The modeling of porous medium has many applications whose techniques can be used in the fields of automotive, aerospace, oil exploration, and biomedical. This work concentrates on the Noise and Vibration (NV) developm...The modeling of porous medium has many applications whose techniques can be used in the fields of automotive, aerospace, oil exploration, and biomedical. This work concentrates on the Noise and Vibration (NV) development of automotive interiors but the ideas can be translated to the aforementioned areas. The NV development requires the setting of NV targets at dif-ferent levels. These targets are then translated to TL (Transmission Loss), IL (Insertion Loss), and Alpha (absorption) performance. Therefore, the ability to manage an efficient product development cycle, that entails analyzing vibro-acoustic environments, hinges on the premise that accurate TL, IL, or Alpha values pertaining to the different multi-layered porous materials can be calculated. Thus, there is a need to have a thorough understanding of the physics behind the energy dissipating mechanism that includes the effects of the fluid meandering through the pores of the material. The goal of this series is to model the acoustic and dynamic coupling via multi-scale and homogenizations techniques, thus subsequently understand where to incorporate the concepts of dynamic tortuosity, viscous and thermal permeability, as well as viscous and thermal lengths. This study will allow the ability to get a better understanding of the underlying processes and also provides tools to create practical concepts for determining the coefficients of the macroscopic equations. This will assist in attaining novel ideas for NV absorption and insulation.展开更多
A mathematical model of optimal energy medium distribution in steelmaking process is formulated. In this model, three kinds of important energy mediums including byproduct gases, steam and electricity are considered, ...A mathematical model of optimal energy medium distribution in steelmaking process is formulated. In this model, three kinds of important energy mediums including byproduct gases, steam and electricity are considered, and the objective function accounts for both the change of generation and consumption of the byproduct gases and the demand of low （or middle） pressure steam and electricity for each period to maximize the benefit of products cost and minimize the consumption of energy. The results indicate that the optimal distribution scheme of byproduct gases, middle pressure steam, low pressure steam and electricity is achieved and case study shows that 6% of operation cost is reduced by using the proposed model comparing with the previous model.展开更多
To achieve the dual demand of resisting violent impact and attenuating vibration in vibration-impact-safety of protection for precision equipment such as MEMS packaging system, a theo- retical mathematical model of mu...To achieve the dual demand of resisting violent impact and attenuating vibration in vibration-impact-safety of protection for precision equipment such as MEMS packaging system, a theo- retical mathematical model of multi-medium coupling shock absorber is presented. The coupling of quadratic damping, linear damping, Coulomb damping and nonlinear spring are considered in the model. The approximate theoretical calculating formulae are deduced by introducing transformation-tactics. The contrasts between the analytical results and numerical integration results are developed. The resisting impact characteristics of the model are also analyzed in progress. In the meantime, the optimum model of the parameters matching selection for design of the shock absorber is built. The example design is illustrated to confirm the validity of the modeling method and the theoretical solution.展开更多
Power line communication(PLC)provides intelligent electrical functions such as power quality measurement,fault surveys,and remote control of electrical network.Most of research works have been done in low voltage(LV)s...Power line communication(PLC)provides intelligent electrical functions such as power quality measurement,fault surveys,and remote control of electrical network.Most of research works have been done in low voltage(LV)scenario due to the fast development of in-home PLC.The aim of this paper is to evaluate the link-level performance of a medium voltage(MV)MIMO-OFDM communication system based on transmission link under underground power line channel.The MIMO channel is modeled as a modified multipath model in the presence of impulsive noise and background noise.We first perform a measurement on the practical MV MIMO channel parameters for a section of buried cable of 1 km long in Ganzhou city,Jiangxi province,China.Based on the measured channel,we design the frame structure based on an IEEE standard for broadband over power line networks[1]to support MV MIMO-OFDM transmission.According to designed frame structure,we design an encoder and a decoder for a dual binary tail-biting turbo code and optimize some key decoder parameters for low bit error rate performance.Finally,the link-level performance for both spatial multiplexing and spatial diversity are evaluated.Numeral results show that MV MIMO-OFDM is a promising approach to provide both high data rate and link reliability for PLC.展开更多
