The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing...The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing velocity vector, temperature field, pressure field, and gas mass field. The mixed finite element (MFE) method is employed to study the system of equations for the vapor deposition chemical reaction processes. The semidiscrete and fully discrete MFE formulations are derived. And the existence and convergence (error estimate) of the semidiscrete and fully discrete MFE solutions are demonstrated. By employing MFE method to treat the system of equations for the vapor deposition chemical reaction processes, the numerical solutions of the velocity vector, the temperature field, the pressure field, and the gas mass field can be found out simultaneously. Thus, these researches are not only of important theoretical means, but also of extremely extensive applied vistas.展开更多
In this article, we have considered the simultaneous influence of ohmic heating and chemical reaction on heat and mass transfer over a stretching sheet. The effects of applied magnetic field are also taken into consid...In this article, we have considered the simultaneous influence of ohmic heating and chemical reaction on heat and mass transfer over a stretching sheet. The effects of applied magnetic field are also taken into consideration while the induced magnetic field is not considered due to very small magnetics Reynolds number. The governing flow problem comprises of momentum, continuity, thermal energy and concentration equation which are transformed into highly nonlinear coupled ordinary differential equations by means of similarity transforms, which are then, solved numerically with the help of Successive Linearization method(SLM) and Chebyshev Spectral collocation method. Numerical values of skin friction coefficient, local Nusselt number, and Sherwood number are also taken into account with the help of tables. The physical influence of the involved parameters of flow velocity, temperature and concentration distribution is discussed and demonstrated graphically. The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.展开更多
The chemical reaction effect on an unsteady magnetohydrodynamic (MHD) flow past a semi-infinite vertical porous plate with viscous dissipation is analyzed. The governing equations of motion, energy, and species are ...The chemical reaction effect on an unsteady magnetohydrodynamic (MHD) flow past a semi-infinite vertical porous plate with viscous dissipation is analyzed. The governing equations of motion, energy, and species are transformed into ordinary differential equations (ODEs) using the time dependent similarity parameter. The resultant ODEs are then solved numerically by a finite element method. The effects of various parameters on the velocity, temperature, and concentration profiles are presented graphically, and the values of the skin-friction, Nusselt number, and Sherwood number for various values of physical parameters are presented through tables.展开更多
A numerical investigation is carried out on the effects of heat source suction and viscous dissipation on Magneto hydrodynamics boundary layer flow of a viscous, steady and incompressible fluid. The flow is assumed to...A numerical investigation is carried out on the effects of heat source suction and viscous dissipation on Magneto hydrodynamics boundary layer flow of a viscous, steady and incompressible fluid. The flow is assumed to be over on exponentially stretching sheet. The governing system of partial differential equations has been transformed into ordinary differential equation using similarity transformation. Keller box method is simulated on the dimensionless system of differential equations. The skin friction coefficient and the heat and mass transfer rates are very significant parameters that are computed, analysed discussed in detail.展开更多
We consider the psychophysical experiments in which the test subject’s binary reaction is determined by the prescribed exposure duration to a stimulus and a random variable subjective threshold. For example, when a s...We consider the psychophysical experiments in which the test subject’s binary reaction is determined by the prescribed exposure duration to a stimulus and a random variable subjective threshold. For example, when a subject is exposed to a millimeter wave beam for a prescribed duration, the occurrence of flight action is binary (yes or no). In experiments, in addition to the binary outcome, the actuation time of flight action is also recorded if it occurs;the delay from the initiation time to the actuation time of flight action is the human reaction time, which is not measurable. In this study, we model the random subjective threshold as a Weibull distribution and formulate an inference method for estimating the human reaction time, from data of prescribed exposure durations, binary outcomes and actuation times of flight action collected in a sequence of tests. Numerical simulations demonstrate that the inference of human reaction time based on the Weibull distribution converges to the correct value even when the underlying true model deviates from the inference model. This robustness of the inference method makes it applicable to real experimental data where the underlying true model is unknown.展开更多
