ORCID Profile
0000-0002-1177-7857
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Publisher: Trans Tech Publications, Ltd.
Date: 09-2018
DOI: 10.4028/WWW.SCIENTIFIC.NET/DDF.387.10
Abstract: In this paper we analyse the heat transfer in a cylindrical spine fin. Here, both the heat transfer coefficient and thermal conductivity are temperature dependent. The resulting 2+1 dimension partial differential equation (PDE) is rendered nonlinear and difficult to solve exactly, particularly with prescribed initial and boundary conditions. We employ the three dimensional differential transform methods (3D DTM) to contract the approximate analytical solutions. Furthermore we utilize numerical techniques to determine approximate numerical solutions. The effects of parameters, appearing in the boundary value problem (BVP), on temperature profile of the fin are studied.
Publisher: Hindawi Limited
Date: 2014
DOI: 10.1155/2014/719102
Publisher: Elsevier BV
Date: 10-2013
Publisher: Springer Science and Business Media LLC
Date: 26-08-2011
Publisher: Hindawi Limited
Date: 2013
DOI: 10.1155/2013/273052
Abstract: Explicit analytical expressions for the temperature profile, fin efficiency, and heat flux in a longitudinal fin are derived. Here, thermal conductivity and heat transfer coefficient depend on the temperature. The differential transform method (DTM) is employed to construct the analytical (series) solutions. Thermal conductivity is considered to be given by the power law in one case and by the linear function of temperature in the other, whereas heat transfer coefficient is only given by the power law. The analytical solutions constructed by the DTM agree very well with the exact solutions even when both the thermal conductivity and the heat transfer coefficient are given by the power law. The analytical solutions are obtained for the problems which cannot be solved exactly. The effects of some physical parameters such as the thermogeometric fin parameter and thermal conductivity gradient on temperature distribution are illustrated and explained.
Publisher: World Scientific Pub Co Pte Lt
Date: 10-11-2016
DOI: 10.1142/S0217979216400191
Abstract: We obtain first integrals of the generalized two-dimensional Ermakov systems, in plane polar form, via the Hamiltonian approaches. There are two methods used for the construction of the first integrals, viz. the standard Hamiltonian and the partial Hamiltonian approaches. In the first approach, [Formula: see text] and [Formula: see text] in the Ermakov system are related as [Formula: see text]. In this case, we deduce four first integrals (three of which are functionally independent) which correspond to the Lie algebra sl[Formula: see text] in a direct constructive manner. We recover the results of earlier work that uses the relationship between symmetries and integrals. This results in the complete integrability of the Ermakov system. By use of the partial Hamiltonian method, we discover four new cases: [Formula: see text] with [Formula: see text], [Formula: see text], [Formula: see text] [Formula: see text] with [Formula: see text], [Formula: see text], [Formula: see text] [Formula: see text] with [Formula: see text], [Formula: see text], [Formula: see text] arbitrary and [Formula: see text] with [Formula: see text], [Formula: see text], [Formula: see text] arbitrary, where the [Formula: see text]s are constants in all cases. In the last two cases, we find that there are three operators each which give rise to three first integrals each. In both these cases, we have complete integrability of the Ermakov system. The first two cases each result in two first integrals each. For every case, both for the standard and partial Hamiltonian, the angular momentum type first integral arises and this is a consequence of the operator which depends on a momentum coordinate which is a generalized symmetry in the Lagrangian context.
Publisher: Elsevier BV
Date: 10-2010
Publisher: Vilnius Gediminas Technical University
Date: 31-12-2009
DOI: 10.3846/1392-6292.2009.14.495-502
Abstract: We consider a bond‐pricing model described in terms of partial differential equations (PDEs). Classical Lie point symmetry analysis of the considered PDEs resulted in a number of point symmetries being admitted. The one‐dimensional optimal system of subalgebras is constructed. Following the symmetry reductions, we determine the group‐invariant solutions.
