Pub Date : 2012-08-31DOI: 10.5923/J.AM.20120204.02
N. Sthanumoorthy, K. Priyadharsini
In this paper, comp lete classificat ions of all BKM Lie superalgebras (with fin ite order and infinite order Cartan matrices) possessing Strictly Imaginary Property are given. These classifications also include, in particular, the Monster BKM Lie superalgebra.
{"title":"Complete Classification of BKM Lie Superalgebras Possessing Strictly Imaginary Property","authors":"N. Sthanumoorthy, K. Priyadharsini","doi":"10.5923/J.AM.20120204.02","DOIUrl":"https://doi.org/10.5923/J.AM.20120204.02","url":null,"abstract":"In this paper, comp lete classificat ions of all BKM Lie superalgebras (with fin ite order and infinite order Cartan matrices) possessing Strictly Imaginary Property are given. These classifications also include, in particular, the Monster BKM Lie superalgebra.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2 1","pages":"100-115"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20120203.06
Abdallah S. Waziri, E. Massawe, O. Makinde
This paper examines the dynamics of HIV/AIDS with treatment and vertical transmission. A nonlinear deterministic mathematical model for the problem is proposed and analysed qualitatively using the stability theory of differential equations. Local stability of the disease free equilibrium of the model was established by the next generation method. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium is not stable due existence of forward bifurcation at threshold parameter equal to unity. However, it is shown that using treatment measures (ARVs) and control of the rate of vertical transmission have the effect of reducing the transmission of the disease significantly. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the spread of the disease.
{"title":"Mathematical Modelling of HIV/AIDS Dynamics with Treatment and Vertical Transmission","authors":"Abdallah S. Waziri, E. Massawe, O. Makinde","doi":"10.5923/J.AM.20120203.06","DOIUrl":"https://doi.org/10.5923/J.AM.20120203.06","url":null,"abstract":"This paper examines the dynamics of HIV/AIDS with treatment and vertical transmission. A nonlinear deterministic mathematical model for the problem is proposed and analysed qualitatively using the stability theory of differential equations. Local stability of the disease free equilibrium of the model was established by the next generation method. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium is not stable due existence of forward bifurcation at threshold parameter equal to unity. However, it is shown that using treatment measures (ARVs) and control of the rate of vertical transmission have the effect of reducing the transmission of the disease significantly. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the spread of the disease.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2 1","pages":"77-89"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Convection-Diffusion Problems occur very frequently in applied sciences and engineering. In this paper, the cru x of research articles published by numerous researchers during 2007-2011 in referred journals has been presented and this leads to conclusions and recommendations about what methods to use on Convection-Diffusion Problems. It is found that engineers and scientists are using finite element method, finite volu me method, finite volu me element method etc. in flu id mechanics. Here we discuss real life problems of fluid engineering solved by various numerical methods .which is very useful for finding solution of those type of governing equation, whose analytical solution are not easily found. Co mputational fluid dynamics is a branch of Engineering and science that,(1) with the help of d igital co mputers, produces quantitative prediction of fluid-flow phenomenon based on those conservation laws governing fluid mot ion. These predictions normally occur under those conditions defined in terms of flow geo metry. Convection- Diffusion Problems arises where fluid flow p lays a significant role .We must account for the effects of convection. Diffusion occurs always alongside convection in nature. The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flo w, in the modeling of semiconductors, and so forth(3). This paper describes several fin ite difference schemes for solving the convection-diffusion equation. Therefore; we examine computation methods to predict comb ined convection- diffusion equation. The convection-diffusion equation is a parabolic partial differential equation combin ing the diffusion equation and the advection equation, which describes physical phenomena where part icles or energy (or other physical quantities) are transferred inside a physical system due to two processes: diffusion and convection. In its simplest form (when the diffusion coefficient and the convection velocity are constant and there are no sources or sinks) the equation takes the form as following: 2 c D c v c t