Proton-rich nuclei are synthesized via photodisintegration and reverse reactions.To examine this mechanism and reproduce the observed p-nucleus abundances,it is crucial to know the reaction rates and thereby the react...Proton-rich nuclei are synthesized via photodisintegration and reverse reactions.To examine this mechanism and reproduce the observed p-nucleus abundances,it is crucial to know the reaction rates and thereby the reaction cross sections of many isotopes.Given that the number of experiments on the reactions in astrophysical energy regions is very rare,the reaction cross sections are determined by theoretical methods whose accuracy should be tested.In this study,given that ^(121)Sb is a stable seed isotope located in the region of medium-mass p-nuclei,we investigated the cross sections and reaction rates of the ^(121)Sb(α,γ)^(125)I reaction using the TALYS computer code with 432 different combinations of input parameters(OMP,LDM,and SFM).The optimal model combinations were determined using the threshold logic unit method.The theoretical reaction cross-sectional results were compared with the experimental results reported in the literature.The reaction rates were determined using the two input parameter sets most compatible with the measurements,and they were compared with the reaction rate databases:STARLIB and REACLIB.展开更多
The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the l...The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.展开更多
In this paper, a formal and systematic method for balancing chemical reaction equations was presented. The results satisfy the law of conservation of matter, and confirm that there is no contradiction to the existing ...In this paper, a formal and systematic method for balancing chemical reaction equations was presented. The results satisfy the law of conservation of matter, and confirm that there is no contradiction to the existing way(s) of balancing chemical equations. A chemical reaction which possesses atoms with fractional oxidation numbers that have unique coefficients was studied. In this paper, the chemical equations were balanced by representing the chemical equation into systems of linear equations. Particularly, the Gauss elimination method was used to solve the mathematical problem with this method, it was possible to handle any chemical reaction with given reactants and products.展开更多
The methods of preparation of endiine and endiallene diols by interaction of cis-1,4-dibrombutene and cis-1,4-dichlor-rbutene with monosubstituted acetylene alcohols in presence of the catalytic systems consisting of ...The methods of preparation of endiine and endiallene diols by interaction of cis-1,4-dibrombutene and cis-1,4-dichlor-rbutene with monosubstituted acetylene alcohols in presence of the catalytic systems consisting of one-iodide copper, triethylamine and K2СО3 in a medium of dimethylformamide have been developed. It has been shown that unlike 1,4-dibrombutene, the nucleophilic substitution reaction with 1,4-dichlorbutene proceeds by acetylene-allene isomerization with formation of endiallene diols. It has been established that the endiine diols can be used in thin organic synthesis (in the reactions of oxidation, splitting, dehydration, epoxidation, hydrolysis, 1,2-cycloaddition and hypochlorination) with the aim of preparation of practically useful substances. It has been revealed during hydrolysis of epoxide compounds by the chemical and microbiological methods that in the course of microbiological hydrolysis (Aspеrgillus niger), the optically active trans-structured diols are formed.展开更多
A mathematical model is presented to study the effect of chemical reaction on unsteady natural convection boundary layer flow over a semi-infinite vertical cylinder. Taking into account the buoyancy force effects, for...A mathematical model is presented to study the effect of chemical reaction on unsteady natural convection boundary layer flow over a semi-infinite vertical cylinder. Taking into account the buoyancy force effects, for the situation in which the surface temperature and are subjected to the power-law surface heat and mass flux as and . The governing equations are solved by an implicit finite difference scheme of Crank-Nicolson method. Numerical results for the velocity, temperature and concentration profiles as well as for the skin-friction, Nusselt and Sherwood numbers are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.展开更多