The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-s...The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf（1985）,and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.展开更多
A novel inverse scattering method to reconstruct the permittivity profile of one-dimensional multi-layered media is proposed in this paper.Based on the equivalent network ofthe medium,a concept of time domain signal f...A novel inverse scattering method to reconstruct the permittivity profile of one-dimensional multi-layered media is proposed in this paper.Based on the equivalent network ofthe medium,a concept of time domain signal flow graph and its basic principles are introduced,from which the reflection coefficient of the medium in time domain can be shown to be a series ofDirac δ-functions(pulse responses).In terms of the pulse responses,we will reconstruct both thepermittivity and the thickness of each layer will accurately be reconstructed.Numerical examplesverify the applicability of this展开更多
This paper presents a new topology to connect high voltage direct current(HVDC) offshore wind farm into the grid.The offshore part consists of five units,each unit contains permanent magnet synchronous generator(PMSG)...This paper presents a new topology to connect high voltage direct current(HVDC) offshore wind farm into the grid.The offshore part consists of five units,each unit contains permanent magnet synchronous generator(PMSG) connected to three-phase/three-phase matrix converter to control the generator speed by using a maximum power point tracking(MPPT) control.The offshore platform consists of a three-phase medium frequency transformer(MFT) and a modular multi-level converter(MMC).The primary of each phase of the transformer connected to one phase from each unit.The secondary of the transformer connected to MMC to get HVDC.The HVDC cable will be used to transfer power from the offshore side to the on-shore side.Five-level MMC is used in the onshore side to control the DC voltage and to connect the offshore wind farm into the grid by converting the HVDC to high voltage alternative current(HVAC).展开更多
The application of porous medium has a myriad of applications in different industries: automotive, aerospace, civil (commercial, residential), environmental noise control, and biomedical. In the past, design questions...The application of porous medium has a myriad of applications in different industries: automotive, aerospace, civil (commercial, residential), environmental noise control, and biomedical. In the past, design questions involving porous material were addressed with seat-of-the-pants decisions that led to multiple/iterative prototypes and experiments that were costly and time consuming. The objective, in this series of publications pertaining to porous medium, is to establish tools that will lead to effective and accurate simulations involving porous medium. In this third installment of this series the focus is on establishing the constitutive equations using tensors and then applying Transfer Matrix Method (TMM) to calculate diffuse field Transmission Loss (TL) across structures that comprises of layers of different porous medium. The constitutive equations are obtained by relating information regarding the micro-structure make-up to macro level properties. In order to apply the TMM, the equations for wave propagation across different mediums need to be developed and in turn represent these propagation properties in a matrix format. Additionally, the boundary condition between each layer type is defined in order to ensure numerical stability. The author’s current research effort is running simulations for the automotive industry to predict NVH environments. Therefore, TL calculations pertaining to the materials that are utilized in the interior of automobiles are used, in this paper, as a test bed for the developed analytical tools. Case in point, the TL for a multi-layered material consisting of one panel and two different layers of foam is calculated and compared to experimental data. Future publication goals will be to apply these tools in the biomedical field;an example will be to model and run simulations of different organs like the liver and lungs that are po-rous in nature.展开更多
