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Conduction Equation (conduction + equation)

Distribution by Scientific Domains
Engineering57%

Kinds of Conduction Equation

  • heat conduction equation
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    Selected Abstracts

    He's homotopy perturbation method for two-dimensional heat conduction equation: Comparison with finite element method

    HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2010
    M. Jalaal
    Abstract Heat conduction appears in almost all natural and industrial processes. In the current study, a two-dimensional heat conduction equation with different complex Dirichlet boundary conditions has been studied. An analytical solution for the temperature distribution and gradient is derived using the homotopy perturbation method (HPM). Unlike most of previous studies in the field of analytical solution with homotopy-based methods which investigate the ODEs, we focus on the partial differential equation (PDE). Employing the Taylor series, the gained series has been converted to an exact expression describing the temperature distribution in the computational domain. Problems were also solved numerically employing the finite element method (FEM). Analytical and numerical results were compared with each other and excellent agreement was obtained. The present investigation shows the effectiveness of the HPM for the solution of PDEs and represents an exact solution for a practical problem. The mathematical procedure proves that the present mathematical method is much simpler than other analytical techniques due to using a combination of homotopy analysis and classic perturbation method. The current mathematical solution can be used in further analytical and numerical surveys as well as related natural and industrial applications even with complex boundary conditions as a simple accurate technique. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20292 [source]

    THERMAL PROCESS EVALUATION OF RETORTABLE POUCHES FILLED WITH CONDUCTION HEATED FOOD

    JOURNAL OF FOOD PROCESS ENGINEERING, Issue 5 2002
    MARCELO CRISTIANINI
    ABSTRACT Two models using the finite element technique (FE) and another using an analytical solution to solve the 3-dimensional heat conduction equation for a finite plate were built. FE models were built considering the actual pouch shape and retort temperature profile. Chi-square and regression lines were obtained for each set of temperatures generated by the models against experimental data. A mass average sterilizing value of 9.9 min was estimated when a critical point sterilizing value was at 8.7 min using the 3-Dimensional FE model. Close agreement was found among the three models for heating phase. Using actual retort temperature profile made FE models more accurate than the one using analytical solution, especially for cooling phase. [source]

    Modification of upwind finite difference fractional step methods by the transient state of the semiconductor device

    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2008
    Yirang Yuan
    Abstract The mathematical model of the three-dimensional semiconductor devices of heat conduction is described by a system of four quasi-linear partial differential equations for initial boundary value problem. One equation of elliptic form is for the electric potential; two equations of convection-dominated diffusion type are for the electron and hole concentration; and one heat conduction equation is for temperature. Upwind finite difference fractional step methods are put forward. Some techniques, such as calculus of variations, energy method multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates and techniques are adopted. Optimal order estimates in L2 norm are derived to determine the error in the approximate solution.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 [source]

    On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation,

    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2005
    Mehdi Dehghan
    Abstract Numerical solution of hyperbolic partial differential equation with an integral condition continues to be a major research area with widespread applications in modern physics and technology. Many physical phenomena are modeled by nonclassical hyperbolic boundary value problems with nonlocal boundary conditions. In place of the classical specification of boundary data, we impose a nonlocal boundary condition. Partial differential equations with nonlocal boundary specifications have received much attention in last 20 years. However, most of the articles were directed to the second-order parabolic equation, particularly to heat conduction equation. We will deal here with new type of nonlocal boundary value problem that is the solution of hyperbolic partial differential equations with nonlocal boundary specifications. These nonlocal conditions arise mainly when the data on the boundary can not be measured directly. Several finite difference methods have been proposed for the numerical solution of this one-dimensional nonclassic boundary value problem. These computational techniques are compared using the largest error terms in the resulting modified equivalent partial differential equation. Numerical results supporting theoretical expectations are given. Restrictions on using higher order computational techniques for the studied problem are discussed. Suitable references on various physical applications and the theoretical aspects of solutions are introduced at the end of this article. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 [source]

    Transient heat conduction analysis in a piecewise homogeneous domain by a coupled boundary and finite element method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2003
    I. Guven
    Abstract A coupled finite element,boundary element analysis method for the solution of transient two-dimensional heat conduction equations involving dissimilar materials and geometric discontinuities is developed. Along the interfaces between different material regions of the domain, temperature continuity and energy balance are enforced directly. Also, a special algorithm is implemented in the boundary element method (BEM) to treat the existence of corners of arbitrary angles along the boundary of the domain. Unknown interface fluxes are expressed in terms of unknown interface temperatures by using the boundary element method for each material region of the domain. Energy balance and temperature continuity are used for the solution of unknown interface temperatures leading to a complete set of boundary conditions in each region, thus allowing the solution of the remaining unknown boundary quantities. The concepts developed for the BEM formulation of a domain with dissimilar regions is employed in the finite element,boundary element coupling procedure. Along the common boundaries of FEM,BEM regions, fluxes from specific BEM regions are expressed in terms of common boundary (interface) temperatures, then integrated and lumped at the nodal points of the common FEM,BEM boundary so that they are treated as boundary conditions in the analysis of finite element method (FEM) regions along the common FEM,BEM boundary. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Freezing time calculations for various products

    INTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 12 2003
    Esmail M. A. Mokheimer
    Abstract This article presents a numerical simulation that estimates the freezing time for different products. In this regard, the freezing process is mathematically modelled by transient heat conduction equations that incorporate the physical properties of the three distinct regions that exist during a freezing process. These regions are namely, the solid phase region, the liquid phase region and the interface region. This model is experimentally validated and used to estimate the freezing time for three different food products, which are namely, fish balls, cherry juice and peas balls. The freezing times estimated numerically through the present model agree well with those reported in the literature and are in excellent agreement with the experimental data. Copyright © 2003 John Wiley & Sons, Ltd. [source]