对流扩散问题在应用科学和工程中经常出现。在本文中，介绍了2007-2011年期间众多研究人员在参考期刊上发表的研究文章的要点，并由此得出结论，并建议使用什么方法来解决对流扩散问题。在流感力学中，工程师和科学家们正在使用有限元法、有限体积法、有限体积元法等。本文讨论了用各种数值方法求解的流体工程实际问题，这对于求解那些不易找到解析解的控制方程是非常有用的。计算流体动力学是工程和科学的一个分支，它:(1)在数字计算机的帮助下，根据控制流体运动的守恒定律对流体流动现象进行定量预测。这些预测通常发生在根据流动几何定义的条件下。对流-扩散问题出现在流体流动p起重要作用的地方，我们必须考虑对流的影响。在自然界中，扩散总是与对流同时发生。对流扩散输运问题的数值解在科学和工程中有许多重要的应用。这些问题出现在许多应用中，如空气和地下水污染物的输送、油藏流动、半导体建模等等(3)。本文介绍了求解对流扩散方程的几种有限差分格式。因此;我们研究了预测梳状对流-扩散方程的计算方法。对流扩散方程是扩散方程和平流方程结合的抛物型偏微分方程，它描述了部分粒子或能量(或其他物理量)在物理系统内通过扩散和对流两个过程传递的物理现象。在最简单的形式下(当扩散系数和对流速度恒定且没有源和汇时)，方程的形式如下:2c D c v ct
{"title":"A Recent Development of Numerical Methods for Solving Convection-Diffusion Problems","authors":"Anand Shukla, Akhilesh Kumar Singh, Pushpinder Singh","doi":"10.5923/J.AM.20110101.01","DOIUrl":"https://doi.org/10.5923/J.AM.20110101.01","url":null,"abstract":"Convection-Diffusion Problems occur very frequently in applied sciences and engineering. In this paper, the cru x of research articles published by numerous researchers during 2007-2011 in referred journals has been presented and this leads to conclusions and recommendations about what methods to use on Convection-Diffusion Problems. It is found that engineers and scientists are using finite element method, finite volu me method, finite volu me element method etc. in flu id mechanics. Here we discuss real life problems of fluid engineering solved by various numerical methods .which is very useful for finding solution of those type of governing equation, whose analytical solution are not easily found. Co mputational fluid dynamics is a branch of Engineering and science that,(1) with the help of d igital co mputers, produces quantitative prediction of fluid-flow phenomenon based on those conservation laws governing fluid mot ion. These predictions normally occur under those conditions defined in terms of flow geo metry. Convection- Diffusion Problems arises where fluid flow p lays a significant role .We must account for the effects of convection. Diffusion occurs always alongside convection in nature. The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flo w, in the modeling of semiconductors, and so forth(3). This paper describes several fin ite difference schemes for solving the convection-diffusion equation. Therefore; we examine computation methods to predict comb ined convection- diffusion equation. The convection-diffusion equation is a parabolic partial differential equation combin ing the diffusion equation and the advection equation, which describes physical phenomena where part icles or energy (or other physical quantities) are transferred inside a physical system due to two processes: diffusion and convection. In its simplest form (when the diffusion coefficient and the convection velocity are constant and there are no sources or sinks) the equation takes the form as following: 2 c D c v c t","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"1 1","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20120202.04
R. Rao, P. Chakravarthy
In this paper, we present a numerical patching technique for solving singularly perturbed nonlinear differen- tial-difference equation with a small negative shift. The nonlinear problem is converted into a sequence of linear problems by quasilinearization process. After linearization, it is divided into two problems, namely inner region problem and outer region problem. The boundary condition at the cutting point is obtained from the theory of singular perturbations. Using stretching transformation, a modified inner region problem is constructed and is solved by using the upwind finite difference scheme. The outer region problem is solved by a Taylor polynomial approach. We combine the solutions of both problems to obtain an approximate solution of the original problem. The proposed method is iterative on the cutting point. The process is repeated for various choices of the cutting point, until the solution profiles stabilize. Some numerical examples have been solved to demonstrate the applicability of the method. The method is analyzed for stability and convergence.