Publisher: IOP Publishing
Date: 12-08-2004
Publisher: Elsevier BV
Date: 08-2010
Publisher: Hindawi Limited
Date: 2014
DOI: 10.1155/2014/138289
Abstract: The transport of chemicals through soils to the groundwater or precipitation at the soils surfaces leads to degradation of these resources. Serious consequences may be suffered in the long run. In this paper, we consider macroscopic deterministic models describing contaminant transport in saturated soils under uniform radial water flow backgrounds. The arising convection-dispersion equation given in terms of the stream functions is analyzed using classical Lie point symmetries. A number of exotic Lie point symmetries are admitted. Group invariant solutions are classified according to the elements of the one-dimensional optimal systems. We analyzed the group invariant solutions which satisfy the physical boundary conditions.
Publisher: Elsevier BV
Date: 2013
Publisher: Hindawi Limited
Date: 2011
DOI: 10.1155/2011/132457
Abstract: Steady heat transfer through a pin fin is studied. Thermal conductivity, heat transfer coefficient, and the source or sink term are assumed to be temperature dependent. In the model considered, the source or sink term is given as an arbitrary function. We employ symmetry techniques to determine forms of the source or sink term for which the extra Lie point symmetries are admitted. Method of separation of variables is used to construct exact solutions when the governing equation is linear. Symmetry reductions result in reduced ordinary differential equations when the problem is nonlinear and some invariant solution for the linear case. Furthermore, we analyze the heat flux, fin efficiency, and the entropy generation.
Publisher: Trans Tech Publications, Ltd.
Date: 09-2017
DOI: 10.4028/WWW.SCIENTIFIC.NET/DDF.377.1
Abstract: In this paper we consider heat transfer in a hot body with different geometries. Here, the thermal conductivity and internal heat generation are both temperature-dependent. This assumption rendered the model considered to be nonlinear. We assume that thermal conductivity is given by a power law function. We employ the preliminary group classification to determine the cases of internal heat generation for which the principal Lie algebra extends by one. Exact solutions are constructed for the case when thermal conductivity is a differential consequence of internal heat generation term. We derive the approximate numerical solutions for the cases where exact solutions are difficult to construct or are nonexistent. The effects of parameters appearing in the model on temperature profile are studied.
Publisher: Hindawi Limited
Date: 2008
DOI: 10.1155/2008/689074
Abstract: In this article, the heat transfer characteristics of natural convection about a vertical permeable flat surface embedded in a saturated porous medium are studied by taking into account the thermal radiation effect. The plate is assumed to have a power-law temperature distribution. Similarity variables are employed in order to transform the governing partial differential equations into a nonlinear ordinary differential equation. Both Adomian decomposition method (ADM) and He's variational iteration method (VIM) coupled with Padé approximation technique are implemented to solve the reduced system. Comparisons with previously published works are performed, and excellent agreement between the results is obtained.
Publisher: Hindawi Limited
Date: 2008
DOI: 10.1155/2008/347568
Abstract: Lie point symmetry analysis is performed for an unsteady nonlinear heat diffusion problem modeling thermal energy storage in a medium with a temperature-dependent power law thermal conductivity and subjected to a convective heat transfer to the surrounding environment at the boundary through a variable heat transfer coefficient. Large symmetry groups are admitted even for special choices of the constants appearing in the governing equation. We construct one-dimensional optimal systems for the admitted Lie algebras. Following symmetry reductions, we construct invariant solutions.
Publisher: AIP
Date: 2012
DOI: 10.1063/1.4756407
Publisher: Elsevier BV
Date: 08-2007
Publisher: Elsevier BV
Date: 10-2012
Publisher: Wiley
Date: 07-02-2017
DOI: 10.1002/HTJ.21261
Publisher: Walter de Gruyter GmbH
Date: 20-02-2020
Abstract: In this article, the differential transform method (DTM) is used to solve the nonlinear boundary value problems describing heat transfer in continuously moving fins undergoing convective-radiative heat dissipation. The thermal conductivity is variable and temperature dependent. The surface of the moving fin is assumed to be gray with a constant emissivity ɛ . The flow in the surrounding medium provides a constant heat transfer coefficient h over the entire surface of the moving fins. The effects of some physical parameters such as the Peclet number, Pe , thermal conductivity parameter, β , convection-conduction parameter, N c , radiation-conduction parameter, N r , and dimensionless convection-radiation sink temperature, θ a , on the temperature distribution are illustrated and explained.