A method of multi-spectral analysis is used to study the spectral characteristics of surface and upper-level meteorological elements over the Great Wall Station (62°12'S, 58°57'W), Antarctica and the...A method of multi-spectral analysis is used to study the spectral characteristics of surface and upper-level meteorological elements over the Great Wall Station (62°12'S, 58°57'W), Antarctica and their phasecorrelation, propagation of mean oscillation at 500hPa level in the Southern Hemisphere and their corresponding synoptic sense. the results are summed up as follows: 1. Over the sub-Antatctic zone, as in the Northern Hemisphere there generally exist quasi-weekly oscillation and quasi-biweekly oscillation. In different seasons the oscillations of meteorological elements are different: in winter season quasi-biweekly oscillation is dominant, while in summer season quasi-weekly oscillation is dominant. 2. From the Earth's surface to the lower stratosphere there is a distinct quasi-weekly oscillation at each isobaric surface, but the most intense oscillation appears at 200-300hPa, and the oscillations of height and temperature are propagated downward. 3. Both in winter and summer seasons the quasi-biweekly oscillation are propagated from west to east, and the mean velocity of its propagation is about 7-17 longtitude / day. 4. The quasi-biweekly oscillation and the quasi-weekly oscillation over the sub - Antarctic zone are closely related to the activity and intensity variation of polar vortex at 500hPa, while at 1000hPa they reflect an interaction between the circumpolar depression and the sub-tropical high. The quasi-biweekly oscillation may be a reflection of inherent oscillation of the polar vortex, where as the quasi-weekly oscillation is a result of forced oscillation by external disturbance.A large number of calculations and analysis made reveals the features of medium-range oscillation over the sub-Antarctic zone. The results are of significance for understanding the behaviour of synoptic dynamics and making the weather forecast.This work is supported by National Committee for Antarctic Research.展开更多
In order to realize further stability of a stack-type thermoelectric power generating module (i.e. no electrical connections inside), flexible materials of metal springs and/or rods having restoring forces were instal...In order to realize further stability of a stack-type thermoelectric power generating module (i.e. no electrical connections inside), flexible materials of metal springs and/or rods having restoring forces were installed between lower-temperature-sides of thermoelectric elements. These flexible materials were expected to play three important roles of interpolating different thermal expansions of the module components, enlarging heat removal area and penetration of any media through themselves. Then, a low-boiling-point medium (i.e. NOVEC manufactured by 3M Japan Ltd.) was also applied for a high-speed direct heat removal via its phase change from the lower-temperature-sides of the thermoelectric elements in the proposing stack-type thermoelectric power generating module. No electrical disconnections inside the module were confirmed for more than 9 years of use, indicating further module stability. The power generating density was improved to about 120 mW·m-2 with SUS304 springs having 0.7 mm diameter. Increasing power generating density can be expected in terms of suitable selection of flexible metal with high Vickers hardness, cavities control on the spring surface, more vigorous multiphase flow with adding powders to the medium and optimization of the module configurations according to numerical simulations.展开更多
为了更好地模拟多材料介质无压渗流问题,提出了一种基于颗粒离散元的离散颗粒渗流模型(discrete seepage element model,DSEM)。该模型将连续介质离散化为密集堆积的颗粒系统,赋予颗粒流体性质,并通过颗粒间压力差模拟渗流过程。DSEM模...为了更好地模拟多材料介质无压渗流问题,提出了一种基于颗粒离散元的离散颗粒渗流模型(discrete seepage element model,DSEM)。该模型将连续介质离散化为密集堆积的颗粒系统,赋予颗粒流体性质,并通过颗粒间压力差模拟渗流过程。DSEM模型能够自动计算自由面位置和水头分布,无须预设自由面位置。为了验证DSEM模型的有效性,首先,模拟了土坝渗流问题,模拟结果与室内模型试验结果一致。随后,模拟了双材料矩形坝和分层土体渗流问题,并与其他数值方法进行比较,证明了DSEM在多种材料问题中的有效性。最后,将DSEM应用于分区梯形坝的渗流问题,成功计算了不同渗透系数下的自由面位置。研究结果表明,DSEM模型适用于多材料介质的无压渗流问题,为工程渗流问题提供了一种新的有效计算方法。展开更多