{"title":"A Numerical Patching Technique for Singularly Perturbed Nonlinear Differential-Difference Equations with a Negative Shift","authors":"R. Rao, P. Chakravarthy","doi":"10.5923/J.AM.20120202.04","DOIUrl":"https://doi.org/10.5923/J.AM.20120202.04","url":null,"abstract":"In this paper, we present a numerical patching technique for solving singularly perturbed nonlinear differen- tial-difference equation with a small negative shift. The nonlinear problem is converted into a sequence of linear problems by quasilinearization process. After linearization, it is divided into two problems, namely inner region problem and outer region problem. The boundary condition at the cutting point is obtained from the theory of singular perturbations. Using stretching transformation, a modified inner region problem is constructed and is solved by using the upwind finite difference scheme. The outer region problem is solved by a Taylor polynomial approach. We combine the solutions of both problems to obtain an approximate solution of the original problem. The proposed method is iterative on the cutting point. The process is repeated for various choices of the cutting point, until the solution profiles stabilize. Some numerical examples have been solved to demonstrate the applicability of the method. The method is analyzed for stability and convergence.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"43 1","pages":"11-20"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20110102.09
R. Arora, Anoop Kumar
In this paper, we obtained a traveling wave solution by using cosine-function algorithm for nonlinear partial differential equations. Here, the method is used to obtain the exact solutions for two different types of nonlinear partial dif- ferential equations such as, Benjamin-Bona-Mahony (BBM) equation and Modified Regularized Long Wave (MRLW) equation which are the important soliton equations.
{"title":"Soliton Solution for the BBM and MRLW Equations by Cosine-function Method","authors":"R. Arora, Anoop Kumar","doi":"10.5923/J.AM.20110102.09","DOIUrl":"https://doi.org/10.5923/J.AM.20110102.09","url":null,"abstract":"In this paper, we obtained a traveling wave solution by using cosine-function algorithm for nonlinear partial differential equations. Here, the method is used to obtain the exact solutions for two different types of nonlinear partial dif- ferential equations such as, Benjamin-Bona-Mahony (BBM) equation and Modified Regularized Long Wave (MRLW) equation which are the important soliton equations.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"1 1","pages":"59-61"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20110101.04
M. Zakerzadeh, H. Sayyaadi, M. Zanjani
Krasnosel'skii-Pokrovskii (KP) model is one of the great operator-based phenomenological models which is used in modeling hysteretic nonlinear behavior in smart actuators. The time continuity and the parametric continuity of this operator are important and valuable factors for physical considerations as well as designing well-posed identification methodologies. In most of the researches conducted about the modeling of smart actuators by KP model, especially SMA actuators, only the ability of the KP model in characterizing the hysteretic behavior of the actuators is demonstrated with respect to some specified experimental data and the accuracy of the developed model with respect to other data is not vali- dated. Therefore, it is not clear whether the developed model is capable of predicting hysteresis minor loops of those ac- tuators or not and how accurate it is in this prediction task. In this paper the accuracy of the KP model in predicting SMA hysteresis minor loops as well as first order ascending curves attached to the major hysteresis loop are experimentally vali- dated, while the parameters of the KP model has been identified only with some first order descending reversal curves at- tached to the major loop. The results show that, in the worst case, the maximum of prediction error is less than 18.2% of the maximum output and this demonstrates the powerful capability of the KP model in characterizing the hysteresis nonlinear- ity of SMA actuators.
{"title":"Characterizing Hysteresis Nonlinearity Behavior of SMA Actuators by Krasnosel'skii-Pokrovskii Model","authors":"M. Zakerzadeh, H. Sayyaadi, M. Zanjani","doi":"10.5923/J.AM.20110101.04","DOIUrl":"https://doi.org/10.5923/J.AM.20110101.04","url":null,"abstract":"Krasnosel'skii-Pokrovskii (KP) model is one of the great operator-based phenomenological models which is used in modeling hysteretic nonlinear behavior in smart actuators. The time continuity and the parametric continuity of this operator are important and valuable factors for physical considerations as well as designing well-posed identification methodologies. In most of the researches conducted about the modeling of smart actuators by KP model, especially SMA actuators, only the ability of the KP model in characterizing the hysteretic behavior of the actuators is demonstrated with respect to some specified experimental data and the accuracy of the developed model with respect to other data is not vali- dated. Therefore, it is not clear whether the developed model is capable of predicting hysteresis minor loops of those ac- tuators or not and how accurate it is in this prediction task. In this paper the accuracy of the KP model in predicting SMA hysteresis minor loops as well as first order ascending curves attached to the major hysteresis loop are experimentally vali- dated, while the parameters of the KP model has been identified only with some first order descending reversal curves at- tached to the major loop. The results show that, in the worst case, the maximum of prediction error is less than 18.2% of the maximum output and this demonstrates the powerful capability of the KP model in characterizing the hysteresis nonlinear- ity of SMA actuators.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"29 1","pages":"28-38"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20110102.12
Oyesanya M. O., Atabong T. A.
