Steady-state Thermal Simulation Research Articles

Temperature field analysis and compensation improvement of load cell

During the operation of load cell, heat is generated by the strain gauge and the electronics on the PCB board, which leads to temperature gradients within the sensor itself. These temperature gradients are unstable at different ambient temperatures. Compensation inaccuracies can also occur when compensating for sensor measurements at different temperatures This paper proposes a method to change the position of temperature compensation resistors to address errors caused by the temperature field effect of the strain gauge sensor itself. Without affecting the sensor’s strain measurement, the correctness of the proposed method is demonstrated through steady-state thermal simulation results in ANSYS and experimental results, effectively addressing errors caused by unstable temperature gradients during the operation of strain gauge sensors.

Studi Numerik Pengaruh Sudut Bukaan Damper dan Flue Gas Temperatur Terhadap Distribusi Temperatur Pada Heat Recovery Steam Generator (HRSG)

The Combined Cycle Gas Turbine Power Plant (PLTGU) utilizes the waste heat from the gas turbine to produce steam in a Heat Recovery Steam Generator (HRSG). The steam from the HRSG is then used to generate electricity in a steam turbine. In HRSG operation, several variables significantly impact its performance, including the damper angle and inlet temperature. At the Tanjung Uncang Power Plant in Batam, the manufacturer's standard operating procedure (SOP) requires that the exhaust gas temperature when the damper is open must be below 400°C. However, the gas turbine with an initial load of 5 MW has an exhaust gas temperature of 560°C - 580°C. Therefore, it is necessary to perform a gas turbine load release or FSNL (Full Speed No Load) to reduce the inlet temperature of the gas turbine. During FSNL, there are SOPs for diverter damper angles of 51°, 68°, and 90°. This leads to the need for analyzing the impact of diverter damper angles and inlet temperature on the flow pattern and temperature distribution. The analysis was conducted using CFD (Computational Fluid Dynamics) with ANSYS Fluent 2020 software. The variations used are diverter damper angles of 51°, 68°, and 90°, combined with inlet temperatures of 400°C and 580°C. The simulation outputs include velocity contours, temperature contours, and equivalent stress on the superheater tubes. The HRSG simulation results show that the flue gas is not distributed uniformly. The turbine exhaust gas only spreads along 4 – 11 meters, leading to slower steam production from the superheater. Additionally, when the superheater tubes are empty, the steady-state thermal and structural simulation results indicate that an inlet temperature of 580°C, whether at damper angles of 51°, 68°, or 90°, can cause a larger temperature difference between the inner and outer walls, ranging from 117.04°C to 125.5°C. This temperature difference can lead to thermal stress on the superheater tubes. This is shown in the S-N Curve for SA 213 T22 material, with a convection coefficient of 5 W/m² K (no steam), where the equivalent stress exceeds the endurance limit (infinite zone).

A Numerical Approach for Predicting Temperature Distribution, Heat Flow, and Material Deformation of Printed Circuit Board during Laser Soldering

This paper presents a numerical simulation approach using the finite element method (FEM) in ANSYS software to overcome the limited accessibility of laser soldering machines which are expensive. The study aims to examine the viability of simulating a laser soldering process using ANSYS steady-state thermal simulation. The simulation aims to produce accurate predictions for temperature distribution, heat flow, and deformation of the material during the process. A Gaussian laser beam equation is used to analyse the interaction between the laser beam and metallic components, particularly on PCB boards. This paper evaluates the properties of a laser beam and the Sn-3.0Ag-0.5Cu (SAC305) lead-free solders which are commonly used in electronic industries. As a result of the thermal analysis, the temperature distribution within the solder spots, as well as the copper as printed circuit board (PCB) can be determined, whereas the mechanical analysis of the materials can be determined by looking at their deformation and stress in the system. The results show that the laser beam effectively contains heat within the solder contacts, reducing the risk of excessive heat transfer. The copper acts as an efficient heat sink, managing thermal energy during the process. However, the solder point experiences substantial deformation and stress, indicating potential limitations in its performance. Nonetheless, the neighbouring components and solder joints exhibit a factor of safety, ensuring the overall safety and reliability of the system.

