Number Of Fins Research Articles

Performance Evaluation of BTMS for Electric Vehicles using Heat Sink - A Numerical Study

Batteries have wide applications in engineering. They are extensively used in hybrid electric vehicles (HEVs) and electric vehicles (EVs), where a suitable battery thermal management system (BTMS) is vital in ensuring the safety and reliability operations of batteries. The purpose of this study is to offer an air-cooling system that utilizes a novel V-type staggered arrangement of plate-fin heat sink for forced air cooling. To keep the temperature of a lithium-ion battery pack within the optimal temperature range for the safety of the battery and the consumer to prevent the battery from catching fire. The paper also presents a comparison between straight rectangular fins and V-type staggered arrangement heat sinks. The thermal management of batteries equipped with a heat sink is numerically controlled, to ensure the battery's overall performance and longevity modules/packs for electric cars. A three-dimensional heat sink model was constructed and a numerical approach was used to explore the impacts of the number of fins on the heat sink, fin spacing and angle of inclination of the fins at different inlet air mass flow rates and varied heat input. The analysis presents a computational approach and traditional heat transfer theory.

Heat transfer enhancement of the air-cooled engine fins through geometrical and material analysis: A review

Energy crisis and air pollution are the two leading scientific issues that require global attention. The fundamental reason for the rise in energy costs is the rapid depletion of fossil fuels which has raised fuel prices. Analysis of IC engines suggests thatthermodynamic constraints cause more than half of energy derived from fossil fuels to be lost to the environment. Prolonged working at high temperatures can alter an engine's performance and characteristics. One way of minimizing these losses is to regulate and keep the engine's temperature within the permissible range. Thus, cylinder blocks often include extended surfaces called finsto transfer away the heat from the engine surface. This study focuses on explaining the effect of variation in material, type, design, number of fins, and other parameters in improving fins' efficiency and enhancing the engine's performance. It has been observed that the optimum number of fins can significantly improve fin efficiency, and a 5% to 13% enhancement in heat transfer is possible through fin extension. Elliptical shape fins perform better than triangular and rectangular fins. However, circular and curved fins increase engine efficiency by reducing engine weight. Amongst various fin materials like Cast Iron, Copper, Magnesium, Aluminum, and its alloys, etc., more thermal flux has been observed for Aluminium Alloy 6082. Finally, authors have come to a conclusion that circular fins with holes and slots offer a higher heat transfer rate and improved engine performance at reduced material requirements. The circular fin geometry with slots and holes provides further scope of improvement by optimizing fin thickness, number of holes and slots, their dimensions and spacing to come with a combination that provides effective cooling along with ease of manufacturing in case of lightweight engines.

Performance analysis of PCM melting in a fin-assisted thermal energy storage system – A numerical study

The study attempts to present the melting phenomena in a Latent Heat Thermal Storage System (LHTSS) where ice is used as Phase Change Material (PCM) with fins incorporated to advance the thermal performance. The PCM-based storage system finds vast potential in addressing the imbalance between energy supply and demand. Computations are carried out to find the optimum fin number to be incorporated in Heat Transfer Fluid (HTF) tube for improved heat transfer and minimum melting time. The effect of incorporating optimum fin number on different influential parameters such as HTF tube arrangement, diameter, and temperature on charging performance is evaluated. The physical phenomena occurring due to increased fin number is also explained. Criteria such as liquid fraction, mean temperature, heat transfer rate, and heat transfer coefficient are used to compare the system's performance under varying parameters. As the number of fins is augmented from 4 to 15, the generated liquid PCM is found to increase by 34.69% followed by a declination rate of 9.03% on further increment in the numbers. Geometrical alteration in the HTF tube arrangement from inline to staggered results in a better melting performance. Considering the HTF tube temperature parameter, it is found that 280 K HTF tube produces 2.08 times more liquid PCM as compared to 275 K case. Increasing HTF tube diameter is found to enhance the charging process with 20 mm diameter HTF tube system generating 2.68 times more liquid PCM as compared to that of 5 mm HTF tube.