针对火星独特的CO_(2)稀薄气体环境以及探测器高超声速进入火星过程中的高温真实气体效应,研究了CO_(2)多振动模式的激发特性。采用非结构网格和直接模拟蒙特卡洛法(Direct Simulation Monte Carlo method, DSMC),基于非谐振子振动激发...针对火星独特的CO_(2)稀薄气体环境以及探测器高超声速进入火星过程中的高温真实气体效应,研究了CO_(2)多振动模式的激发特性。采用非结构网格和直接模拟蒙特卡洛法(Direct Simulation Monte Carlo method, DSMC),基于非谐振子振动激发模型,通过将CO_(2)离解能均分到4种振动模态,进而限制各模态最高振动能级,模拟了含CO_(2)的5组分17反应的高温稀薄真实气体化学反应模型。计算了“火星探路者”在火星大气环境65 km高度、进入速度为7 453 m/s、攻角为0°下的高温化学非平衡效应流场。结果表明:CO_(2)在激波后大量分解并消耗大量能量;迎风面激波中各组分占比与探测器物面特性等均与文献结果相符,证明了本文对于CO_(2)振动激发处理方法的可行性。在此基础上加入N_2组分,模拟火星大气8组分44基元化学反应流场,通过改变来流密度与马赫数分析了流场特性的变化。结果表明:随着来流密度减小,流场温度呈现先增加后减小的趋势,物面热流密度增大;来流马赫数增加使得流场温度和压力上升,物面热流密度提高但是热流密度系数变化幅度很小。展开更多
基金Project supported by the National Natural Science Foundation of China (Nos.10471100 and 40437017)the Science and Technology Foundation of Beijing Jiaotong University
文摘The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing velocity vector, temperature field, pressure field, and gas mass field. The mixed finite element (MFE) method is employed to study the system of equations for the vapor deposition chemical reaction processes. The semidiscrete and fully discrete MFE formulations are derived. And the existence and convergence (error estimate) of the semidiscrete and fully discrete MFE solutions are demonstrated. By employing MFE method to treat the system of equations for the vapor deposition chemical reaction processes, the numerical solutions of the velocity vector, the temperature field, the pressure field, and the gas mass field can be found out simultaneously. Thus, these researches are not only of important theoretical means, but also of extremely extensive applied vistas.
文摘In this article, we have considered the simultaneous influence of ohmic heating and chemical reaction on heat and mass transfer over a stretching sheet. The effects of applied magnetic field are also taken into consideration while the induced magnetic field is not considered due to very small magnetics Reynolds number. The governing flow problem comprises of momentum, continuity, thermal energy and concentration equation which are transformed into highly nonlinear coupled ordinary differential equations by means of similarity transforms, which are then, solved numerically with the help of Successive Linearization method(SLM) and Chebyshev Spectral collocation method. Numerical values of skin friction coefficient, local Nusselt number, and Sherwood number are also taken into account with the help of tables. The physical influence of the involved parameters of flow velocity, temperature and concentration distribution is discussed and demonstrated graphically. The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.
文摘The chemical reaction effect on an unsteady magnetohydrodynamic (MHD) flow past a semi-infinite vertical porous plate with viscous dissipation is analyzed. The governing equations of motion, energy, and species are transformed into ordinary differential equations (ODEs) using the time dependent similarity parameter. The resultant ODEs are then solved numerically by a finite element method. The effects of various parameters on the velocity, temperature, and concentration profiles are presented graphically, and the values of the skin-friction, Nusselt number, and Sherwood number for various values of physical parameters are presented through tables.
文摘A numerical investigation is carried out on the effects of heat source suction and viscous dissipation on Magneto hydrodynamics boundary layer flow of a viscous, steady and incompressible fluid. The flow is assumed to be over on exponentially stretching sheet. The governing system of partial differential equations has been transformed into ordinary differential equation using similarity transformation. Keller box method is simulated on the dimensionless system of differential equations. The skin friction coefficient and the heat and mass transfer rates are very significant parameters that are computed, analysed discussed in detail.
文摘We consider the psychophysical experiments in which the test subject’s binary reaction is determined by the prescribed exposure duration to a stimulus and a random variable subjective threshold. For example, when a subject is exposed to a millimeter wave beam for a prescribed duration, the occurrence of flight action is binary (yes or no). In experiments, in addition to the binary outcome, the actuation time of flight action is also recorded if it occurs;the delay from the initiation time to the actuation time of flight action is the human reaction time, which is not measurable. In this study, we model the random subjective threshold as a Weibull distribution and formulate an inference method for estimating the human reaction time, from data of prescribed exposure durations, binary outcomes and actuation times of flight action collected in a sequence of tests. Numerical simulations demonstrate that the inference of human reaction time based on the Weibull distribution converges to the correct value even when the underlying true model deviates from the inference model. This robustness of the inference method makes it applicable to real experimental data where the underlying true model is unknown.