An efficient thermal model of chiplet heterogeneous integration system for steady-state temperature prediction

As the silicon-based CMOS technology faces significant challenges in terms of physical principles and process limitations by reducing the device dimensions to improve integration, the chiplet heterogeneous integration (CHI) system has become an important solution to continue Moore's law. The wafer-scale CHI systems have also emerged nowadays to achieve more powerful performance for artificial intelligence (AI) applications. Due to the high power and small space, the thermal problems are big challenges. Those problems can lead to severe damages if they are not well solved. In this paper, an efficient thermal model is proposed to predict the steady-state temperature distribution of CHI 2.5-D systems. Specifically, since an oversimplified heat sink can result in huge inaccuracy, the heat sink is modeled according to its actual shape. In addition, the RDL, TSVs and bumps are modeled in an equivalent manner to make this model more accurate. Those efforts enable steady-state thermal simulation of the CHI system. In order to extend the thermal model to wafer-scale CHI systems, an efficient method is developed to transform the circular components into regular shape. Finally, this thermal model is evaluated to be highly accurate with errors <1.8 % and quite fast. Based on this verification, several cases are analyzed to illustrate the applicability of our methodology in describing the thermal dissipation behaviors. The present thermal model is an instructive simulation tool which can be used to perform large scale thermal simulation of heterogeneous integration systems. The proposed methodology of the present simulation work is expected to help the designers to detect the potential temperature-dependent hotspots and improve the reliability and robustness of CHI systems in the early-stage of the design flow.

Combined Thermal and Wear Analysis of Linear Rolling Guide Subjected to Rigid–Flexible Coupling Motion Stage

The local heat and wear generated due to friction in a precision motion stage in electronic packaging equipment have a significant impact on its positioning precision. In this paper, we studied the temperature changes over time and the wear of a linear rolling guide (LRG) in a rigid–flexible coupling motion stage (RFCMS), both analytically and experimentally, and we proposed an evaluation method for LRG wear in an RFCMS. According to Fourier’s law and the law of conservation of energy, the differential equation of heat conduction for the LRG and the thermal boundary conditions were established. Steady-state and transient thermal simulations were carried out using ANSYS Workbench to predict the temperature increase in the LRG due to friction. Finally, a test apparatus was built to demonstrate that an RFCMS reduced the operating temperature of the LRG, which also reduced the wear on the contact surface. Through response surface methodology, the levels of the influence of different flexure hinge thicknesses, strokes, velocities, and accelerations on the temperature change rate (TCR) of the LRG were obtained, as well as the approximate regression equation of four variables of the TCR. This provided a new research method for precision maintenance, life design, and operational parameter selection for high-precision motion stages.

Thermal Analysis of Flip-Chip Bonding Designs for GaN Power HEMTs with an On-Chip Heat-Spreading Layer

In this work, we demonstrated the thermal analysis of different flip-chip bonding designs for high power GaN HEMT developed for power electronics applications, such as power converters or photonic driver applications, with large gate periphery and chip size, as well as an Au metal heat-spreading layer deposited on top of a planarized dielectric/passivation layer above the active region. The Au bump patterns can be designed with high flexibility to provide more efficient heat dissipation from the large GaN HEMT chips to an AlN package substrate heat sink with no constraint in the alignment between the HEMT cells and the thermal conduction bumps. Steady-state thermal simulations were conducted to study the channel temperatures of GaN HEMTs with various Au bump patterns at different levels of current and voltage loadings, and the results were compared with the conventional face-up GaN die bonding on an AlN package substrate. The simulations were started from a single finger isolated HEMT cell and then extended to multiple fingers HEMT cells (total gate width > 40 mm) to investigate the "thermal cross-talk" effect from neighboring devices. Thermal analysis of the GaN HEMT under pulse operation was also performed to better reflect the actual conditions in power conversion or pulsed laser driver applications. Our analysis provides a combinational assessment of power GaN HEMT dies under a working condition (e.g., 1MHz, 25% duty cycle) with different flip chip packaging schemes. The analysis indicated that the channel temperature rise (∆T) of a HEMT cell in operation can be reduced by 44~46% by changing from face-up die bonding to a flip-chip bonding scheme with an optimized bump pattern design.