Comparative study on different cooling techniques for photovoltaic thermal management: Hollow fins, wavy channel and insertion of porous object with hybrid nanofluids

The present work considers performance of different cooling methods applicable to photovoltaic (PV) panels. Hollow fins and two different channel cooling systems are considered. Flat and hollow fins types are used while cooling channels with wavy wall and with porous layer insert are compared. Effects of different fin numbers (between 2 and 16), hollow fin radius (between 0.8h and 3.2h, h-panel height), Reynolds number (between 100 and 500), wavy channel amplitude (between 0.01H and 0.5H, H-channel height), porous insert permeability (Darcy number between 10−6 and 10−1), porous layer size (between 0.1L and 0.7L, L-channel length) and nanoparticle volume fraction (between 0 and 0.02) on the cooling performance are numerically assessed. When nanofluid is used in the cooling channels, additional improvements in the cooling performance are obtained while temperature drop of 2.5 °C is achieved at the highest loading. When different cooling systems are compared, channel cooling with porous layer and wavy walls provide the highest cooling performance followed by hollow fin and flat fin systems while 37.6 °C , 37 °C, 33.6 °C and 29 °C temperature drops are obtained as compared to reference panel case without cooling system. When compared to flat fins, hollow fins perform better and additional temperature drop of 8.5 °C can be obtained by using 16 number of fins. It also provides a lightweight design as less material is used. Artificial neural networks are successfully used for performance estimation of wavy cooling channel system with 15 neurons in the hidden layer. The outcomes of this work is useful in further optimization and system development of PV cooling technologies as the need for thermal management in renewable energy sources is increasing due to the energy cost and environmental side concerns.

Hydro-dynamically and thermally fully developed flow analysis of magneto-hydrodynamic fluid through annular duct

A hydro-dynamic thermal fully developed forced convective heat transfer analysis of magneto-hydrodynamics fluid flow through an annular sector duct is presented in this paper. Two types of thermal boundary conditions i.e., axially uniform heat flux along with peripherally uniform temperature (known as H1-condition) and, axially and peripherally uniform temperature (known as T condition), have been considered to carry out the thermal analysis of fluid. The velocity components along r and [Formula: see text] direction are transformed into algebraic form by using power law discretized scheme, whereas cross-sectional pressure [Formula: see text] is estimated with the help of well know technique [Formula: see text]. The governing partial differential equations are solved by numerically with the help of [Formula: see text] code. Furthermore, simulated results have been compared with the existing results of literature to validate the results. From the results, it is noted that hydro-dynamically and thermally impacts relate directly by increasing the Hartman number, (M). It is further reported that the effect of magnetic field becomes insignificant for the higher number of fins, N. The findings of the present analysis will be applicable in various types of thermal systems.

Simulation of conductive fins effect on mixed convection heat transfer in a two-dimensional inclined channel using the lattice Boltzmann method

The simulation of the laminar mixed convection heat transfer inside a 2-D inclined channel was investigated here by employing the lattice Boltzmann method (LBM). The channel was equipped with conductive fins. The effects of inclination angle (φ), geometrical parameters (e and A), and a wide range of the Richardson numbers (Ri = 0.1-10) at fixed Reynolds number (Re = 100) on the heat transfer and flow structure were studied. The numerical model was validated by the published benchmark problems. Results were analyzed in terms of isotherms, streamlines, average Nusselt number, and average temperature. It found that the Nu increases with a decrease in the number, height, and width of fins. Results showed that when the channel equipped with 16 fins the reduction in Nu value reaches 62% compared to the empty channel. In addition, at Ri = 1 and N = 8, the Nusselt number decreased by about 52-77% for different fin widths compared to the channel without fins. However, the Richardson number and inclination angle enhanced the heat transfer rate in terms of the average Nusselt number. It revealed that a higher heat transfer rate belongs to the Ri = 10 and φ = 60°. The finding of this work showed the capability of LBM in simulating the mixed convection heat transfer in an inclined channel equipped with fins. A numerical analysis of the results produced a comprehensive set of results that could be utilized to reduce heat transfer. This paper can provide a novel framework for the design of air solar collectors and heat exchange systems.

Design optimization of a novel annular fin on a latent heat storage device for building heating

The poor heat transfer performance of the heat exchanger leads to low heat storage efficiency of the latent heat storage device. To improve the heat transfer performance of the heat exchanger, a novel annular fin with inclined angle is proposed to enhance heat transfer of the heat exchanger. 12 fins with different structural parameters are designed and welded to the inner tube wall of the heat exchanger. The simulation model is in good agreement with the literature and the model is considered to be reliable. Based on the enthalpy-porosity model, the liquid fraction, temperature distribution, melting front, energy storage density and heat storage rate were used to compare and optimize the structural parameters of the annular fins. Results demonstrated that the difference in complete melting time due to the number of fins, fin arrangement, fin length and fin angle were 43 min, 85 min, 17 min and 10 min, respectively. The fin arrangement was the most significant in reducing the heat storage time. Compared to N = 4 and uniformly distributed fins, non-uniformly distributed fins reduced the total melting time of stearic acid by 53.13 % and 20.54 %. To be conclusive, the addition of non-uniformly distributed annular fins with 70° inclination enhanced the heat transfer in the heat exchanger and saved a significant amount of heat storage time.