Separate administration of either chemotherapy or immunotherapy has been studied and applied to clinical experiments but however, this administration has shown some side effects such as increased acidity which gives a selective advantage to tumor cell growth. We introduce a model for the combined action of chemotherapy and immunotherapy using fractional derivatives. This model with non-integer derivative was analysed analytically and numerically for stability of the disease free equilibrium. The analytic result shows that the disease free equilibrium exist and if the prescriptions of food and drugs are followed strictly (taken at the right time and right dose) and in addition if the basic tumor growth factor, ���� 21≥1 then the only realistic steady state is the disease free steady state. We also show analytically that this steady state is stable for some parameter values. Our analytical results were confirmed with a numerical simulation of the full non linear fractional diffusion system.
{"title":"Complex Stability Analysis of Therapeutic Actions in a Fractional Reaction Diffusion Model of Tumor","authors":"Oyesanya M. O., Atabong T. A.","doi":"10.5923/J.AM.20110102.12","DOIUrl":"https://doi.org/10.5923/J.AM.20110102.12","url":null,"abstract":"Separate administration of either chemotherapy or immunotherapy has been studied and applied to clinical experiments but however, this administration has shown some side effects such as increased acidity which gives a selective advantage to tumor cell growth. We introduce a model for the combined action of chemotherapy and immunotherapy using fractional derivatives. This model with non-integer derivative was analysed analytically and numerically for stability of the disease free equilibrium. The analytic result shows that the disease free equilibrium exist and if the prescriptions of food and drugs are followed strictly (taken at the right time and right dose) and in addition if the basic tumor growth factor, ���� 21≥1 then the only realistic steady state is the disease free steady state. We also show analytically that this steady state is stable for some parameter values. Our analytical results were confirmed with a numerical simulation of the full non linear fractional diffusion system.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"1 1","pages":"69-83"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20120202.07
K. Zhukovsky
We present a general method of operational nature to obtain solutions for several types of differential equations. Methodology of inverse differential operators for the solution of differential equations is developed. We apply operational approach to construct inverse differential operators and develop operational identities, involving inverse derivatives and generalized families of orthogonal polynomials. We employ them together with the exponential operator to investigate various differential equations. Advantages of operational technique for finding solutions of a wide spectrum of differential equations are demonstrated, in particular with regard to fractional differential equations.
{"title":"Inverse Derivative and Solutions of Some Ordinary Differential Equations","authors":"K. Zhukovsky","doi":"10.5923/J.AM.20120202.07","DOIUrl":"https://doi.org/10.5923/J.AM.20120202.07","url":null,"abstract":"We present a general method of operational nature to obtain solutions for several types of differential equations. Methodology of inverse differential operators for the solution of differential equations is developed. We apply operational approach to construct inverse differential operators and develop operational identities, involving inverse derivatives and generalized families of orthogonal polynomials. We employ them together with the exponential operator to investigate various differential equations. Advantages of operational technique for finding solutions of a wide spectrum of differential equations are demonstrated, in particular with regard to fractional differential equations.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2 1","pages":"34-39"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20110102.19
P. Yadav
This paper concerns the slow viscous flow through a swarm of concentric clusters of porous spherical parti- cles. An aggregate of clusters of porous spherical particles is considered as a hydro-dynamically equivalent to a porous spherical shell enclosing a solid spherical core. The Brinkman equation inside and the Stokes equation outside the porous spherical shell in their stream function formulations are used. As boundary conditions, continuity of velocity, continuity of normal stress and stress-jump condition at the porous and fluid interface, the continuity of velocity components on the solid spherical core are employed. On the hypothetical surface, uniform velocity and Happel boundary conditions are used. The drag force experienced by each porous spherical shell in a cell is evaluated. As a particular case, the drag force experienced by a porous sphere in a cell with jump is also investigated. The earlier results reported for the drag force by Davis and Stone(5) for the drag force experienced by a porous sphere in a cell without jump, Happel(2) for a solid sphere in a cell and Qin and Kaloni(4) for a porous sphere in an unbounded medium have been then deduced. Representative results are pre- sented in graphical form and discussed.