Publisher: IOP Publishing
Date: 08-2008
Publisher: Walter de Gruyter GmbH
Date: 2013
DOI: 10.2478/S11534-013-0306-1
Abstract: Some new conservation laws for the transient heat conduction problem for heat transfer in a straight fin are constructed. The thermal conductivity is given by a power law in one case and by a linear function of temperature in the other. Conservation laws are derived using the direct method when thermal conductivity is given by the power law and the multiplier method when thermal conductivity is given as a linear function of temperature. The heat transfer coefficient is assumed to be given by the power law function of temperature. Furthermore, we determine the Lie point symmetries associated with the conserved vectors for the model with power law thermal conductivity.
Publisher: Elsevier BV
Date: 10-2011
Publisher: SAGE Publications
Date: 2013
DOI: 10.1155/2013/983962
Abstract: We consider a system of coupled partial differential equations describing transient fluid flow and heat transfer with variable flow properties. Classical Lie point symmetry analysis of this system resulted in admitted large Lie algebras for some special cases of the arbitrary constants and the source term. Symmetry reductions are performed and as such the system of partial differential equations is reduced to the system of ordinary differential equations. Some reduced ordinary differential equation could be solved exactly with restrictions on the parameters appearing in it. In addition, shooting quadrature is employed to numerically tackle the nonlinear model boundary value problem and pertinent results are presented graphically and discussed quantitatively.
Publisher: Author(s)
Date: 2016
DOI: 10.1063/1.4952116
Publisher: Hindawi Limited
Date: 2014
DOI: 10.1155/2014/417098
Abstract: We consider a steady state problem for heat transfer in fins of various geometries, namely, rectangular, radial, and spherical. The nonlinear steady state problem is linearizable provided that the thermal conductivity is the differential consequence of the term involving the heat transfer coefficient. As such, one is able to construct exact solutions. On the other hand, we employ the Lie point symmetry methods when the problem is not linearizable. Some interesting results are obtained and analyzed. The effects of the parameters such as thermogeometric fin parameter and the exponent on temperature are studied. Furthermore, fin efficiency and heat flux along the fin length of a spherical geometry are also studied.
Publisher: Trans Tech Publications, Ltd.
Date: 09-2018
DOI: 10.4028/WWW.SCIENTIFIC.NET/DDF.387.23
Abstract: In this paper we consider heat transfer in a wall with temperature dependent heat conductivity and internal heat generation. It turns out the model considered is non-linear. We employ the classical Lie point symmetry analysis to determine the exact solutions. A number of cases for thermal conductivity and internal heat generation are considered. In some cases the exact solutions are not possible to construct. However, we first use the obtained exact solution as a bench mark for the quasilinear method. Since confidence is established, we then use the quasilinear method to solve some other applicable problem.
Publisher: Hindawi Limited
Date: 2012
DOI: 10.1155/2012/671548
Abstract: We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. The effects of thermogeometric fin parameter and the exponent on temperature are studied. Also, the fin efficiency is analyzed.
Publisher: Springer Science and Business Media LLC
Date: 10-2005
Publisher: Trans Tech Publications, Ltd.
Date: 05-2020
DOI: 10.4028/WWW.SCIENTIFIC.NET/DDF.401.1
Abstract: In this article, heat transfer through a moving fin with convective and radiative heat dissipation is studied. The analytical solutions are generated using the two-dimensional Differential Transform Method (2D DTM) which is an analytical solution technique that can be applied to various types of differential equations. The accuracy of the analytical solution is validated by benchmarking it against the numerical solution obtained by applying the inbuilt numerical solver in MATLAB ($pdepe$). A good agreement is observed between the analytical and numerical solutions. The effects of thermo-physical parameters, such as the Peclet number, surface emissivity coefficient, power index of heat transfer coefficient, convective-conductive parameter, radiative-conductive parameter and non-dimensional ambient temperature on non-dimensional temperature is studied and explained. Since numerous parameters are studied, the results could be useful in industrial and engineering applications.
