Graphite as a promising anode candidate of K-ion batteries(KIBs)has been increasingly studied currently,but corresponding rate performance and cycling stability are usually inferior to amorphous carbon materials.To pr...Graphite as a promising anode candidate of K-ion batteries(KIBs)has been increasingly studied currently,but corresponding rate performance and cycling stability are usually inferior to amorphous carbon materials.To protect the layer structure and further boost performance,tempura-like carbon/carbon nanocomposite of graphite@pitch-derived S-doped carbon(G@PSC)is designed and prepared by a facile and low-temperature modified molten salt method.This robust encapsulation structure makes their respective advantages complementary to each other,showing mutual promotion of electrochemical performances caused by synergy effect.As a result,the G@PSC electrode is applied in KIBs,delivering impressive rate capabilities(465,408,370,332,290,and 227 m A h g^(-1)at 0.05,0.2,0.5,1,2,and 5 A g^(-1))and ultralong cyclic stability(163 m A g^(-1)remaining even after 8000 cycles at 2 A g^(-1)).On basis of ex-situ studies,the sectionalized K-storage mechanism with adsorption(pseudocapacitance caused by S doping)-intercalation(pitch-derived carbon and graphite)pattern is revealed.Moreover,the exact insights into remarkable rate performances are taken by electrochemical kinetics tests and density functional theory calculation.In a word,this study adopts a facile method to synthesize high-performance carbon/carbon nanocomposite and is of practical significance for development of carbonaceous anode in KIBs.展开更多
Hierarchical Sb_2S_3 hollow microspheres assembled by nanowires have been successfully synthesized by a simple and practical hydrothermal reaction. The possible formation process of this architecture was investigated ...Hierarchical Sb_2S_3 hollow microspheres assembled by nanowires have been successfully synthesized by a simple and practical hydrothermal reaction. The possible formation process of this architecture was investigated by X-ray diffraction, focused-ion beam-scanning electron microscopy dual-beam system, and transmission electron microscopy. When used as the anode material for lithium-ion batteries, Sb_2S_3 hollow microspheres manifest excellent rate property and enhanced lithium-storage capability and can deliver a discharge capacity of 674 m Ah g^(-1) at a current density of 200 m A g^(-1) after 50 cycles. Even at a high currentdensity of 5000 m A g^(-1), a discharge capacity of541 m Ah g^(-1) is achieved. Sb_2S_3 hollow microspheres also display a prominent sodium-storage capacity and maintain a reversible discharge capacity of 384 m Ah g^(-1) at a current density of 200 m A g^(-1) after 50 cycles. The remarkable lithium/sodium-storage property may be attributed to the synergetic effect of its nanometer size and three-dimensional hierarchical architecture, and the outstanding stability property is attributed to the sufficient interior void space,which can buffer the volume expansion.展开更多
In this paper, modified two-dimensional peri- odic lattice materials with local resonance phononic band gaps are designed and investigated. The design concept is to introduce some auxiliary structures into conventiona...In this paper, modified two-dimensional peri- odic lattice materials with local resonance phononic band gaps are designed and investigated. The design concept is to introduce some auxiliary structures into conventional pe- riodic lattice materials. Elastic wave propagation in this kind of modified two-dimensional lattice materials is studied us- ing a combination of Bloch's theorem with finite element method. The calculated frequency band structures of illus- trative modified square lattice materials reveal the existence of frequency band gaps in the low frequency region due to the introduction of the auxiliary structures. The mechanism underlying the occurrence of these frequency band gaps is thoroughly discussed and natural resonances of the auxiliary structures are validated to be the origin. The effect of geo- metric parameters of the auxiliary structures on the width of the local resonance phononic band gaps is explored. Finally, a conceptual broadband vibration-insulating structure based on the modified lattice materials is designed and its capabil- ity is demonstrated. The present work is anticipated to be useful in designing structures which can insulate mechanical vibrations within desired frequency ranges.展开更多
The role of the National Laboratories is summarized from the era of post World War II to the present time. The U.S. federal government policy for the National Laboratories and its influence on their materials science ...The role of the National Laboratories is summarized from the era of post World War II to the present time. The U.S. federal government policy for the National Laboratories and its influence on their materials science infrastructure is reviewed with respect to .determining overall research strategies, various initiatives to interact with industry (especially in recent years),building facilities that serve the nation, and developing leading edge research in the materials sciences. Despite reductions in support for research in the U.S. in recent years, and uncertainties regarding the specific policies for Research &Development (R&D) in the U.S., there are strong roles for materials research at the National Laboratories. These roles will be centered on the abilities of the National Laboratories to field multidisciplinary teams, the use of unique cutting edge facilities, a focus on areas of strength within each of the labs,increased teaming and partnerships, and the selection of motivated research areas. It is hoped that such teaming opportunities will include new alliances with China, in a manner similar, perhaps, to those recently achieved between the U.S. and other countries.展开更多
