Hierarchical parallelism in finite difference analysis of heat conduction

... grant NAG3-644
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National Aeronautics and Space Administration, Lewis Research Center, National Technical Information Service, distributor , [Cleveland, Ohio], [Springfield, VA
StatementJoseph Padovan, Lala Krishna, and Douglas Gute.
Series[NASA contractor report] -- NASA CR--97-206226., NASA contractor report -- NASA CR-206226.
ContributionsKrishna, Lala B., Gute, Douglas., Lewis Research Center.
The Physical Object
Pagination1 v.
ID Numbers
Open LibraryOL17826954M

Hierarchical Parallelism in Finite Difference Analysis of Heat Conduction Joseph Padovan, l Lala Krishna I and Douglas Gute 2 The University of Akron, Akron, Ohio PART I - FORMULATION SUMMARY Based on the concept of hierarchical parallelism, this series of papers develops highly efficient.

Hierarchical parallelism in finite difference analysis of heat conduction: grant NAG Finite-Difference Formulation of Differential Equation If this was a 2-D problem we could also construct a similar relationship in the both the x and Y-direction at a point (m,n) i.e., Now the finite-difference approximation of the 2-D heat conduction equation is.

The convection and conduction heat transfer, thermal conductivity, and phase transformations are significant issues in a design of wide range of industrial processes and devices. This book includes 18 advanced and revised contributions, and it covers mainly (1) heat convection, (2) heat conduction, and (3) heat transfer analysis.

Description Hierarchical parallelism in finite difference analysis of heat conduction FB2

The first section introduces mixed convection studies on Cited by: A finite‐difference method is presented for solving three‐dimensional transient heat conduction problems.

The method is a modification of the method of Douglas and Rachford which achieves the higher‐order accuracy of a Crank‐Nicholson formulation while preserving the advantages of the Douglas‐Rachford method: unconditional stability and simplicity of solving the equations at each Cited by:   4.

Cell-centered finite-difference discretization of the Laplacian. In this section we present the main idea to discretize the Laplacian. A similar approach is used for the gradients. There are two natural choices to discretize differential operators on hierarchical grids: vertex-centered or cell-centered.

Here we considerer a cell-centered. Nonlinear, Transient Conduction Heat Transfer Using A Discontinuous Galerkin Hierarchical Finite Element Method by Jerome Charles Sanders B.S.

in Physics, May The College of New Jersey A Thesis submitted to The faculty of The School of Engineering and Applied Science of The George Washington University. Finite Difference Methods in Heat Transfer, Second Edition focuses on finite difference methods and their application to the solution of heat transfer problems.

Such methods are based on the discretization of governing equations, initial and boundary conditions, which then replace a continuous partial differential problem by a system of algebraic equations.

Introduction, 1D heat conduction 4 Form and expectations To give the participants an understanding of the basic elements of the finite element method as a tool for finding approximate solutions of linear boundary value problems.

These will be exemplified with examples within stationary heat conduction. The heat transfer can be expressed as () Here, r 1 and r 2 represent the radii of annular section. A thermal resistance for this case is as sh own below.

() The Overall Heat Transfer Coefficient The overall heat transfer coefficient concept is valuable in several aspects of heat transfer. It involves. The finite difference formulation above can easily be extended to two-or-three-dimensional heat transfer problems by replacing each second derivative by a difference equation in that direction.

For example, the finite difference formulation for steady two dimensional heat conduction in a region with heat generation and constant thermal.

Numerical methods in Transient heat conduction: • In transient conduction, temperature varies with both position and time. • So, to obtain finite difference equations for transient conduction, we have to discretize Aug.

MT/SJEC/ 7 transient conduction, we have to discretize both space and time domains.

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69 1 % This Matlab script solves the one-dimensional convection 2 % equation using a finite difference algorithm. The 3 % discretization uses central differences in space and forward 4 % Euler in time. 5 6 clear all; 7 close all; 8 9 % Number of points 10 Nx = 50; 11 x = linspace(0,1,Nx+1); 12 dx = 1/Nx; 13 14 % velocity 15 u = 1; 16 17 % Set final time 18 tfinal = ; 19 20 % Set timestep.

As we proved in Theoremthe element-wise difference between both matrices is O (3 − k) and, therefore, by choosing sufficiently large k, the results of the analysis by using the original matrix are reliable to predict the practical results obtained by using the H-matrix representation (see Remark ).

We will see in the following. Heat conduction page 2. The general equations for heat conduction are the energy balance for a control mass, d d E t QW = +, and the constitutive equations for heat conduction (Fourier's law) which relates heat flux to temperature gradient, q kT =−∇.

