipped with a pair of rigid pectoral fins. We use dynamic-grid technology and user-defined functions to simulate a novel butterfly-mode flapping propulsion of the fins. This pattern of propulsion is composed of three angular degrees of freedom including the pitch angle ϕp, the azimuth angle ϕa and the roll angle ϕr, which can be divided into four stages for analysis within a single cycle. The stroke of one single pectoral fin can be approximated as an ellipse trajectory, where the amplitudes of ϕa and ϕp, respectively, determine the major and minor axes of the ellipse. The fluid dynamics involved in the specific butterfly pattern is mathematically formulated, and numerical simulation is conducted to investigate the propulsion quantitatively. The results show that the dolphin with a higher water striking frequency f can acquire higher propulsion speed and efficiency. Furthermore, the shape of the ellipse trajectory under different conditions could also have different propulsion effects. The periodic generation and disappearance of vortex structures in the butterfly flapping mode show the evolution process of fluid flow around a pair of pectoral fins, which reveals the influence of motion parameters on fluid dynamics under different working conditions.

Comparison of Heat Sinks with Different Perforations Number

In this paper, the influence of perforation number Np is experimentally studied (or in the other word, the effect of perforation space Ps on the heat sink performance). Three types of rectangular heat sinks were investigated; two types have been perforated by lateral holes (4 mm the hole diameter) distributed on two rows in the fin. First one has 12 holes in a fin (its Ps is 14.3mm) called (PHS-12p). Second heat sink has 8 holes in a single fin (its Ps is 20mm) called (PHS-8p). These two perforated types compared with the third heat sink, which has no perforation (solid heat sink). The comparison was investigated, presented and discussed. The experiment was conducted by forced convection device. The obtained results showed that dissipated heat, Nusslet number, and convective heat transfer coefficient were increased by using perforations compared with non-perforated heat sink. The use of more perforations has a positive effect on heat dissipation. The enhancement in heat transfer was 6.57% for PHS-12P, while PHS_8P improved by 1.75% only at Re 20000. Moreover, the heat sink weight decreases with the use perforated heat sink compared with the solid heat sink.

Analysis of the Impact of Parameters of Gravity Heat Pipe Radiator on the Temperature Control of Gangue Hill and Engineering Test

ABSTRACT Deep within coal gangue hills, there is a substantial amount of wasted thermal energy. Prolonged accumulation of these hills leads to significant damage to the atmosphere and soil. Gravity heat pipes, as efficient heat transfer components, can safely, efficiently, and conveniently extract the accumulated heat in gangue hills to achieve effective thermal control. In this study, we first analyzed the optimal height of the heat dissipation fins through a single fin heat dissipation model. Then, we determined the optimum spacing between the heat dissipation fins through analysis with multiple fins. The results showed that when the height of the heat dissipation fins was 80 mm and the spacing between fins was 80 mm, the heat dissipation performance and economic costs were most reasonable. Through an engineering trial conducted for 143 days at the Maotergou coal mine gangue hill, it was found that the average heat dissipation rate of a single gravity heat pipe ranged from 243.52W to 494.32W. The total heat dissipation during the entire experimental process was 54.39 kJ, and the total heat dissipation at the elevation of 890 meters was 1087.71 kJ. This indicates that managing the internal temperature accumulation in coal gangue hills using gravity heat pipes is entirely feasible.

Thermo-hydraulic performance evaluation of a NACA 63-015 heat exchanger with shark denticles as surface textures

In this study, the effect of using bio-inspired surface texturing as a technique to further enhance the efficiency of a single Plate Fin Heat Exchanger (PFHX) was investigated experimentally. By using biomimicry across disciplines, the denticle, which is a body adaptation from shark skin for enhanced hydrodynamics, was identified as a surface texture to be used on the fin of a PFHX. A smooth NACA 63-015 PFHX (HX0) was used as baseline for thermo-hydraulic performance comparisons. Initially, three PFHXs (HX1, HX2 and HX3), consisting of arrays of denticles upscaled to different scale factors, were designed and printed in ABS plastic to evaluate Additive Manufacturing (AM) limits. By analysing optical images and pressure drop results, HX2 was found to be the best performing array in terms of printing quality and pressure drop performance. Both HX0 and HX2 were then printed in stainless steel 17-4PH by using a Markforged Metal X printer, and then experimentally compared to evaluate their flow and heat transfer behaviours. Results demonstrate that the addition of shark denticles as surface textures on HX2 shifted the onset of turbulence from a fully turbulent to a transitional regime compared to HX0. For Re < 5.7×104, the friction factor for HX2 was less than that of HX0, while at higher Re values the trend was reversed due to increases in skin friction drag. At Re = 3.9×104, the friction factor for HX2 was 56% lower than that of HX0. Overall, a mean improvement of 14% in Nusselt number was noted for HX2 compared to HX0. Further, a mean thermo-hydraulic performance of 1.11 was noted for HX2 for the range of tested Re values, which demonstrated that the addition surface textures in the form of shark denticles to a NACA 63-015 profile yielded a more efficient PFHX compared to a smooth one.