A 3-D Thermal Network Model for Monitoring of IGBT Modules

With the continuous improvement of power densities and power levels for power converters, temperature information at critical sites of the power modules has become essential in health monitoring and thermal management. However, existing thermal models often ignore the temperature distributions of the chip and rarely discuss their applicability under high-temperature operation conditions. Here, a novel 3-D physical RC network model is proposed for insulated-gate bipolar transistor (IGBT) modules, which considers the temperature effects. This model can be efficiently and conveniently obtained with the assistance of finite-element method (FEM) steady-state thermal simulations. Based on the heat flux curves inside the power module, a novel method for 3-D RC parameters extraction is presented to monitor the temperatures at critical sites of the IGBT chip, and meanwhile, the temperature effects and uneven power loss distribution on the chip are considered. Compared with the prior-art Foster-type temperature-dependent 3-D thermal models, the modeling time cost for the proposed model has been remarkably reduced under the same computing hardware facilities since the temperature responses are no longer needed. Finally, FEM simulation and experimental results verify the effectiveness and accuracy of the proposed 3-D physical RC network model.

Simulation and Property Characterization of Nanoparticle Thermal Conductivity for a Microscale Selective Laser Sintering System

Abstract Current additive manufacturing (AM) technologies are typically limited by the minimum feature sizes of the parts they can produce. This issue is addressed by the microscale selective laser sintering system (μ-SLS), which is capable of building parts with single micrometer resolutions. Despite the resolution of the system, the minimum feature sizes producible using the μ-SLS tool are limited by unwanted heat dissipation through the particle bed during the sintering process. To address this unwanted heat flow, a particle scale thermal model is needed to characterize the thermal conductivity of the nanoparticle bed during sintering and facilitate the prediction of heat affected zones. This would allow for the optimization of process parameters and a reduction in error for the final part. This paper presents a method for the determination of the effective thermal conductivity of copper nanoparticle beds in a μ-SLS system using finite element simulations performed in ansys. A phase field model (PFM) is used to track the geometric evolution of the particle groups within the particle bed during sintering. Computer aided design (CAD) models are extracted from the PFM output data at various time-steps, and steady-state thermal simulations are performed on each particle group. The full simulation developed in this work is scalable to particle groups with variable sizes and geometric arrangements. The particle thermal model results from this work are used to calculate the thermal conductivity of the copper nanoparticles as a function of the density of the particle group.

FEM heat transfer modelling with tomography-based SiCf/SiC unit cell

Modern industry has become increasingly reliant on composite materials for a variety of applications, and the nuclear industry is no exception to this. Among the materials being researched as Enhanced Accident Tolerant Fuels, ceramic matrix composites such as SiC-fiber-reinforced SiC (SiCf/SiC) figure as some prime candidates due to their excellent high temperature performances. SiCf/SiC so far shows adequate nuclear, mechanical and chemical properties; still, the thermal properties need further investigation. The thermal behavior of a material is an important factor for its performance as a nuclear fuel cladding, i.e. the first barrier encapsulating the fuel pellets. Many features determine the resulting properties of composite materials, such as matrix and fiber reinforcement properties and orientation, void fraction, and pore morphology. This study establishes a methodology to study the physical properties of composite materials and applies it to SiCf/SiC. A FEM model is used to characterize the thermal properties of a fundamental SiCf/SiC element, referred to as a �unit cell�, with the objective of accurately predicting the thermal properties of this complex class of materials where experimental data is often difficult to obtain. The unit cell is built based on data acquired with high-resolution tomographic microscopy performed at the TOMCAT beamline of the Swiss Light Source. By using phase-retrieval prior to tomographic reconstruction, the pores, fibers and matrix that compose the material can be distinguished in the data analysis. The separated information is processed to obtain geometrical information about the individual pores and fibers, which is then used to parametrize them as cylindrical objects. This allows constructing a FEM model of a cubic unit cell that is used to extract the effective thermal properties of SiCf/SiC. The analysis scheme includes steady-state and dynamic thermal transport simulations, which yield directional effective thermal conductivity and diffusivity values, respectively. Both modes of analysis show isotropic thermal conductivity values in the range of 71 W/m/K at room temperature, more than three times that of currently employed nuclear cladding materials. Combining these results with the data on the larger structural features of the material will lead to realistic results on the macroscopic thermal properties.

