CHE/ME 109 Heat Transfer in Electronics LECTURE 10 – SPECIFIC TRANSIENT CONDUCTION MODELS.

Slides:

Advertisements

Similar presentations

FEA Course Lecture V – Outline

Advertisements

Transient Conduction: The Lumped Capacitance Method

Fourier’s Law and the Heat Equation

Fourier’s Law and the Heat Equation

Louisiana Tech University Ruston, LA Slide 1 Energy Balance Steven A. Jones BIEN 501 Wednesday, April 18, 2008.

Numerical modeling example A simple s teel reheat furnace model – pg Reheat furnace Hot steel slabRolling mill Final product.

HW/Tutorial Week #10 WWWR Chapters 27, ID Chapter 14 Tutorial #10 WWWR # 27.6 & To be discussed on March 31, By either volunteer or class list.

Louisiana Tech University Ruston, LA Slide 1 Krogh Cylinder Steven A. Jones BIEN 501 Friday, April 20, 2007.

Momentum Heat Mass Transfer MHMT10 Multidimensional heat conduction problems. Fins and heat conduction with internal sources or sinks. Unsteady heat conduction.

Heat Transfer Chapter 2.

CHE/ME 109 Heat Transfer in Electronics LECTURE 6 – ONE DIMENSIONAL CONDUTION SOLUTIONS.

1 Dr. R. Nagarajan Professor Dept of Chemical Engineering IIT Madras Advanced Transport Phenomena Module 5 Lecture 20 Energy Transport: Transient Heat.

Chapter 2: Overall Heat Transfer Coefficient

Analysis of Simple Cases in Heat Transfer P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Gaining Experience !!!

CHE/ME 109 Heat Transfer in Electronics LECTURE 17 – INTERNAL FORCED CONVECTION FUNDAMENTALS.

CHE/ME 109 Heat Transfer in Electronics LECTURE 12 – MULTI- DIMENSIONAL NUMERICAL MODELS.

Nusselt Number Calculator Travis Kenworthy and and Matthew Christensen.

CHE/ME 109 Heat Transfer in Electronics

CHE/ME 109 Heat Transfer in Electronics

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.

CHE/ME 109 Heat Transfer in Electronics LECTURE 7 – EXAMPLES OF CONDUCTION MODELS.

The Heat Conduction Equation P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi An Easy Solution to Industrial Heat Transfer.

Solutions of the Conduction Equation P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi An Idea Generates More Mathematics….

CHAPTER 8 APPROXIMATE SOLUTIONS THE INTEGRAL METHOD

CHE/ME 109 Heat Transfer in Electronics LECTURE 5 – GENERAL HEAT CONDUCTION EQUATION.

Heat Transfer Rates Conduction: Fourier’s Law

UNSTEADY STATE HEAT TRANSFER. This case of heat transfer happens in different situations. It is complicated process occupies an important side in applied.

Chapter 3: Unsteady State [ Transient ] Heat Conduction

Chapter 4 TRANSIENT HEAT CONDUCTION

CHE/ME 109 Heat Transfer in Electronics LECTURE 9 – GENERAL TRANSIENT CONDUCTION MODELS.

CHE/ME 109 Heat Transfer in Electronics LECTURE 4 – HEAT TRANSFER MODELS.

Heat Transfer in Structures

STEADY HEAT TRANSFER AND THERMAL RESISTANCE NETWORKS

CHAPTER 2 ONE-DIMENSIONAL STEADY STATE CONDUCTION

Multidimensional Heat Transfer This equation governs the Cartesian, temperature distribution for a three-dimensional unsteady, heat transfer problem involving.

Transient Conduction: Spatial Effects and the Role of Analytical Solutions Chapter 5 Sections 5.4 to 5.8.

Industrial Calculations For Transient Heat Conduction

CBE 150A – Transport Spring Semester 2014 Non-Steady State Conduction.

One Dimensional Non-Homogeneous Conduction Equation P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi A truly non-homogeneous.

One-Dimensional Steady-State Conduction

TRANSIENT CONDUCTION Lumped Thermal Capacitance Method Analytical Method: Separation of Variables Semi-Infinite Solid: Similarity Solution Numerical Method:

Unsteady State Heat Conduction

Heat flux through the wall

Food Freezing Basic Concepts (cont'd) - Prof. Vinod Jindal 1 FST 151 FOOD FREEZING FOOD SCIENCE AND TECHNOLOGY 151 Food Freezing - Basic concepts (cont’d)

One Dimensional Models for Conduction Heat Transfer in Manufacturing Processes P M V Subbarao Professor Mechanical Engineering Department I I T Delhi.

Chapter 7 Natural convection systems. 7-1 Introduction  natural or free convection: the motion of the fluid due to density changes arising from heating.