Two mathematical models of flow boiling and flow instability in rectangular expanding microchannel heat exchangers and structure optimization

Flow boiling instability in microchannels was widely studied to improve the reliability of microchannel heat exchangers. Two rectangular expanding microchannel heat exchangers have been experimentally investigated, one channel with cross-cutting and the other without cross-cutting. This study aims to optimize the heat transfer capabilities of heat exchangers. Two mathematical models containing heat transfer correlation and instability parameters have been developed. The experimental heat transfer coefficient (HTC) was used to validate them. Based on the models, the structure of the expanding microchannel was optimized, and the effect of expanding microchannel on flow instability was analyzed. As analyzed, in the models for two heat exchangers with and without cross-cutting, the mean deviations are 10.03% and 5.95%, respectively. The effect of flow instability suppression increases with the increase of the radiation angle. Moreover, the cross-cutting in expanding microchannels could further steady flow when adding fins in downstream channels. When adjusting the number of cross-cutting in cold plates from 1 to 4, the maximum increment of HTC is 58.17 kW/(m2·K). The influences of adjusting the number of fins in microchannels on the HTC are obvious for cold plates without cross-cutting. When the position of added fins is moved downstream in channels, the HTC of the heat exchanger could be increased by 26.58%. The results of this study provide some insights for inhibiting flow boiling instability and further optimizing the expanding microchannel structure to enhance heat transfer capability.

Hybrid battery thermal management by coupling fin intensified phase change material with air cooling

Phase change material (PCM) based passive battery thermal management (BTMS) is a promising strategy for controlling lithium-ion battery temperature during operation. However, the drawbacks of low thermal conductivity and poor secondary heat dissipation of PCM still need to be addressed. Herein, the metal fin intensified PCM system coupling with air cooling is proposed for battery thermal management. The effects of PCM thickness, metal fin diameter and number, air inlet velocity, and airflow temperature on the performance of the proposed BTMS are numerically investigated. Results indicate that the novel hybrid BTMS exhibits a superior cooling performance than fin-air BTMS without PCM and PCM-air BTMS without fins, reducing the maximum battery temperature by 18.6% and 3.2%, respectively. The embedded fins can improve the heat dissipation of the battery and PCM. Increasing air velocity can help recover the PCM latent heat but consume additional power. The proposed BTMS is investigated and optimized considering the cooling performance and power consumption tradeoff. The optimal design has a 1.0mm PCM thickness, 162fin numbers, and a 3.0mm fin diameter. Under such an optimal design, battery temperature can be controlled below the desired value of 40°C with less power consumption. The run-out of PCM latent heat is also effectively prevented in continuous cycle operation with an air velocity of 2.0m/s. This study can provide new insights into an advanced BTMS design for next-generation battery systems with high charging and discharging rates.

Effect of fin width ratio on thermal performance of fin based-heat sink with phase change materials

The rapid development of electronics, coupled with need of miniaturization in the design and manufacture, makes heat dissipation, which is critical for the performance, lifetime, and reliability of the components extremely challenging. To achieve higher heat dissipation rates, novel fin geometry with variable cross-section considering melting behaviour in medium is presented for PCM-based heat sink beyond previous efforts in literature. In this experimental study, effect of different variable cross-section, which refer different fin width ratio (s = 1, 0.5, 0.2 and 0) values are performed on the thermal performance of plate fin-based heat sink with PCM to enhance melting heat transfer. Decreasing fin width ratios point out increasing heat transfer surface area downwardly. N-eicosane is used. The constant input power is provided at the heat sink base. Thermal performance of novel fin design is evaluated by time-dependent temperature distributions, solid–liquid interface tracking photographs, reliable operating time, enhancement ratio, and thermal conductance. The results reveal that the proposed plate-fin geometry has a significant effect on the cooling performance of PCM-based heat sink. With the decrease of fin width ratio, higher temperature profile with more uniformity of 52% in the PCM medium, and so lower temperature distribution of 4.5% on the heat sink base are provided. Reliable operating time and thermal conductance values go up 15 % and 38%, respectively, for proposed fin geometry. The improvement on the thermal performance is achieved by the form of the plate-fin, which has increased surface area downward. This provides a great contribution to the conduction and convection heat transfer mechanisms at the lower half of the enclosure. Further, in this study, nearly the same reliable operating time is figured out with proposed fin geometry and fin number of s = 0 compared to higher fin number installation of s = 1 previously reported.