The article investigates the influences of a variable thermal conductivity and wall slip on a peristaltic motion of Carreau nanofluid. The model is concerned with heat and mass transfer inside asymmetric channel. The ...The article investigates the influences of a variable thermal conductivity and wall slip on a peristaltic motion of Carreau nanofluid. The model is concerned with heat and mass transfer inside asymmetric channel. The blood is considered as the base Carreau non-Newtonian fluid and gold (Au) as nanoparticles stressed upon. The Fronchiener effect of the non-Darcian medium is taken in consideration. The system is stressed upon a strong magnetic field and the Hall currents are completed. The problem is modulated mathematically by a system of non-linear partial differential equations which describe the fluid velocity, temperature and concentration. The system is reformulated under the approximation of long wavelength and low Reynolds number. It is solved on using multi-step differential transform method (Ms-DTM) as a semi-analytical method. A gold nanoparticle has increased the temperature distribution which is of great importance in destroying the cancer cells.展开更多
文摘The modeling of porous medium has many applications whose techniques can be used in the fields of automotive, aerospace, oil exploration, and biomedical. This work concentrates on the Noise and Vibration (NV) development of automotive interiors but the ideas can be translated to the aforementioned areas. The NV development requires the setting of NV targets at dif-ferent levels. These targets are then translated to TL (Transmission Loss), IL (Insertion Loss), and Alpha (absorption) performance. Therefore, the ability to manage an efficient product development cycle, that entails analyzing vibro-acoustic environments, hinges on the premise that accurate TL, IL, or Alpha values pertaining to the different multi-layered porous materials can be calculated. Thus, there is a need to have a thorough understanding of the physics behind the energy dissipating mechanism that includes the effects of the fluid meandering through the pores of the material. The goal of this series is to model the acoustic and dynamic coupling via multi-scale and homogenizations techniques, thus subsequently understand where to incorporate the concepts of dynamic tortuosity, viscous and thermal permeability, as well as viscous and thermal lengths. This study will allow the ability to get a better understanding of the underlying processes and also provides tools to create practical concepts for determining the coefficients of the macroscopic equations. This will assist in attaining novel ideas for NV absorption and insulation.
基金Item Sponsored by Fundamental Research Funds for Central University of China(N090302010)National High-Tech Researchand Development Program of China(2008AA042901)National Key Science and Technology Support Plan of Ministry of Science and Technology of China(2006BAE03A00)
文摘A mathematical model of optimal energy medium distribution in steelmaking process is formulated. In this model, three kinds of important energy mediums including byproduct gases, steam and electricity are considered, and the objective function accounts for both the change of generation and consumption of the byproduct gases and the demand of low （or middle） pressure steam and electricity for each period to maximize the benefit of products cost and minimize the consumption of energy. The results indicate that the optimal distribution scheme of byproduct gases, middle pressure steam, low pressure steam and electricity is achieved and case study shows that 6% of operation cost is reduced by using the proposed model comparing with the previous model.
基金This project is supported by National Defense Science Foundation of China (No.00J16.2.5.DZ0502)Foundation for Qualified Personnel of Jiangsu University, China(No.04JDG027)Provincial Natural Science Foundation of Guangxi. China(No.0339037, No.0141042).
文摘To achieve the dual demand of resisting violent impact and attenuating vibration in vibration-impact-safety of protection for precision equipment such as MEMS packaging system, a theo- retical mathematical model of multi-medium coupling shock absorber is presented. The coupling of quadratic damping, linear damping, Coulomb damping and nonlinear spring are considered in the model. The approximate theoretical calculating formulae are deduced by introducing transformation-tactics. The contrasts between the analytical results and numerical integration results are developed. The resisting impact characteristics of the model are also analyzed in progress. In the meantime, the optimum model of the parameters matching selection for design of the shock absorber is built. The example design is illustrated to confirm the validity of the modeling method and the theoretical solution.