Finite-Difference Solutions Part 2

ERT 216 HEAT & MASS TRANSFER Sem 2/ Dr Akmal Hadi Ma’ Radzi School of Bioprocess Engineering University Malaysia Perlis.

Introduction:- If the temperature of the body does not very with time it said to be in steady state. if there is an abrupt change in its surface temperature.

HEAT TRANSFER Problems with FEM solution

Chapter 4: Transient Heat Conduction Yoav Peles Department of Mechanical, Aerospace and Nuclear Engineering Rensselaer Polytechnic Institute Copyright.

Extended Surfaces (Fins) Bhagwat Singh Shishodia Associate Professor Manav Rachna International University.

AFE BABALOLA UNIVERSITY

differential equations of heat transfer

Fourier’s Law and the Heat Equation

Chapter 3: One-Dimensional Steady-State Conduction

Fourier’s Law and the Heat Equation

Heat Transfer Transient Conduction.

Dimensional Analysis in Mass Transfer

Lesson 12 CONDUCTION HEAT TRANSFER

Transient Heat Conduction

Multi-Dimensional Transient Conduction

INTRODUCTION TO FOOD ENGINEERING

Transient Heat Conduction

Heat Transfer in common Configuration

What are Fins ? Fins are extended surfaces used to increase the rate of heat transfer. It is made of highly conductive materials such as aluminum.

Chapter 19 FORCED CONVECTION

Example-cylindrical coordinates

Chapter 19 FORCED CONVECTION

Presentation transcript:

CHE/ME 109 Heat Transfer in Electronics LECTURE 10 – SPECIFIC TRANSIENT CONDUCTION MODELS

SEMI-INFINITE SOLID SOLUTIONS  SEMI-INFINITE SOLIDS HAVE ONE PLANE SURFACE ON AN INFINITE VOLUME  THIS MODEL APPLIES TO SYSTEMS THAT CAN BE TREATED AS VERY THICK SLABS, SUCH AS THE SURFACE OF THE EARTH.  THE HEAT TRANSFER IS MODELED IN ONE DIMENSION, NORMAL TO THE SURFACE  PRIMARY MODEL EQUATION IS:

SEMI-INFINITE TRANSIENT CONDUCTION MODELS  CRITERIA FOR SOLUTIONS ARE  INITIAL TEMPERATURE IS UNIFORM IN THE SOLID  A UNIFORM HEAT FLOW IS INTRODUCED AT THE PLANE SURFACE AT t = 0, SO THE SURFACE TEMPERATURE BECOMES T  THE CONVECTION HEAT TRANSFER COEFFICIENT AT THE SURFACE, h, IS UNIFORM AND CONSTANT FOR t >0.

SEMI-INFINITE TRANSIENT CONDUCTION MODELS  VARIATIONS ON SOLUTIONS FOR INFINITE h VALUE (NO THERMAL RESISTANCE AT THE SURFACE)  USING THE GAUSSIAN ERROR FUNCTION:  OR USING THE COMPLEMENTARY ERROR FUNCTION :

TRANSIENT CONDUCTION EXAMPLE  AN EXAMPLE OF THIS CALCULATION IS SHOWN FOR A TEMPERATURE CHANGE IN A CONCRETE SLAB. TIME IS IN ½ HOUR INCREMENTS AND DEPTH IS IN 5 cm INCREMENTS

TRANSIENT CONDUCTION EXAMPLE

3 DIMENSIONAL OUTPUT

TRANSIENT CONDUCTION EXAMPLE  THE SURFACE GRADIENT CAN BE CALCULATED AS:  THE TOTAL HEAT CHANGE OVER TIME IS THEN:

TRANSIENT CONDUCTION EXAMPLE  SOLUTION FOR A FINITE VALUE OF THE CONVECTION COEFFICIENT, USING THE GAUSSIAN ERROR FUNCTION:  USING THE COMPLEMENTARY ERROR FUNCTION:

SUPERPOSITION METHODS  FOR SOLID TRANSIENT SYSTEMS  THE PRODUCTS OF ONE DIMENSIONAL SOLUTIONS ARE USED TO OBTAIN THE TEMPERATURE GRADIENTS IN TWO DIMENSIONAL SYSTEMS  FOR TEMPERATURE PROFILES  ONE DIMENSIONAL SOLUTIONS USED INCLUDE:  PLANE WALL  INFINITE CYLINDER  SEMI-INFINITE SOLID  APPLICATION WILL RESULT IN THE TEMPERATURE WITHIN THE SOLID AT A SPECIFIC LOCATION AND TIME  TABLE 4-5 PROVIDES A SUMMARY FOR VARIOUS SYSTEMS

SUPERPOSITION METHODS

 FOR TOTAL HEAT TRANSFERRED, THE DIMENSIONLESS HEAT TERMS ARE USED:  FOR TWO DIMENSIONAL GEOMETRIES  FOR THREE DIMENSIONAL GEOMETRIES