Publisher: Elsevier BV
Date: 03-2015
Publisher: Elsevier BV
Date: 09-2010
Publisher: Elsevier BV
Date: 04-2011
Publisher: Hindawi Limited
Date: 2014
DOI: 10.1155/2014/947160
Abstract: One-dimensional steady-state heat transfer in fins of different profiles is studied. The problem considered satisfies the Dirichlet boundary conditions at one end and the Neumann boundary conditions at the other. The thermal conductivity and heat coefficients are assumed to be temperature dependent, which makes the resulting differential equation highly nonlinear. Classical Lie point symmetry methods are employed, and some reductions are performed. Some invariant solutions are constructed. The effects of thermogeometric fin parameter, the exponent on temperature, and the fin efficiency are studied.
Publisher: National Inquiry Services Center (NISC)
Date: 04-03-2015
Publisher: Wiley
Date: 11-11-2015
DOI: 10.1002/HTJ.21104
Publisher: Hindawi Limited
Date: 2013
DOI: 10.1155/2013/602902
Abstract: This study is based upon constructing a new class of closed-form shock wave solutions for some nonlinear problems arising in the study of a third grade fluid model. The Lie symmetry reduction technique has been employed to reduce the governing nonlinear partial differential equations into nonlinear ordinary differential equations. The reduced equations are then solved analytically, and the shock wave solutions are constructed. The conditions on the physical parameters of the flow problems also fall out naturally in the process of the derivation of the solutions.
Publisher: Hindawi Limited
Date: 2007
DOI: 10.1155/2007/38278
Abstract: A class of coupled system of diffusion equations is considered. Lie group techniques resulted in a rich array of admitted point symmetries for special cases of the source term. We also employ potential symmetry methods for chosen cases of concentration and a zero source term. Some invariant solutions are constructed using both classical Lie point and potential symmetries.
Publisher: Elsevier BV
Date: 03-2010
Publisher: Elsevier BV
Date: 12-2009
Publisher: National Inquiry Services Center (NISC)
Date: 03-2006
Publisher: Hindawi Limited
Date: 2011
DOI: 10.1155/2011/826819
Abstract: Exact solutions for models describing heat transfer in a two-dimensional rectangular fin are constructed. Thermal conductivity, internal energy generation function, and heat transfer coefficient are assumed to be dependent on temperature. We apply the Kirchoff transformation on the governing equation. Exact solutions satisfying the realistic boundary conditions are constructed for the resulting linear equation. Symmetry analysis is carried out to classify the internal heat generation function, and some reductions are performed. Furthermore, the effects of physical parameters such as extension factor (the purely geometric fin parameter) and Biot number on temperature are analyzed. Heat flux and fin efficiency are studied.
Publisher: Elsevier BV
Date: 11-2009
Publisher: Elsevier BV
Date: 05-2007
Publisher: Elsevier BV
Date: 09-2013
Publisher: Trans Tech Publications, Ltd.
Date: 09-2018
DOI: 10.4028/WWW.SCIENTIFIC.NET/DDF.387.403
Abstract: In this article, the variational iteration method (VIM) is used to analyze heat transfer in longitudinal fins of various profiles with temperature dependent thermal conductivity and heat transfer coefficient. In order to show the efficiency of the VIM, the results obtained using the VIM are compared with the previously obtained results using the differential transform method (DTM) and Lie group analysis of a fin problem with the rectangular profile. After establishing confidence in VIM, heat transfer is analyzed to determine the temperature profiles in longitudinal fins of various profiles with power law thermal properties. The temperature distribution is compared between various profiles. The effects of some physical parameters such as the thermo-geometric fin parameter and thermal conductivity gradient on temperature distribution are illustrated.
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