Their combination: () d d d d dd p A d p AV H Q KA T q n A H t Q kTnA kT A t q kT. The following Matlab project contains the source code and Matlab examples used for 3d heattransfer software.

With this software you can simulate heat distribution on 3D plate and cylinder. In this project I used finite difference method to solve differential equations.

Download free books at 4 Introductory Finite Difference Methods for PDEs Contents Contents Preface 9 1. Introduction 10 Partial Differential Equations 10 Solution to a Partial Differential Equation 10 PDE Models 11 &ODVVL¿FDWLRQRI3'(V 'LVFUHWH1RWDWLRQ &KHFNLQJ5HVXOWV ([HUFLVH 2.

Fundamentals The numerical methods allow obtaining the approximate values of unknowns at discrete points (nodes). Various numerical methods have been developed and applied to solve numerous engineering problems – the finite difference method (FDM), the finite volume method (FVM), and the finite element method (FEM) are most frequently used is practice.

Very often books published on Computational Fluid Dynamics using the Finite Element Method give very little or no significance to thermal or heat transfer problems. From the research point of view, it is important to explain the handling of various types of heat transfer problems with different types of complex boundary conditions.

HT-7 ∂ ∂−() = −= f TT kA L 2 AB TA TB 0. () In equation (), k is a proportionality factor that is a function of the material and the temperature, A is the cross-sectional area and L is the length of the bar. In the limit for any temperature difference ∆T across a length ∆x as both L, T A.

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Finite-difference analysis of the generalized Graetz problem with heat convection boundary condition Article in Heat Transfer Research January with 13 Reads How we measure 'reads'. For convective heat transfer, the rate equation is given by Newton’s law of cooling as q = h (T w - T a) where q is the convective heat flux (W/m 2), (T w - T a) is the temperature difference.

Finite element software for structural, geotechnical, heat transfer and seepage analysis: Intuition Software: Proprietary software: Free educational version available: Mac OS X, Windows: JCMsuite: Finite element software for the analysis of electromagnetic waves, elasticity and heat conduction: JCMwave GmbH:   This introductory text presents the applications of the finite element method to the analysis of conduction and convection problems.

The book is divided into seven chapters which include basic ideas, application of these ideas to relevant problems, and development of solutions.

Important concepts are illustrated with examples. This book includes revised contributions, and it covers: heat convection, heat conduction, and heat transfer analysis. The first section introduces mixed convection studies on inclined channels, double diffusive coupling, and on lid driven trapezoidal cavity, forced natural convection through a roof, convection on non-isothermal jet oscillations, unsteady pulsed flow, and hydromagnetic flow.

These are lecture notes for AME Intermediate Heat Transfer, a second course on heat transfer for undergraduate seniors and beginning graduate students.

At this stage the student can begin to apply knowledge of mathematics and computational methods to the problems of heat transfer. Thus. Heat transfer in heat sinks (combined conduction–convection).

Analysis of a heat exchanger. Transient Heat Transfer Problem (Propagation Problem). Summary. Exercise. Bibliography. 3 The Finite Elemen t Method. Introduction. Elements and Shape Functions.

One-dimensional linear element. The preservation of the basic qualitative properties besides the convergence is a basic requirement in the numerical solution process.

For solving the heat conduction equation, the finite difference/linear finite element Crank-Nicolson type full discretization process is a widely used approach. coupled to heat conduction has been formulated by my supervisor Docent Johan Claesson. analysis is illustrated by a few examples.

xiv. Nomenclature Note that a few symbols do not follow the ISO standard. For example, the ISO standard uses £ for the temperature in degree Celsius. Chapter 7, dealing with radiation, has its.

Finite Element Principles in Heat Conduction Next Offering. Start Date: August 24th, End Date: November 2nd, This is the third course in a four course series. Students must complete all four courses to earn the Certification in Practice of Finite Element Principles. Jankowska M.A., Sypniewska-Kaminska G.

() Interval Finite Difference Method for Solving the One-Dimensional Heat Conduction Problem with Heat Sources. In: Manninen P., Öster P. (eds) Applied Parallel and Scientific Computing. PARA Lecture Notes in Computer Science, vol Springer, Berlin, Heidelberg.Heat transfer analysis is a problem of major significance in a vast range of industrial applications.

These extend over the fields of mechanical engineering, aeronautical engineering, chemical engineering and numerous applications in civil and electrical engineering. If one considers the heat conduction equation alone the number of practical problems amenable to solution is extensive.techniques to the solution of heat transfer problems [], the predominant numerical method for anal- ysis of heat transfer problems remained the finite difference method.

It is only during the very recent years that the advantages of a finite element analysis have become more clear.

Apart from the .