FINITE DIFFERENCE In numerical analysis, two different approaches are commonly used: The finite difference and the finite element methods. In heat transfer.

Slides:



Advertisements
Similar presentations
Computational Modeling for Engineering MECN 6040
Advertisements

Parabolic Partial Differential Equations
Solving Equations = 4x – 5(6x – 10) -132 = 4x – 30x = -26x = -26x 7 = x.
Finite Element Method (FEM) Different from the finite difference method (FDM) described earlier, the FEM introduces approximated solutions of the variables.
By S Ziaei-Rad Mechanical Engineering Department, IUT.
Chapter 3 Steady-State Conduction Multiple Dimensions
CHE/ME 109 Heat Transfer in Electronics LECTURE 12 – MULTI- DIMENSIONAL NUMERICAL MODELS.
CHE/ME 109 Heat Transfer in Electronics LECTURE 10 – SPECIFIC TRANSIENT CONDUCTION MODELS.
CE An Intro Problem—will lead to first homework Fluid is contained in along square duct, see cross section below, three faces of the duct are kept.
CHE/ME 109 Heat Transfer in Electronics LECTURE 11 – ONE DIMENSIONAL NUMERICAL MODELS.
CHE/ME 109 Heat Transfer in Electronics LECTURE 8 – SPECIFIC CONDUCTION MODELS.
Chapter 5 NUMERICAL METHODS IN HEAT CONDUCTION
CHAP 5 FINITE ELEMENTS FOR HEAT TRANSFER PROBLEMS
Two-Dimensional Conduction: Flux Plots and Shape Factors
Numerical Methods Due to the increasing complexities encountered in the development of modern technology, analytical solutions usually are not available.
Tutorial 5: Numerical methods - buildings Q1. Identify three principal differences between a response function method and a numerical method when both.
1 Convection Boundary Condition –Happens when a structure is surrounded by fluid –Does not exist in structural problems –BC includes unknown temperature.
Lecture Objectives: Analyze the unsteady-state heat transfer Conduction Introduce numerical calculation methods Explicit – Implicit methods.
Finite Elements: 1D acoustic wave equation
Two-Dimensional Conduction: Finite-Difference Equations and Solutions
Chapter 6. Plane Stress / Plane Strain Problems
MECH593 Finite Element Methods
Module 4 Multi-Dimensional Steady State Heat Conduction.
Chapter 5: Numerical Methods in Heat Transfer
HOT PLATE CONDUCTION NUMERICAL SOLVER AND VISUALIZER Kurt Hinkle and Ivan Yorgason.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Part 8 - Chapter 29.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Chapter 31.
Transient Conduction: Finite-Difference Equations and Solutions Chapter 5 Section 5.9  
MSE 430 © 2006, J.C.LaCombe 1 Numerical Methods in Diffusion Portions of this lecture were adapted from Elements of Heat and Mass Transfer, 3 rd ed., F.P.
An Introduction to Heat Transfer Morteza Heydari.
HW2 Due date Next Tuesday (October 14). Lecture Objectives: Unsteady-state heat transfer - conduction Solve unsteady state heat transfer equation for.
MECN 3500 Inter - Bayamon Lecture 9 Numerical Methods for Engineering MECN 3500 Professor: Dr. Omar E. Meza Castillo
The Configuration Factors between Ring Shape Finite Areas in Cylinders and Cones Cosmin DAN, Gilbert DE MEY.
HEAT TRANSFER FINITE ELEMENT FORMULATION
The Finite Element Method Prof. Su-Jin Kim Gyeongsang National University.
Heat flux through the wall
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Chapter 27.
FALL 2015 Esra Sorgüven Öner
Discretization Methods Chapter 2. Training Manual May 15, 2001 Inventory # Discretization Methods Topics Equations and The Goal Brief overview.
MULTIDIMENSIONAL HEAT TRANSFER  This equation governs the Cartesian, temperature distribution for a three-dimensional unsteady, heat transfer problem.
Finite-Difference Solutions Part 2
Evan Selin & Terrance Hess.  Find temperature at points throughout a square plate subject to several types of boundary conditions  Boundary Conditions:
3/23/05ME 2591 Numerical Methods in Heat Conduction Reference: Incropera & DeWitt, Chapter 4, sections Chapter 5, section 5.9.
ERT 216 HEAT & MASS TRANSFER Sem 2/ Dr Akmal Hadi Ma’ Radzi School of Bioprocess Engineering University Malaysia Perlis.
Lecture Objectives: - Numerics. Finite Volume Method - Conservation of  for the finite volume w e w e l h n s P E W xx xx xx - Finite volume.
Model Anything. Quantity Conserved c  advect  diffuse S ConservationConstitutiveGoverning Mass, M  q -- M Momentum fluid, Mv -- F Momentum fluid.
HEAT TRANSFER Problems with FEM solution
The Finite Element Approach to Thermal Analysis Appendix A.
Part 8 - Chapter 29.
EEE 431 Computational Methods in Electrodynamics
Christopher Crawford PHY
Applied Numerical Methods
Chapter 30.
Notes Over 9.6 An Equation with One Solution
PDEs and Examples of Phenomena Modeled
Objective Numerical methods.
Chapter 27.
Numerical Examples Example: Find the system of finite difference equations for the following problem. Steady state heat conduction through a plane wall.
Numerical Method (Special Cases)
finite element method node point based strong form
Heat Transfer in Extended Surface
finite element method node point based strong form
Numerical Method (Special Cases)
Linear Algebra Lecture 3.
What is Fin? Fin is an extended surface, added onto a surface of a structure to enhance the rate of heat transfer from the structure. Example: The fins.
Mathematical Solution of Non-linear equations : Newton Raphson method
Steady-State Heat Transfer (Initial notes are designed by Dr
X ⦁ X = 64 ±8 ±14 X ⦁ X ⦁ X =
Home assignment #3 (1) (Total 3 problems) Due: 12 November 2018
Presentation transcript:

FINITE DIFFERENCE In numerical analysis, two different approaches are commonly used: The finite difference and the finite element methods. In heat transfer problems, the finite difference method is used more often and will be discussed here. The finite difference method involves:  Establish nodal networks  Derive finite difference approximations for the governing equation at both interior and exterior nodal points  Develop a system of simultaneous algebraic nodal equations  Solve the system of equations using numerical schemes

The Nodal Networks

Finite Difference Approximation

Finite Difference Approximation cont.

A System of Algebraic Equations

Matrix Form

Numerical Solutions

Iteration

Example

Example (cont.)

Summary of nodal finite-difference relations for various configurations: Case 1 Interior Node

Case 2 Node at an internal corner with convection

Case 3 Node at a plane surface with convection

Case 4 Node at an external corner with convection

Case 5 Node at a plane surface with uniform heat flux

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com Inc. All rights reserved.