文摘Power line communication(PLC)provides intelligent electrical functions such as power quality measurement,fault surveys,and remote control of electrical network.Most of research works have been done in low voltage(LV)scenario due to the fast development of in-home PLC.The aim of this paper is to evaluate the link-level performance of a medium voltage(MV)MIMO-OFDM communication system based on transmission link under underground power line channel.The MIMO channel is modeled as a modified multipath model in the presence of impulsive noise and background noise.We first perform a measurement on the practical MV MIMO channel parameters for a section of buried cable of 1 km long in Ganzhou city,Jiangxi province,China.Based on the measured channel,we design the frame structure based on an IEEE standard for broadband over power line networks[1]to support MV MIMO-OFDM transmission.According to designed frame structure,we design an encoder and a decoder for a dual binary tail-biting turbo code and optimize some key decoder parameters for low bit error rate performance.Finally,the link-level performance for both spatial multiplexing and spatial diversity are evaluated.Numeral results show that MV MIMO-OFDM is a promising approach to provide both high data rate and link reliability for PLC.
基金National Natural Science Foundation of China under grant No.51578373 and 51578372the Natural Science Foundation of Tianjin Municipality under Grant No.16JCYBJC21600
文摘The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf（1985）,and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.
文摘A novel inverse scattering method to reconstruct the permittivity profile of one-dimensional multi-layered media is proposed in this paper.Based on the equivalent network ofthe medium,a concept of time domain signal flow graph and its basic principles are introduced,from which the reflection coefficient of the medium in time domain can be shown to be a series ofDirac δ-functions(pulse responses).In terms of the pulse responses,we will reconstruct both thepermittivity and the thickness of each layer will accurately be reconstructed.Numerical examplesverify the applicability of this
文摘This paper presents a new topology to connect high voltage direct current(HVDC) offshore wind farm into the grid.The offshore part consists of five units,each unit contains permanent magnet synchronous generator(PMSG) connected to three-phase/three-phase matrix converter to control the generator speed by using a maximum power point tracking(MPPT) control.The offshore platform consists of a three-phase medium frequency transformer(MFT) and a modular multi-level converter(MMC).The primary of each phase of the transformer connected to one phase from each unit.The secondary of the transformer connected to MMC to get HVDC.The HVDC cable will be used to transfer power from the offshore side to the on-shore side.Five-level MMC is used in the onshore side to control the DC voltage and to connect the offshore wind farm into the grid by converting the HVDC to high voltage alternative current(HVAC).
文摘The application of porous medium has a myriad of applications in different industries: automotive, aerospace, civil (commercial, residential), environmental noise control, and biomedical. In the past, design questions involving porous material were addressed with seat-of-the-pants decisions that led to multiple/iterative prototypes and experiments that were costly and time consuming. The objective, in this series of publications pertaining to porous medium, is to establish tools that will lead to effective and accurate simulations involving porous medium. In this third installment of this series the focus is on establishing the constitutive equations using tensors and then applying Transfer Matrix Method (TMM) to calculate diffuse field Transmission Loss (TL) across structures that comprises of layers of different porous medium. The constitutive equations are obtained by relating information regarding the micro-structure make-up to macro level properties. In order to apply the TMM, the equations for wave propagation across different mediums need to be developed and in turn represent these propagation properties in a matrix format. Additionally, the boundary condition between each layer type is defined in order to ensure numerical stability. The author’s current research effort is running simulations for the automotive industry to predict NVH environments. Therefore, TL calculations pertaining to the materials that are utilized in the interior of automobiles are used, in this paper, as a test bed for the developed analytical tools. Case in point, the TL for a multi-layered material consisting of one panel and two different layers of foam is calculated and compared to experimental data. Future publication goals will be to apply these tools in the biomedical field;an example will be to model and run simulations of different organs like the liver and lungs that are po-rous in nature.