{"title":"On the Slow Viscous Flow through a Swarm of Solid Spherical Particles Covered by Porous Shells","authors":"P. Yadav","doi":"10.5923/J.AM.20110102.19","DOIUrl":"https://doi.org/10.5923/J.AM.20110102.19","url":null,"abstract":"This paper concerns the slow viscous flow through a swarm of concentric clusters of porous spherical parti- cles. An aggregate of clusters of porous spherical particles is considered as a hydro-dynamically equivalent to a porous spherical shell enclosing a solid spherical core. The Brinkman equation inside and the Stokes equation outside the porous spherical shell in their stream function formulations are used. As boundary conditions, continuity of velocity, continuity of normal stress and stress-jump condition at the porous and fluid interface, the continuity of velocity components on the solid spherical core are employed. On the hypothetical surface, uniform velocity and Happel boundary conditions are used. The drag force experienced by each porous spherical shell in a cell is evaluated. As a particular case, the drag force experienced by a porous sphere in a cell with jump is also investigated. The earlier results reported for the drag force by Davis and Stone(5) for the drag force experienced by a porous sphere in a cell without jump, Happel(2) for a solid sphere in a cell and Qin and Kaloni(4) for a porous sphere in an unbounded medium have been then deduced. Representative results are pre- sented in graphical form and discussed.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"1 1","pages":"112-121"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.5923/J.AM.20110102.15
H. Rani, G. Reddy
Numerical analysis is performed to study the conjugate heat transfer and heat generation effects on the tran- sient free convective boundary layer flow over a vertical slender hollow circular cylinder with the inner surface at a con- stant temperature. A set of non-dimensional governing equations namely, the continuity, momentum and energy equations is derived and these equations are unsteady non-linear and coupled. As there is no analytical or direct numerical method available to solve these equations, they are solved using the CFD techniques. An unconditionally stable Crank-Nicolson type of implicit finite difference scheme is employed to obtain the discretized forms of the governing equations. The dis- cretized equations are solved using the tridiagonal algorithm. Numerical results for the transient velocity and temperature profiles, average skin-friction coefficient and average Nusselt number are shown graphically. In all these profiles it is ob- served that the time required to reach the steady-state increases as the conjugate-conduction parameter or heat generation parameter increases.
{"title":"Conjugate Transient Free Convective Heat Transfer from a Vertical Slender Hollow Cylinder with Heat Generation Effect","authors":"H. Rani, G. Reddy","doi":"10.5923/J.AM.20110102.15","DOIUrl":"https://doi.org/10.5923/J.AM.20110102.15","url":null,"abstract":"Numerical analysis is performed to study the conjugate heat transfer and heat generation effects on the tran- sient free convective boundary layer flow over a vertical slender hollow circular cylinder with the inner surface at a con- stant temperature. A set of non-dimensional governing equations namely, the continuity, momentum and energy equations is derived and these equations are unsteady non-linear and coupled. As there is no analytical or direct numerical method available to solve these equations, they are solved using the CFD techniques. An unconditionally stable Crank-Nicolson type of implicit finite difference scheme is employed to obtain the discretized forms of the governing equations. The dis- cretized equations are solved using the tridiagonal algorithm. Numerical results for the transient velocity and temperature profiles, average skin-friction coefficient and average Nusselt number are shown graphically. In all these profiles it is ob- served that the time required to reach the steady-state increases as the conjugate-conduction parameter or heat generation parameter increases.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"1 1","pages":"90-98"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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