The mutual control mechanism between magnetization and polarization in multiferroic materials is studied. The system contains a ferromagnetic sublattice and a ferroelectric sublattice. To describe the magneto–electri...The mutual control mechanism between magnetization and polarization in multiferroic materials is studied. The system contains a ferromagnetic sublattice and a ferroelectric sublattice. To describe the magneto–electric coupling, we propose a linear coupling Hamiltonian between ferromagnetism and ferroelectricity without microscopic derivation. This coupling enables one to retrieve the hysteresis loops measured experimentally. The thermodynamic properties of the system are calculated, such as the temperature dependences of the magnetization, polarization, internal energy and free energy.The ferromagnetic and ferroelectric hysteresis loops driven by either a magnetic or an electric field are calculated, and the magnetic spin and pseudo-spin are always flipped synchronously under the external magnetic and electric field. Our theoretical results are in agreement with the experiments.展开更多
A dynamic contact problem for elastic-viscoplastic materials with thermal effects is investigated. The contact is bilateral, and the friction is modeled with Tresca's friction law with heat exchange. A variational fo...A dynamic contact problem for elastic-viscoplastic materials with thermal effects is investigated. The contact is bilateral, and the friction is modeled with Tresca's friction law with heat exchange. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear first order evolution inequalities, the equations with monotone operators, and the fixed point arguments. Finally, the continuous dependence of the solution on the friction yield limit is studied.展开更多
In this paper, we report the growth of single crystals of Co_x Zn_(1-x)S and Co_x Zn_(1-x)Se (0<x<0.3) by the method of chemical transport, using iodine as a transport agent. The light green color of single crys...In this paper, we report the growth of single crystals of Co_x Zn_(1-x)S and Co_x Zn_(1-x)Se (0<x<0.3) by the method of chemical transport, using iodine as a transport agent. The light green color of single crystal Co_xZn_(1-x)S as well as the light brown color of Co_xZn_(1-x)Se become deep with an increase in x. The compositions of the single crystals were nearly stoichiometric. The transfer rate decreases with an increase of the x value. The growth rate was related to the temperature difference. The large temperature difference speed up the growth rate, but the size of crystal obtained was small. In general, the optimal temperature difference was 15℃. From X-ray diffraction measurements, the structures of crystals Co_xZn_(1-x)S and Co_xZn_(1-x)Se (0<x<0.1) were identified to be zinc blende structure similar to that of ZnS and ZnSe.展开更多
In order to mitigate the risks stemming from the utilization of mineral and synthetic organic substances,consensus exists in the literature that additional efforts should be devoted to the identification of adequate e...In order to mitigate the risks stemming from the utilization of mineral and synthetic organic substances,consensus exists in the literature that additional efforts should be devoted to the identification of adequate equivalent natural(ecological)materials.This work presents the outcomes of a preliminary study where the physical,mechanical,chemical and thermal properties of natural fibers have been considered.Initially,areca,and materials such as Moroccan doum and jute are considered.As a case study,a brake pad based on natural fibers is critically assessed.展开更多
China’s building materials industry experienced great development in 1993 with rapid increases in production and record output and profits. The industry produced 360 million tons of cement, 96.163 million cases of pl...China’s building materials industry experienced great development in 1993 with rapid increases in production and record output and profits. The industry produced 360 million tons of cement, 96.163 million cases of plate glass, 20.4 million pieces of sanitation ceramics and 173 million square metres of construction ceramics, showing rises of 12.89, 12.83, 123.8 and 127 percent respectively over the previous year. The output of cement and展开更多
The development of tissue-engineered technology brings hope to the treatment of spinal cord injury. Preparation of a tissue-engineered spinal cord stent with three-dimensional bionic structure has important value in t...The development of tissue-engineered technology brings hope to the treatment of spinal cord injury. Preparation of a tissue-engineered spinal cord stent with three-dimensional bionic structure has important value in the construction of tissue-engineered spinal cord and the repair of spinal cord injury. Acellular scaffolds can be produced with chemical extraction,展开更多
Iron & Steel Industry China's outputs of crude steel, steel products, coke and ferrous alloys in 2012 were 716.54 million tons (up 3.1% YOY), 051.86 million tons (up 7.7% YOY), 443.23 million tons (up 5.2% YOY...Iron & Steel Industry China's outputs of crude steel, steel products, coke and ferrous alloys in 2012 were 716.54 million tons (up 3.1% YOY), 051.86 million tons (up 7.7% YOY), 443.23 million tons (up 5.2% YOY) and 31.29 million tons (up 15% YOY),展开更多
On April 20-22 2011,China's Refractories Raw Materials SYmposium,co-sponsored by Refractories Branch of The Chinese Society for Metals and China Henan Refractory Industry Association,was held successfully in Zhengzhou.