Optimization of Conductive Fins to Minimize UO2 Fuel Temperature and Radial Temperature Gradient

To further the development of low-enriched uranium fuels, precedence has been placed on delivering the same amount of power while lowering the fuel temperature and radial temperature gradient. To address this, modeling efforts have resulted in a novel design featuring conductive fins of varying thermal conductivities and geometries inserted into the fuel matrix. These conductive inserts were not allowed to exceed 6% of the original fuel volume. This constraint was imposed due to other designs displacing 10% of fuel volume. A parametric study was performed that consisted of 2.56 million BISON simulations involving varying fin characteristics (i.e., fin thermal conductivity, number, and geometry) to determine the optimal geometric configuration for a desired amount of fuel volume displaced. The results from this study show that the thickness and length of each fin affect the fuel temperature and temperature gradient more than varying the number and thermal conductivity of the fins. The parametric study resulted in the development of an optimized combination to produce the lowest peak fuel temperature, lowest radial temperature gradient, and highest temperature reduction for the amount of original fuel volume displaced. The simulations presented in this work will eventually be compared with irradiation experiments of similar fuel designs at Idaho National Laboratory’s Advanced Test Reactor.

Experimental investigation of the performance of an air type photovoltaic thermal collector system with fixed cooling fins

Solar energy may now be captured in two ways: heat extraction in solar collectors and electricity generation in photovoltaic panels. It may effectively reduce the degradation of PV cell efficiency caused by overheating of the battery by collecting the heat from the PV/T system. The heat dissipation cooling fin is directly mounted to the rear of the solar panel in this study and coated with an insulating layer to create an air-cooling channel. The heat dissipation fin transfers heat from the back of the photovoltaic panel to a certain mass flow of air in the flow channel, resulting in combined heat and power. The electrical and thermal capabilities of three distinct fin numbers were studied by monitoring electrical power and temperature data. A fixed mass flow rate (0.011 kg/s) for air, three different numbers of fins (0-5-10) and solar irradiance (200 W/m2–600 W/m2) are the experimental conditions. After the system was run stably for 10 min, the average temperature of the back of the PV panel, the device’s inlet and outlet temperatures, and the PV panel’s electric power were recorded. These figures are used to calculate the PV/T system’s electrical and thermal efficiency. When the median electrical efficiency of the three types of fins is compared with varying solar irradiation, it is discovered that the electric efficiency value of the three types of fins is approximately 16%, with a difference of less than 0.6%. The comprehensive efficiency of five groups of fins and ten groups of fins was 61.08% and 69.85%, respectively, based on the median comparison of photoelectric photothermal comprehensive efficiency. The overall efficiency of the zero groups of fins was 26.27%, which was only 14.59% greater than the control plate, and there was a considerable difference between the five and ten groups of fins. This suggests that selecting the right number of fins has a substantial impact on improving PV/T thermal performance. This research will assist in further optimizing the design of PV/T systems for heat collection and will provide valuable information for PV/T system application in building integration.

Performance analysis of thermoelectric generator system in different aspect ratio collector channels

Rectangular collector channels are widely used in thermoelectric generator (TEG) systems. The aspect ratio greatly influences the heat transfer of the channel and thus affects the TEG output performance. However, the effect of aspect ratio on TEG output performance has not been intensively analyzed. Thus this paper studies the effect of aspect ratio on TEG output performance under the same heated area for the first time and clarifies the reasons for the high output power of low aspect ratio channels. A numerical model of the TEG system is developed, and the model's accuracy is verified. Then, the output performance of the collector channel TEG system with different aspect ratios, such as output power, net power, and heat conversion efficiency, is investigated to obtain the optimal channel aspect ratio. Finally, the effects of the fin number and the load resistance on the output performance of the TEG system are further analyzed. The results show that the TEG system with low aspect ratio channels exhibits better output performance; the TEG system with an aspect ratio of 0.1 has an 18.3% higher output power than the TEG system with an aspect ratio of 1. When the Re number is 2400, the TEG with an aspect ratio of 0.1 has the highest net power of 2.77 W. The lower aspect ratio reduces the collector channel's hydraulic diameter and improves the TEG's heat transfer performance. When the fin number is increased from 16 to 34, the output power increases by 10%, but the lower number of fins exhibits a higher heat conversion efficiency. This study provides some new ideas for improving the output performance of TEG systems.