文摘Proton-rich nuclei are synthesized via photodisintegration and reverse reactions.To examine this mechanism and reproduce the observed p-nucleus abundances,it is crucial to know the reaction rates and thereby the reaction cross sections of many isotopes.Given that the number of experiments on the reactions in astrophysical energy regions is very rare,the reaction cross sections are determined by theoretical methods whose accuracy should be tested.In this study,given that ^(121)Sb is a stable seed isotope located in the region of medium-mass p-nuclei,we investigated the cross sections and reaction rates of the ^(121)Sb(α,γ)^(125)I reaction using the TALYS computer code with 432 different combinations of input parameters(OMP,LDM,and SFM).The optimal model combinations were determined using the threshold logic unit method.The theoretical reaction cross-sectional results were compared with the experimental results reported in the literature.The reaction rates were determined using the two input parameter sets most compatible with the measurements,and they were compared with the reaction rate databases:STARLIB and REACLIB.
文摘The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.
文摘In this paper, a formal and systematic method for balancing chemical reaction equations was presented. The results satisfy the law of conservation of matter, and confirm that there is no contradiction to the existing way(s) of balancing chemical equations. A chemical reaction which possesses atoms with fractional oxidation numbers that have unique coefficients was studied. In this paper, the chemical equations were balanced by representing the chemical equation into systems of linear equations. Particularly, the Gauss elimination method was used to solve the mathematical problem with this method, it was possible to handle any chemical reaction with given reactants and products.
文摘The methods of preparation of endiine and endiallene diols by interaction of cis-1,4-dibrombutene and cis-1,4-dichlor-rbutene with monosubstituted acetylene alcohols in presence of the catalytic systems consisting of one-iodide copper, triethylamine and K2СО3 in a medium of dimethylformamide have been developed. It has been shown that unlike 1,4-dibrombutene, the nucleophilic substitution reaction with 1,4-dichlorbutene proceeds by acetylene-allene isomerization with formation of endiallene diols. It has been established that the endiine diols can be used in thin organic synthesis (in the reactions of oxidation, splitting, dehydration, epoxidation, hydrolysis, 1,2-cycloaddition and hypochlorination) with the aim of preparation of practically useful substances. It has been revealed during hydrolysis of epoxide compounds by the chemical and microbiological methods that in the course of microbiological hydrolysis (Aspеrgillus niger), the optically active trans-structured diols are formed.
文摘A mathematical model is presented to study the effect of chemical reaction on unsteady natural convection boundary layer flow over a semi-infinite vertical cylinder. Taking into account the buoyancy force effects, for the situation in which the surface temperature and are subjected to the power-law surface heat and mass flux as and . The governing equations are solved by an implicit finite difference scheme of Crank-Nicolson method. Numerical results for the velocity, temperature and concentration profiles as well as for the skin-friction, Nusselt and Sherwood numbers are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.
文摘针对火星独特的CO_(2)稀薄气体环境以及探测器高超声速进入火星过程中的高温真实气体效应,研究了CO_(2)多振动模式的激发特性。采用非结构网格和直接模拟蒙特卡洛法(Direct Simulation Monte Carlo method, DSMC),基于非谐振子振动激发模型,通过将CO_(2)离解能均分到4种振动模态,进而限制各模态最高振动能级,模拟了含CO_(2)的5组分17反应的高温稀薄真实气体化学反应模型。计算了“火星探路者”在火星大气环境65 km高度、进入速度为7 453 m/s、攻角为0°下的高温化学非平衡效应流场。结果表明:CO_(2)在激波后大量分解并消耗大量能量;迎风面激波中各组分占比与探测器物面特性等均与文献结果相符,证明了本文对于CO_(2)振动激发处理方法的可行性。在此基础上加入N_2组分,模拟火星大气8组分44基元化学反应流场,通过改变来流密度与马赫数分析了流场特性的变化。结果表明:随着来流密度减小,流场温度呈现先增加后减小的趋势,物面热流密度增大;来流马赫数增加使得流场温度和压力上升,物面热流密度提高但是热流密度系数变化幅度很小。