In 2013, China's outputs of cement and flat glass were 2. 414 billion tons and 778.98 million weight cases, increasing by 9.6% and 11.2% YOY, respectively.
Single-pulse chaos are studied for a functionally graded materials rectangular plate. By means of the global perturbation method, explicit conditions for the existence of a SiZnikov-type homoclinic orbit are obtained ...Single-pulse chaos are studied for a functionally graded materials rectangular plate. By means of the global perturbation method, explicit conditions for the existence of a SiZnikov-type homoclinic orbit are obtained for this sys- tem, which suggests that chaos are likely to take place. Then, numerical simulations are given to test the analytical predic- tions. And from our analysis, when the chaotic motion oc- curs, there are a quasi-period motion in a two-dimensional subspace and chaos in another two-dimensional supplemen- tary subspace.展开更多
By making the use of the processes which includes separating trash and solid materials from the wastewater-ammonia stripping tower-UASB-biological oxidation pond, we have treated the wastewater which comes from the sw...By making the use of the processes which includes separating trash and solid materials from the wastewater-ammonia stripping tower-UASB-biological oxidation pond, we have treated the wastewater which comes from the swine factory. The treated wastewater can meet the primary standard of The People's Republic of China based on sewage discharge standards and the wastewater treatment project design contract (GBl8596-2001), and the effluent will be used as irrigation-water. We introduce this project including the quality of influent and effluent and the flow scheme, the statement of every part, the investment and the effect, etc. The operation indicated that this process has many merits such as the stability in operation-effect and the convenience in management. So it will provide some help for the similar wastewater treatment.展开更多
In this technical paper, the oxidation mechanism and kinetics of aluminum powders are discussed in great details. The potential applications of spherical aluminum powders after oxidation to be part of the surging arre...In this technical paper, the oxidation mechanism and kinetics of aluminum powders are discussed in great details. The potential applications of spherical aluminum powders after oxidation to be part of the surging arresting materials are discussed. Theoretical calculations of oxidation of spherical aluminum powders in a typical gas fluidization bed are demonstrated. Computer software written by the author is used to carry out the basic calculations of important parameters of a gas fluidization bed at different temperatures. A mathematical model of the dynamic system in a gas fluidization bed is developed and the analytical solution is obtained. The mathematical model can be used to estimate aluminum oxide thickness at a defined temperature. The mathematical model created in this study is evaluated and confirmed consistently with the experimental results on a gas fluidization bed. Detail technical discussion of the oxidation mechanism of aluminum is carried out. The mathematical deviations of the mathematical modeling have demonstrated in great details. This mathematical model developed in this study and validated with experimental results can bring a great value for the quantitative analysis of a gas fluidization bed in general from a theoretical point of view. It can be applied for the oxidation not only for aluminum spherical powders, but also for other spherical metal powders. The mathematical model developed can further enhance the applications of gas fluidization technology. In addition to the development of mathematical modeling of a gas fluidization bed reactor, the formation of oxide film through diffusion on both planar and spherical aluminum surfaces is analyzed through a thorough mathematical deviation using diffusion theory and Laplace transformation. The dominant defects and their impact to oxidation of aluminum are also discussed in detail. The well-controlled oxidation film on spherical metal powders such as aluminum and other metal spherical powders can potentially become an important part of switch devices of surge arresting materials, in general.展开更多