Optimization of melting performance of a heat storage tank under rotation conditions: Based on taguchi design and response surface method

The melting performance of a rotating triplex-tube latent heat thermal energy storage unit is studied by numerical simulation method. The Taguchi design and response surface method are applied to its optimized design. Firstly, the Taguchi design method is used to quantitatively reveal the specific effects of fin distribution, fin number, and fin material on the melting performance of the unit. Compared with all-inner tube-fin or all-outer tube-fin structures, the melting time of alternating inside and outside fin structures is shortened by 52.64% and 32.42%, the average heat absorption rate is greatly increased by 105.56% and 47.26%, and the total heat is reduced by 2.64% and 2.17%, respectively. Then, the response surface method is applied to the eight alternating fins obtained by the Taguchi design, and the effects of fin length, width, and rotation angle on the melting time and average heat absorption rate of the unit are studied. Compared with the original structure, the optimal structure reduces the total melting time by 7.37% and increases the average heat absorption rate by 7.23%. The geometric parameters’ interaction with the relevant target response is studied, and the corresponding fluid-structure interaction equation is fitted. Finally, the melt growth phenomenon near the wall is found in the initial melting stage of the optimized model by mechanism analysis.

Analysis of Multiple Fin-type Vertical GaN Power Transistors based on Bulk GaN Substrates

In this study, the multiple fin-type vertical GaN power transistor based on the GaN-on-GaN were analyzed using the two-dimensional technical computer-aided design (2-D TCAD) simulations. In the field of the electric vehicle systems requiring a high operation voltage of 1,000 V or more, the power devices have a large device area because of the long distance between the gate region and the drain region. This problem can be addressed by using the fin-type vertical GaN power transistor, which can reduce the device area due to its vertical channel. For the high current performance, the multiple fin-type structure was required. Thus, we investigated characteristics depending on the number of fin (NSUBfin/SUB). By comparing the on-state drain currents (ISUBon/SUB), the breakdown voltages (BV), and the on-resistances (RSUBon/SUB) with different NSUBfin/SUB, this study provides an understanding of the electrical properties of the multiple fin-type vertical GaN power transistor affected by NSUBfin/SUB.

Experimental study of convective heat transfer characteristics of ventilated passages formed by uniform diameter circular pin fins of disc brake

The heat transfer ability of ventilated passage of the disc brake has important effect on heat dissipation rate of the disc brake. The disc brake using uniform diameter circular pin fins to form ventilated passages has been widely used, but there is less reported heat transfer performance data of this type of ventilated passage. This paper investigated the heat transfer characteristics of the ventilated passage which is 10 times smaller than the real ventilated passage. The effects of the geometric parameters of the passage on its heat transfer ability are studied. The results show that the diameter and the number of the pin fin have stronger effect than the height of the pin fin has on the heat transfer. The results show great difference between the results predicted by the available correlation for ventilated passage formed by straight vane at small or large Reynolds number region. The reasons that cause the difference between the present results and other reported results are discussed. A correlation of Nusselt number vs. Reynolds number, the diameter, the number and the height of the pin fin is provided.

A novel numerical study on the melting process of phase change materials in a heat exchanger for energy storage

In this article, a new model with a different geometry is presented for application in systems of energy storage that contain phase change materials (PCMs). The main innovation of this research is designing two tubes instead of one tube inside the heat exchanger and investigation of its impact on the melting process of the PCM. Also, the influence of extended surfaces is studied to evaluate the reduction of melting time, and the changes of related geometrical parameters, including the number and length of fins, are examined in detail. The finite volume commercial code has been employed for numerical simulation and the obtained outcomes have very good agreement with a published experimental study. Results indicate that the utilizing of two tubes and reduce the distance between these tubes has a considerable influence on energy storage and reduction of melting time. Further, it can be concluded that for a certain number of fins, the melting time of PCM reduces by enhancing the fin length.