文摘A method of multi-spectral analysis is used to study the spectral characteristics of surface and upper-level meteorological elements over the Great Wall Station (62°12'S, 58°57'W), Antarctica and their phasecorrelation, propagation of mean oscillation at 500hPa level in the Southern Hemisphere and their corresponding synoptic sense. the results are summed up as follows: 1. Over the sub-Antatctic zone, as in the Northern Hemisphere there generally exist quasi-weekly oscillation and quasi-biweekly oscillation. In different seasons the oscillations of meteorological elements are different: in winter season quasi-biweekly oscillation is dominant, while in summer season quasi-weekly oscillation is dominant. 2. From the Earth's surface to the lower stratosphere there is a distinct quasi-weekly oscillation at each isobaric surface, but the most intense oscillation appears at 200-300hPa, and the oscillations of height and temperature are propagated downward. 3. Both in winter and summer seasons the quasi-biweekly oscillation are propagated from west to east, and the mean velocity of its propagation is about 7-17 longtitude / day. 4. The quasi-biweekly oscillation and the quasi-weekly oscillation over the sub - Antarctic zone are closely related to the activity and intensity variation of polar vortex at 500hPa, while at 1000hPa they reflect an interaction between the circumpolar depression and the sub-tropical high. The quasi-biweekly oscillation may be a reflection of inherent oscillation of the polar vortex, where as the quasi-weekly oscillation is a result of forced oscillation by external disturbance.A large number of calculations and analysis made reveals the features of medium-range oscillation over the sub-Antarctic zone. The results are of significance for understanding the behaviour of synoptic dynamics and making the weather forecast.This work is supported by National Committee for Antarctic Research.
文摘In order to realize further stability of a stack-type thermoelectric power generating module (i.e. no electrical connections inside), flexible materials of metal springs and/or rods having restoring forces were installed between lower-temperature-sides of thermoelectric elements. These flexible materials were expected to play three important roles of interpolating different thermal expansions of the module components, enlarging heat removal area and penetration of any media through themselves. Then, a low-boiling-point medium (i.e. NOVEC manufactured by 3M Japan Ltd.) was also applied for a high-speed direct heat removal via its phase change from the lower-temperature-sides of the thermoelectric elements in the proposing stack-type thermoelectric power generating module. No electrical disconnections inside the module were confirmed for more than 9 years of use, indicating further module stability. The power generating density was improved to about 120 mW·m-2 with SUS304 springs having 0.7 mm diameter. Increasing power generating density can be expected in terms of suitable selection of flexible metal with high Vickers hardness, cavities control on the spring surface, more vigorous multiphase flow with adding powders to the medium and optimization of the module configurations according to numerical simulations.
文摘为了更好地模拟多材料介质无压渗流问题,提出了一种基于颗粒离散元的离散颗粒渗流模型(discrete seepage element model,DSEM)。该模型将连续介质离散化为密集堆积的颗粒系统,赋予颗粒流体性质,并通过颗粒间压力差模拟渗流过程。DSEM模型能够自动计算自由面位置和水头分布,无须预设自由面位置。为了验证DSEM模型的有效性,首先,模拟了土坝渗流问题,模拟结果与室内模型试验结果一致。随后,模拟了双材料矩形坝和分层土体渗流问题,并与其他数值方法进行比较,证明了DSEM在多种材料问题中的有效性。最后,将DSEM应用于分区梯形坝的渗流问题,成功计算了不同渗透系数下的自由面位置。研究结果表明,DSEM模型适用于多材料介质的无压渗流问题,为工程渗流问题提供了一种新的有效计算方法。
文摘The article investigates the influences of a variable thermal conductivity and wall slip on a peristaltic motion of Carreau nanofluid. The model is concerned with heat and mass transfer inside asymmetric channel. The blood is considered as the base Carreau non-Newtonian fluid and gold (Au) as nanoparticles stressed upon. The Fronchiener effect of the non-Darcian medium is taken in consideration. The system is stressed upon a strong magnetic field and the Hall currents are completed. The problem is modulated mathematically by a system of non-linear partial differential equations which describe the fluid velocity, temperature and concentration. The system is reformulated under the approximation of long wavelength and low Reynolds number. It is solved on using multi-step differential transform method (Ms-DTM) as a semi-analytical method. A gold nanoparticle has increased the temperature distribution which is of great importance in destroying the cancer cells.