The Green's function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage....The Green's function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage. The thickness of the solid PCM on the fin varies with time and is obtained by the Megerlin method. The models are found with the Bessel equation to form an analytical solution. Three different kinds of boundary conditions are investigated. The comparison between analytical and numerical solutions is given. The results demonstrate that the significant accuracy is obtained for the temperature distribution for the fin in all cases.展开更多
基金the financial support from the National Natural Science Foundation of China(No.91963118)the 111 Project(No.B13013)supported by the Open Project Program of Key Laboratory of Preparation and Application of Environmental Friendly Materials(Jilin Normal University),Ministry of Education,China(No.2020004)。
文摘Graphite as a promising anode candidate of K-ion batteries(KIBs)has been increasingly studied currently,but corresponding rate performance and cycling stability are usually inferior to amorphous carbon materials.To protect the layer structure and further boost performance,tempura-like carbon/carbon nanocomposite of graphite@pitch-derived S-doped carbon(G@PSC)is designed and prepared by a facile and low-temperature modified molten salt method.This robust encapsulation structure makes their respective advantages complementary to each other,showing mutual promotion of electrochemical performances caused by synergy effect.As a result,the G@PSC electrode is applied in KIBs,delivering impressive rate capabilities(465,408,370,332,290,and 227 m A h g^(-1)at 0.05,0.2,0.5,1,2,and 5 A g^(-1))and ultralong cyclic stability(163 m A g^(-1)remaining even after 8000 cycles at 2 A g^(-1)).On basis of ex-situ studies,the sectionalized K-storage mechanism with adsorption(pseudocapacitance caused by S doping)-intercalation(pitch-derived carbon and graphite)pattern is revealed.Moreover,the exact insights into remarkable rate performances are taken by electrochemical kinetics tests and density functional theory calculation.In a word,this study adopts a facile method to synthesize high-performance carbon/carbon nanocomposite and is of practical significance for development of carbonaceous anode in KIBs.
基金supported financially by the National Natural Foundation of China(Grant No.51672234)the Research Foundation for Hunan Youth Outstanding People from Hunan Provincial Science and Technology Department(2015RS4030)+1 种基金Hunan 2011 Collaborative Innovation Center of Chemical Engineering&Technology with Environmental Benignity and Effective Resource UtilizationProgram for Innovative Research Cultivation Team in University of Ministry of Education of China(1337304)
文摘Hierarchical Sb_2S_3 hollow microspheres assembled by nanowires have been successfully synthesized by a simple and practical hydrothermal reaction. The possible formation process of this architecture was investigated by X-ray diffraction, focused-ion beam-scanning electron microscopy dual-beam system, and transmission electron microscopy. When used as the anode material for lithium-ion batteries, Sb_2S_3 hollow microspheres manifest excellent rate property and enhanced lithium-storage capability and can deliver a discharge capacity of 674 m Ah g^(-1) at a current density of 200 m A g^(-1) after 50 cycles. Even at a high currentdensity of 5000 m A g^(-1), a discharge capacity of541 m Ah g^(-1) is achieved. Sb_2S_3 hollow microspheres also display a prominent sodium-storage capacity and maintain a reversible discharge capacity of 384 m Ah g^(-1) at a current density of 200 m A g^(-1) after 50 cycles. The remarkable lithium/sodium-storage property may be attributed to the synergetic effect of its nanometer size and three-dimensional hierarchical architecture, and the outstanding stability property is attributed to the sufficient interior void space,which can buffer the volume expansion.