Numerical Simulation of Heat Transfer in a Wavy Enclosure with and without the Presence of Fins

This study focuses on numerically simulating heat transfer in an enclosure with a wavy shape, both with and without the presence of fins. The research paper specifically investigates the case of a single vertical fin attached to the lower heated wall of the enclosure. The lower wall is maintained at a constant cold temperature, while the upper wall is kept cold, and the wavy walls are assumed to be constant heated temperature. The top wall lid moves left to right and bottom wall lid moves right to left with constant velocity. Additionally, a magnetic field of certain strength is applied parallel to the x-axis. The flow inside the enclosure is characterized by a Prandtl number of 0.71. The results are presented through various graphical representations, such as streamlines, isotherms, velocity and temperature distributions, as well as the local Nusselt number. The researchers conducted a parametric study to examine the impact of the Richardson number on the fluid flow and heat transfer characteristics within the enclosure. The findings indicate that as the fluid flow and heat transfer characteristics within the enclosure. The findings indicate that as the Hartmann number increases (while keeping the Hartmann number constant) the heat transfer rate is enhanced. To validate their findings, the researchers compare their results with previously published works in the field.

Impact of fin aspect ratio on enhancement of external quantum efficiency in single AlGaN fin light-emitting diodes pixels

Previously, we showed within a sub-micron fin shape heterojunction, as current density increases, the non-radiative Auger recombination saturates mediated by the extension of the depletion region into the fin, resulting in a droop-free behavior. Here, we investigate the dependence of the fin aspect ratio (height to width ratio) on external quantum efficiency (EQE) of single n-AlGaN fin/p-GaN heterojunctions. Fins are arranged in an array format varying in width from 3000 to 200 nm. In this architecture, an n-metal contact is interfaced with the non-polar side facet of the fin. At a fixed current density, as the aspect ratio increases from 0.2 to 3 (the fin width reduces), we systematically observe an increase in the ultraviolet (UV) excitonic emission of the AlGaN fin and a 7× enhancement in the EQE. We explain this phenomenon by conserving the volume of the carrier depletion region within a fin. As the fin gets thinner, the base area of the depletion volume shrinks, whereas its height increases within the fin. This geometrical advantage allows a 200 nm wide fin to operate at 1/3rd the current density compared to a 3000 nm wide fin while generating a UV emission with a comparable power of 1 μW. These findings show additional parameters that can be used for developing brighter light sources, including the shape and aspect ratio of a heterojunction at the micro- or nano-scale.

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.

Numerical study of the thermal behavior of a cylindrical fin formed by two orthotropic media

Numerical solutions are constructed and presented for the thermal distribution, the dimensionless heat flux rate, and fin efficiency for a two-dimensional orthotropic fin of cylindrical geometry formed by two media subject to a convection limit condition on the side surface and at the high fin base, and to a uniform temperature imposed on the other base of the fin. The results are presented and discussed according to the study parameters, radial thermal conductivity ratio, radial Biot number, and axial Biot number for each medium. Many specific cases are obtained from the global solution presented in this work, among others, the temperature distribution and the dimensionless heat flux rate at the base of a single orthotropic or isotropic fin as well as the case of a fin formed by an orthotropic and isotropic media. The findings of the present study demonstrate that the newly proposed fin design significantly improves the dimensionless heat flux rate of the fin compared to the conventional design. This improvement is particularly significant when the axial Biot number of the outer medium is high and the axial Biot number of the inner medium is low, regardless of the ratio of radial thermal conductivities. These results suggest that the proposed fin design is better suited for applications where heat transfer is critical, and the external environment has a high thermal resistance. In addition, the proposed design also provides a more compact geometry, which not only improves the mechanical performance of the fin but also reduces the cost of the material used in its fabrication.

Experimental Investigation Utilizing Thermal Image Technique to the Heat Transfer Enhancement Using Oscillated Fins

Heat transfer around a flat plate fin integrated with piezoelectric actuator used as oscillated fin in laminar flow has been studied experimentally utilizing thermal image camera. This study is performedfor fixed and oscillated single and triple fins. Different substrate-fin models have been tested, using fins of (35mm and 50mm) height, two sets of triple fins of (3mm and 6mm) spacing and three frequenciesapplied to piezoelectric actuator (5, 30 and 50HZ). All tests are carried out for (0.5 m/s and 3m/s) in subsonic open type wind tunnel to evaluate temperature distribution, local and average Nusselt number (Nu) along the fin. It is observed, that the heat transfer enhancement with oscillation is significant compared to without oscillation for low air inlet velocity. Higher thermal performance of triple fins is obtained compared to the single rectangular fin, also triple fins with (height=50mm and finspacing=3mm) gives better enhancement as compared to other cases. This work shows that the piezoelectric actuator when mounted on the rectangular fins shows great promise for enhancing the heat transfer rate.