Predicting the Thermal Behavior in Functional Textile Fibers Having Embedded Electronics

In this paper, both steady-state and transient thermal simulations were performed on functional fibers having an embedded electronic chip acting as a heat source. Simulations were conducted for a range of different fiber materials and arbitrary fiber cross-sectional shapes. We show that under steady-state heating conditions, the thermal response for any arbitrary fiber shape and fiber material system was convection dominated regardless of the effective thermal conductivity of the fiber, and that the corresponding temperature rise within the fiber can be predicted analytically allowing for the maximum temperature to be estimated for any known heat load and fiber geometry. In the case of transient heating, we show that for pulsed power operation of the embedded electronic device, the maximum temperature reached in the fiber is always greater than the maximum temperature of the equivalent steady-state average power. However, high peak powers can be safely achieved if the power-on pulse time and duty cycle are selected to limit the maximum temperature reached in the fiber. Based on the results from the transient simulations, a set of criteria was developed to determine whether the operating conditions would be: (1) allowable for the fiber system, thus requiring no transient simulations, (2) requiring a transient simulation to verify that the maximum temperature is acceptable, and (3) the operating conditions are too severe and device operation at these conditions are not practical.Graphical

Development of gradient structural composite for improving tribological performance of PU material in water-lubricated bearings

Polymer materials have poor thermal conductivity and prone to aging at high temperatures. Severe wear occurs at material friction interfaces at high or locally high temperatures. In this study, gradient structural design for polyurethane was realized by adding high thermal-conductivity wire into water-lubricated bearing material. Tribological performance was evaluated by analysis of friction coefficients, wear microscopy, and average temperature during steady-state thermal simulation analysis. The results showed that metal wire effectively transferred heat and reduced sample temperature and the formed surface film effectively reduced the friction coefficient. These findings provided a new method for improving the thermal conductivity and wear resistance of water-lubricated bearing materials. The poor thermal conductivity of polymer bushing and the tribological performance of bearing is improved.

Heat transfer performance analysis of a novel circular microchannel heat sink

Electronic component heat dissipation is a significant issue in the development of electronic equipment. A unique circular micro-channel heat sink is proposed in this study. Cylinders and cones are evenly arranged inside the micro-channel to change the flow state of the liquid. Using the fluid analysis Fluent to calculate and simulate the heat sink, the pressure distribution and flow velocity distribution in the heat sink are obtained. The temperature field of the heat sink during operation is obtained through the Steady-State Thermal simulation, and the heat transfer performance of the heat sink is determined. The results indicate that the microchannel structure proposed in this research has great heat transfer performance.

Thermal Simulation and Experimental Analysis of Optically Pumped InP-on-Si Micro- and Nanocavity Lasers.

There is a general trend of downscaling laser cavities, but with high integration and energy densities of nanocavity lasers, significant thermal issues affect their operation. The complexity of geometrical parameters and the various materials involved hinder the extraction of clear design guidelines and operation strategies. Here, we present a systematic thermal analysis of InP-on-Si micro- and nanocavity lasers based on steady-state and transient thermal simulations and experimental analysis. In particular, we investigate the use of metal cavities for improving the thermal properties of InP-on-Si micro- and nanocavity lasers. Heating of lasers is studied by using Raman thermometry and the results agree well with simulation results, both revealing a temperature reduction of hundreds of kelvins for the metal-clad cavity. Transient simulations are carried out to improve our understanding of the dynamic temperature variation under pulsed and continuous wave pumping conditions. The results show that the presence of a metal cladding not only increases the overall efficiency in heat dissipation but also causes a much faster temperature response. Together with optical experimental results under pulsed pumping, we conclude that a pulse width of 10 ns and a repetition rate of 100 kHz is the optimal pumping condition for a 2 μm wide square cavity.

Design simulation of nonlinear static 2D and steady state thermal for sustainability downlight casing base

This paper explains the design and simulation of nonlinear static 2D and steady state thermal for sustainability downlight casing base. The main problem in designing of downlight casing base is to ensure the heat transferred to the surrounding while maintaining the quality of light. This study simulates of 6-in casing base downlight and Polycarbonate/acrylonitrile butadiene styrene (PC-ABS) based material. New product design methodology was presented using SolidWorks simulation to represent the phenomena of heat transfer in the downlight casing base at the design stage. The result shows the nonlinear static 2D for main base was achieved. The parameters of materials, dimension, and thickness was contributed in the seamless of heat transferred form casing base to the surrounding at ambient temperature. This practice prevents the quality of light while heat flux as applied to be further study. In addition, the steady state thermal simulation shows significant heat flux and convection changes to every face of casing base parts. Thus, this study is proposed to manage the development of new design relates with nonlinear static 2D and steady state thermal analysis for sustainability downlight casing base.