基金supported by the National Natural Science Foundation of China (90916007)
文摘In this paper, modified two-dimensional peri- odic lattice materials with local resonance phononic band gaps are designed and investigated. The design concept is to introduce some auxiliary structures into conventional pe- riodic lattice materials. Elastic wave propagation in this kind of modified two-dimensional lattice materials is studied us- ing a combination of Bloch's theorem with finite element method. The calculated frequency band structures of illus- trative modified square lattice materials reveal the existence of frequency band gaps in the low frequency region due to the introduction of the auxiliary structures. The mechanism underlying the occurrence of these frequency band gaps is thoroughly discussed and natural resonances of the auxiliary structures are validated to be the origin. The effect of geo- metric parameters of the auxiliary structures on the width of the local resonance phononic band gaps is explored. Finally, a conceptual broadband vibration-insulating structure based on the modified lattice materials is designed and its capabil- ity is demonstrated. The present work is anticipated to be useful in designing structures which can insulate mechanical vibrations within desired frequency ranges.
文摘The role of the National Laboratories is summarized from the era of post World War II to the present time. The U.S. federal government policy for the National Laboratories and its influence on their materials science infrastructure is reviewed with respect to .determining overall research strategies, various initiatives to interact with industry (especially in recent years),building facilities that serve the nation, and developing leading edge research in the materials sciences. Despite reductions in support for research in the U.S. in recent years, and uncertainties regarding the specific policies for Research &Development (R&D) in the U.S., there are strong roles for materials research at the National Laboratories. These roles will be centered on the abilities of the National Laboratories to field multidisciplinary teams, the use of unique cutting edge facilities, a focus on areas of strength within each of the labs,increased teaming and partnerships, and the selection of motivated research areas. It is hoped that such teaming opportunities will include new alliances with China, in a manner similar, perhaps, to those recently achieved between the U.S. and other countries.
基金supported by the National Basic Research Program of China(Grant No.2012CB927402)the National Natural Science Foundation of China(Grant Nos.61275028 and 11074145)
文摘The mutual control mechanism between magnetization and polarization in multiferroic materials is studied. The system contains a ferromagnetic sublattice and a ferroelectric sublattice. To describe the magneto–electric coupling, we propose a linear coupling Hamiltonian between ferromagnetism and ferroelectricity without microscopic derivation. This coupling enables one to retrieve the hysteresis loops measured experimentally. The thermodynamic properties of the system are calculated, such as the temperature dependences of the magnetization, polarization, internal energy and free energy.The ferromagnetic and ferroelectric hysteresis loops driven by either a magnetic or an electric field are calculated, and the magnetic spin and pseudo-spin are always flipped synchronously under the external magnetic and electric field. Our theoretical results are in agreement with the experiments.
文摘A dynamic contact problem for elastic-viscoplastic materials with thermal effects is investigated. The contact is bilateral, and the friction is modeled with Tresca's friction law with heat exchange. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear first order evolution inequalities, the equations with monotone operators, and the fixed point arguments. Finally, the continuous dependence of the solution on the friction yield limit is studied.
文摘In this paper, we report the growth of single crystals of Co_x Zn_(1-x)S and Co_x Zn_(1-x)Se (0<x<0.3) by the method of chemical transport, using iodine as a transport agent. The light green color of single crystal Co_xZn_(1-x)S as well as the light brown color of Co_xZn_(1-x)Se become deep with an increase in x. The compositions of the single crystals were nearly stoichiometric. The transfer rate decreases with an increase of the x value. The growth rate was related to the temperature difference. The large temperature difference speed up the growth rate, but the size of crystal obtained was small. In general, the optimal temperature difference was 15℃. From X-ray diffraction measurements, the structures of crystals Co_xZn_(1-x)S and Co_xZn_(1-x)Se (0<x<0.1) were identified to be zinc blende structure similar to that of ZnS and ZnSe.
文摘In order to mitigate the risks stemming from the utilization of mineral and synthetic organic substances,consensus exists in the literature that additional efforts should be devoted to the identification of adequate equivalent natural(ecological)materials.This work presents the outcomes of a preliminary study where the physical,mechanical,chemical and thermal properties of natural fibers have been considered.Initially,areca,and materials such as Moroccan doum and jute are considered.As a case study,a brake pad based on natural fibers is critically assessed.