Thermal performance analysis of a new type of branch-fin enhanced battery thermal management PCM module

To solve the problem of the lightweight design of metal fins and strengthen the heat transfer between phase change material (PCM) and lithium batteries, the synergistic design of fins and phase change material-battery thermal management system (PCM-BTMS) is particularly important. In this paper, 9 new branch fin design schemes were proposed based on the conventional straight fin. The reliability of the computational fluid dynamics model was verified through the heat transfer experiments at different discharge rates. Firstly, the thermal performances of 9 new fins and the conventional straight fin under 5C discharge rate were compared and analyzed, and the optimal model was selected. Secondly, the effects of transverse fin coverage area, number, arc length, thickness, and arc length of inner and outer arc fins on the thermal performance were analyzed considering the effects of different heat transfer coefficients. The results show that the preferred fins have less effect on the heat transfer coefficient enhanced thermal performance compared with the conventional fins; the average cell temperature is reduced by 3.14 K and 3.92 K respectively by increasing the fin coverage area and the number of transverse fins to increase the contact area with PCM to enhance heat dissipation; the average cell temperature changes more significantly with the inner arc fins, and the cell temperature of Case H6 was reduced by 7.2 K; while the transverse fin arc length extension reduced the thermal performance of the system in high temperature cases. The volume of system remained the same, and the thickness of the transverse fins decreased the heat storage capacity of the system when the thickness of the transverse fins was larger. The optimal fins could keep the average cell temperature within 318.15 K. The heat transfer capability was improved by 14.98%, the operating time was extended by 131.5%, and the system weight was reduced by 10.28%.

Micro pin fins with topologically optimized configurations enhance flow boiling heat transfer in manifold microchannel heat sinks

The manifold microchannel heat sink (MMCHS) is a promising design for heat dissipation in high power electronics. However, the configuration of the microchannels in MMCHS is generally rectangular straight channels, which would limit the further improvement of heat transfer performance. Topology optimization has been proven to be an effective approach to design single-phase heat sinks, which only depends on the iterative algorithm. In this work, we first design three single-phase heat transfer structures (2D) by a density-based topology optimization method, and then systematically investigate the two-phase flow and heat transfer characteristics of MMCHS (3D configurations that are converted based on 2D designs). The thermohydraulic performances of three topologically optimized MMCHS obtained by varying the constrained pressure drop (named TOC-I, TOC-II and TOC-III for simplicity) and the baseline rectangular MMCHS are compared. The results show that the flow paths in the TOCs exhibit root-like configurations and the number of pin fins increases with the increase in constrained pressure drop (i.e., TOC-III has the most complex flow path). Due to the differences in velocity distribution and channel width among various configurations, churn flow and confined bubbly flow are observed in BC and TOCs, respectively. Compared to BC, the maximum average heat transfer coefficients of TOC-I, TOC-II and TOC-III are increased by 40%, 62% and 87%, respectively. The TOC-I has the lowest pressure drop due to the minimum number of pin fins and the relatively large channel width. The maximum values of Figure of Merit (FOM), a parameter usually employed to analyze the comprehensive performance of MMCHS, for TOC-I, TOC-II and TOC-III are 1.72, 1.77 and 1.8 at Qb= 1000 W/cm2, respectively. Moreover, TOC-I and TOC-III have the best comprehensive performance at 300 W/cm2≤ Qb ≤ 800 W/cm2 and 900 W/cm2 ≤ Qb ≤ 1000 W/cm2, respectively.

Hamiltonian-Based Efficient Algorithms for Legalization with Neighbor Diffusion Effect

Neighbor diffusion effect (NDE) is a crucial aspect in advanced technology node that is well-known for its infamous consequence of significant performance decrement of the circuit. In this paper, we observe that NDE is caused by different diffusion heights (the number of fins) between two adjacent cells, and consider reducing the number of height differences in single row to reduce NDE violations. Ignoring the movement of the cells, we first propose a Hamiltonian-completion-based algorithm that reorders the cells in the row such that the number of NDE violations is reduced to a near-optimal value. Then, for a given fixed integer [Formula: see text], we devise an algorithm to compute the new positions of cells, such that the number of NDE violations is bounded by [Formula: see text] and the maximum displacement is minimized. Moreover, we extend our algorithm for legalization in multiple rows against mixed-height cells. Experimental results show that our algorithm reduces the NDE violations to a near-optimal minimum without any area overheads while achieving a better practical running time compared to baselines conforming with the theoretical analysis.