Engine Performance Analysis by Studying Heat Transfer in the Valve Seat through Steady-State Thermal Simulation

As the engine reached high speed, the exhaust valve temperature increased exponentially due to the exhaust gas produced by the combustion process between the mixture of air and fuel within the combustion chamber of the internal combustion engine. The valve is subjected to thermal loading due to high temperature and pressure within the cylinder, which must withstand a material temperature for sustainable and optimal operation. To avoid this loss, a perfect medium must be prepared to ensure that the heat is extracted smoothly. This can be done when the valve is in contact with the seat and there is a periodic heat transfer contact. Therefore, it is imperative to research the correlation between valve and valve seat to understand the two sections’ heat transfer mechanism. In this study, thermal contact analysis was used to identify heat transfer between the valve and the valve seat as both parts are interconnected. This research also has an interest in studying the two surface conduction mechanisms as the exhaust valve closed in steady-state conditions. Thus, this study portrays a significant method, particularly for the determining the distribution of temperature, heat flux, and heat flux direction between the valve and its seat using ANSYS Workbench.

Machine Learning-Based Predictions of Benefits of High Thermal Conductivity Encapsulation Materials for Power Electronics Packaging

Abstract Machine learning (ML)-based predictive techniques are used in conjunction with a game-theoretic approach to predict the thermal behavior of a power electronics package, and study the relative influence of encapsulation material properties and thermal management techniques in influencing hotspot temperatures. Parametric steady-state and transient thermal simulations are conducted for a commercially available 1.2 kV/444 A silicon carbide (SiC) half-bridge module. An extensive databank of 2592 (steady-state) and 1200 (transient) data points generated via numerical simulations is used to train and evaluate the performance of three ML algorithms (random forest, support vector regression, and neural network) in modeling the thermal behavior. The parameter space includes the thermal conductivities of the encapsulant, baseplate, heat sink, and cooling conditions deployed at the sink and covers a variety of materials and cooling scenarios. Excellent prediction accuracies with R2 values &amp;gt; 99.5% are obtained for the algorithms. Shapley additive explanations (SHAP) dependence plots are used to quantify the relative impact of device and heat sink parameters on junction temperatures. We observe that while heatsink cooling conditions significantly influence the steady-state junction temperature, their contribution in determining the junction temperature in dynamic mode is diminished. Using ML-SHAP models, we quantify the impact of emerging polymeric nanocomposites (with high conductivities and diffusivities) on hotspot temperature reduction, with the device operating in steady-state and transient modes. Overall, this study highlights the attractiveness of ML-based approaches for thermal design, and provides a framework for setting targets for future encapsulation materials.

Graphene double cross-linked thermally conductive hydrogel with low thermal contact resistance, flexibility and self-healing performance

With the booming development of electronic devices usually used in a dynamic working environment, there is an urgent need for thermal interface materials with low thermal contact resistance, high thermal conductivity, excellent elasticity, and self-healing properties. A novel thermal interface material is obtained by incorporating graphene into a polyacrylate-based double cross-linked hydrogel. The introduction of graphene into the hydrogel can improve the thermal conductivity of the thermal interface material and enhance the tensile properties of the hydrogel. The composite thermally conductive hydrogel has self-healing properties, precisely meeting the thermal interface material's dynamic working environment. Besides, the effects of pressure and temperature on the thermal contact resistance are investigated. When the pressure increases from 10 Psi to 50 Psi at 35 °C, the thermal contact resistance is reduced to 0.069 K ∙ cm2/W. Under certain pressure, the effect of temperature on the thermal contact resistance is minor. Overall, the thermal contact resistance remains low (0.5–0.9 K ∙ cm2/W). The composite hydrogel is demonstrated excellent thermal management performance under the combined effect of high thermal conductivity and low thermal contact resistance by steady-state thermal analysis simulations and infrared thermography. Highly elastic, self-healing, low thermal resistance composites will present ideas for further construction of new thermal interface materials.