文摘China’s building materials industry experienced great development in 1993 with rapid increases in production and record output and profits. The industry produced 360 million tons of cement, 96.163 million cases of plate glass, 20.4 million pieces of sanitation ceramics and 173 million square metres of construction ceramics, showing rises of 12.89, 12.83, 123.8 and 127 percent respectively over the previous year. The output of cement and
文摘The development of tissue-engineered technology brings hope to the treatment of spinal cord injury. Preparation of a tissue-engineered spinal cord stent with three-dimensional bionic structure has important value in the construction of tissue-engineered spinal cord and the repair of spinal cord injury. Acellular scaffolds can be produced with chemical extraction,
文摘Iron & Steel Industry China's outputs of crude steel, steel products, coke and ferrous alloys in 2012 were 716.54 million tons (up 3.1% YOY), 051.86 million tons (up 7.7% YOY), 443.23 million tons (up 5.2% YOY) and 31.29 million tons (up 15% YOY),
文摘On April 20-22 2011,China's Refractories Raw Materials SYmposium,co-sponsored by Refractories Branch of The Chinese Society for Metals and China Henan Refractory Industry Association,was held successfully in Zhengzhou.
文摘In 2013, China's outputs of cement and flat glass were 2. 414 billion tons and 778.98 million weight cases, increasing by 9.6% and 11.2% YOY, respectively.
基金supported by the National Natural Science Foundation of China(11172125,11202095 and 11201226)Natural Science Foundation of Henan,China(2009B110009,B2008-56 and 649106)
文摘Single-pulse chaos are studied for a functionally graded materials rectangular plate. By means of the global perturbation method, explicit conditions for the existence of a SiZnikov-type homoclinic orbit are obtained for this sys- tem, which suggests that chaos are likely to take place. Then, numerical simulations are given to test the analytical predic- tions. And from our analysis, when the chaotic motion oc- curs, there are a quasi-period motion in a two-dimensional subspace and chaos in another two-dimensional supplemen- tary subspace.
文摘By making the use of the processes which includes separating trash and solid materials from the wastewater-ammonia stripping tower-UASB-biological oxidation pond, we have treated the wastewater which comes from the swine factory. The treated wastewater can meet the primary standard of The People's Republic of China based on sewage discharge standards and the wastewater treatment project design contract (GBl8596-2001), and the effluent will be used as irrigation-water. We introduce this project including the quality of influent and effluent and the flow scheme, the statement of every part, the investment and the effect, etc. The operation indicated that this process has many merits such as the stability in operation-effect and the convenience in management. So it will provide some help for the similar wastewater treatment.
文摘In this technical paper, the oxidation mechanism and kinetics of aluminum powders are discussed in great details. The potential applications of spherical aluminum powders after oxidation to be part of the surging arresting materials are discussed. Theoretical calculations of oxidation of spherical aluminum powders in a typical gas fluidization bed are demonstrated. Computer software written by the author is used to carry out the basic calculations of important parameters of a gas fluidization bed at different temperatures. A mathematical model of the dynamic system in a gas fluidization bed is developed and the analytical solution is obtained. The mathematical model can be used to estimate aluminum oxide thickness at a defined temperature. The mathematical model created in this study is evaluated and confirmed consistently with the experimental results on a gas fluidization bed. Detail technical discussion of the oxidation mechanism of aluminum is carried out. The mathematical deviations of the mathematical modeling have demonstrated in great details. This mathematical model developed in this study and validated with experimental results can bring a great value for the quantitative analysis of a gas fluidization bed in general from a theoretical point of view. It can be applied for the oxidation not only for aluminum spherical powders, but also for other spherical metal powders. The mathematical model developed can further enhance the applications of gas fluidization technology. In addition to the development of mathematical modeling of a gas fluidization bed reactor, the formation of oxide film through diffusion on both planar and spherical aluminum surfaces is analyzed through a thorough mathematical deviation using diffusion theory and Laplace transformation. The dominant defects and their impact to oxidation of aluminum are also discussed in detail. The well-controlled oxidation film on spherical metal powders such as aluminum and other metal spherical powders can potentially become an important part of switch devices of surge arresting materials, in general.
文摘The Green's function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage. The thickness of the solid PCM on the fin varies with time and is obtained by the Megerlin method. The models are found with the Bessel equation to form an analytical solution. Three different kinds of boundary conditions are investigated. The comparison between analytical and numerical solutions is given. The results demonstrate that the significant accuracy is obtained for the temperature distribution for the fin in all cases.