Impact of Rooftop PV Shading on Net Electrical Energy Demand of Buildings in Pakistan

This work performs a quantitative assessment of the impact of rooftop PV installation on building’s net energy demand using model of roof structure and steady state thermal simulations. For this purpose, roof structure typically used in Faisalabad, Pakistan is modeled with and without the shading effect due to a 395 W commercial rooftop PV setup. The simulated parameters include the impact of PV module’s dimensions, mounting position/angle alongside roof size and ambient conditions on heat load of air-conditioning system to maintain a temperature of 25 °C within building’s top floor. During the daylight hours of July, the heat load added by the roof on average reduces from 150.87 BTU/h/m2 without PV to 118.16 BTU/h/m2 with PV structure. This 20.05% reduction in energy demand has been achieved with July’s maximum daytime solar and infrared irradiances of 792.2 W/m2 and 466 W/m2 recorded at an average ambient temperature of 35.5 °C and wind speed of 2.75 m/s. This study provides valuable data on optimization of roof layer structure during building’s construction in anticipation of PV system installation at a later stage. Also developed techniques/methods to reduce building’s energy budget due to PV installation, can be valuable input for construction industry as well.

PACT: An Extensible Parallel Thermal Simulator for Emerging Integration and Cooling Technologies

Thermal analysis is an essential step that enables co-design of the computing system (i.e., integrated circuits and computer architectures) with the cooling system (e.g., heat sink). Existing thermal simulation tools are limited by several major challenges that prevent them from providing fast solutions to large problem sizes that are necessary to conduct standard-cell level thermal analysis or to evaluate new technologies or large chips. To overcome these challenges, we introduce a SPICE-based parallel compact thermal simulator (PACT) that achieves fast and accurate, standard cell to architecture-level, steady-state, and transient parallel thermal simulations. PACT utilizes the advantages of multicore processing (OpenMPI) and includes several solvers to speed up both steady-state and transient simulations. PACT can be easily extended to model a variety of emerging integration and cooling technologies by simply modifying the thermal netlist. In addition, PACT can also be used with popular architecture-level performance and power simulators. In comparison to a state-of-the-art finite-element method (FEM)-based simulator (COMSOL), PACT has a maximum error of 2.77% and 3.28% for steady-state and transient thermal simulations, respectively. Compared to a popular compact thermal simulator, HotSpot, PACT demonstrates a speedup of up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.83\times $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$186\times $ </tex-math></inline-formula> for steady-state and transient simulations, respectively. We also show the applicability and extensibility of PACT through modeling emerging integration and cooling technologies, such as monolithic 3-D integrated circuits and liquid cooling via microchannels, and full-system simulation integration on a 2.5-D system with silicon-photonic network-on-chips (PNoCs).

Heat Transfer Analysis of Flat Heat Pipe With Enhanced Microchannel Shape

Flat heat pipe has many excellent characteristics such as high thermal conductivity, reversibility of heat flow direction and so on. In this paper, a flat heat pipe model with multiple microchannels is established, and the effects of different microchannel shapes and different materials on the heat transfer efficiency of flat heat pipe are studied. Then, based on the general rectangular and inverted trapezoidal microchannel shape, the enhancement is carried out. That is to fill a number of materials in the bottom of the microchannel to change the bottom shape of the microchannel. In the steady-state thermal simulation of flat heat pipe, the axial temperature of the flat heat pipe with enhanced microchannel shape is lower than that of the flat heat pipe with general microchannel, which shows that the enhanced microchannel shape is helpful to the heat dissipation of flat heat pipe. The fluid simulation results show that the enhanced rectangular microchannel shape can accelerate the flow velocity of working fluid. Therefore, the flat heat pipe with enhanced microchannel shape has better heat transfer performance. In order to obtain the local temperature of flat heat pipe quickly, the transient analytical solution is provided. In this paper, the temperature field calculated by using transient analytical solution is compared with that simulated by COMSOL. The results show that the maximum error between the results of discrete heat source model and continuous heat source model calculated by transient solution and COMSOL simulation results is less than 2%.