# Integration of a fin experiment into the undergraduate heat transfer laboratory

 To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video
Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Integration of a fin experiment into the undergraduate heat transfer laboratory H. I. Abu-Mulaweh Mechanical Engineering Department, Purdue University at Fort Wayne, Fort Wayne, IN 46805, USA Abstract A fin experimental apparatus was designed, developed and constructed for the undergraduate heat transfer laboratory at Purdue University at Fort Wayne. This paper presents a fin experiment that can be integrated into the undergraduate heat transfer laboratory. The objective of this experiment is to enhance the understanding of the transfer of thermal energy by undergraduate mechanical engineering students. This experiment exposes the students to several important concepts in heat transfer, such as one-dimensional, steady-state heat transfer by conduction and fin efficiency. In this type of experiment, the students get the opportunity to compare the measured temperature profiles in the fin to both analytical and numerical solutions. The experimental apparatus required to carry out this experiment is simple and inexpensive. Keywords fins; experiment; Laboratory; heat transfer Notation A c cross-sectional area A f surface area of fin h convection heat transfer coefficient k thermal conductivity L length of fin n nodal point P perimeter of fin Q f rate of heat loss from fin T temperature T o base temperature T ambient temperature x axial location h fin efficiency q(x) excess temperature (T(x) - T ) q o T o - T Introduction Heat transfer is a very important subject and has long been an essential part of mechanical engineering curricula all over the world. Heat transfer is encountered in a wide variety of engineering applications where heating and cooling are required. Heat transfer plays an important role in the design of many devices, such as spacecraft, radiators, heating and air conditioning systems, refrigerators and power plants.

2 84 H. I. Abu-Mulaweh It is important for engineers to understand the principles of thermodynamics (especially the first and second laws) and of heat transfer, and to be able to use the rate equations that govern the amount of energy being transferred via the three different modes of heat transfer (i.e., conduction, convection, and radiation). However, the majority of students perceive thermodynamics and heat transfer as difficult subjects. A portable experimental apparatus (refrigeration system) was designed, developed and constructed by Abu-Mulaweh [1] to demonstrate processes and systems which are fundamental to an understanding of the basic concepts of thermodynamics, such as the first and second laws. Similarly, the integration of the present experiment into the undergraduate heat transfer laboratory would enhance and add another dimension to the teaching and learning of the subject of heat transfer. The students would be able to apply to real-life situations the principles of conductive heat transfer, such as Fourier s law, fin efficiency, and others that they have learned in classroom lectures. This approach could make the subject of heat transfer a more pleasant experience for undergraduate mechanical engineering students. Purdue University at Fort Wayne is a state-supported institution. This makes the purchase of new instructional laboratory apparatus a challenge, due to typical budgetary limitations. Moreover, the apparatus designed by companies specializing in education equipment may not exactly reflect the educational objectives intended by the faculty. These obstacles had forced the author to seek different ways to acquire a fin experimental laboratory apparatus for demonstrating some heat transfer principles. The author concluded that such an apparatus can be designed, developed and constructed in house within a manageable budget. Extended surfaces (fins) are used to enhance the heat transfer rate between a solid surface and adjoining fluid. The fin is a good application that involves combined conduction and convection effects. In this experiment the fin is assumed to be infinitely long (i.e., the tip of the fin is at the same temperature as the adjacent fluid) and the heat flow is one dimensional. Under steady-state conditions, the students estimate the convective heat transfer coefficient from the measured temperature profile of the fin and the rate of heat dissipation from it. The measured temperature profile of the fin is compared with both the analytical and numerical (finitedifference) solutions. The fin s efficiency is also evaluated. Experimental apparatus and procedure A portable fin experimental apparatus was designed and constructed. The experimental apparatus is relatively simple and inexpensive. It consists of a constanttemperature energy source (a heated aluminum plate) into which the end of a circular cross-section rod is attached, as shown in Fig. 1. An aluminum circular crosssection test rod (90 cm in length) with a diameter of 9.5 mm is employed as the fin. This 90 cm length was chosen, based on analytical calculations, to ensure that the tip of the fin is at the same temperature as the adjacent fluid. Nine copper constantan thermocouples are inserted at equal intervals into the rod to measure the axial temperature distributions. The heated aluminum plate is made of four composite layers that are held together by screws. The upper layer is an aluminum plate

3 Fin experiment in heat transfer 85 Fig. 1 A picture of the fin apparatus. (15.24cm cm, and 0.95 cm thick). The second layer consists of a heating pad that can be controlled for electrical energy input. The third layer is a 0.64 cm thick Transite insulating material. The bottom layer of the heated plate is aluminum plate 1.6 cm thick serving as backing and support for the heated plate structure. The aluminum plate can be heated and maintained at a constant temperature by adjusting and controlling the level of electrical energy input to the heating pad. This is accomplished utilizing a variable-voltage transformer. The temperature of the aluminum plate is measured by a thermocouple that is inserted into the plate from the back. The heated aluminum plate and the fin attachment assembly are rigidly mounted on a short stand, as shown in Fig. 1. A portable thermocouple is also used to measure the ambient temperature (i.e., air temperature). The heat is dissipated by the fin to the adjacent air by natural convection. The experimental procedure is very simple, quick, and straightforward to carry out. First, turn on the energy source and adjust the electrical energy input to the desired heating level using the variable-voltage transformer. Second, when the system reaches steady-state conditions, measure the axial temperature distribution, T(x), of the rod. In addition, measure the surrounding air temperature, T, using a portable thermocouple.

4 86 H. I. Abu-Mulaweh Theory Analytical solution The analysis for fins of uniform cross-sectional area can be found in any standard heat transfer textbook (see, for example, Incropera and DeWitt [2] and Özisik [3]). In this experiment, the fin is assumed to be infinitely long (i.e., the tip of the fin is at the same temperature as the adjacent fluid) and the temperature at the base (x = 0) is constant, T o. The analysis is simplified by the following assumptions: onedimensional conduction in the x direction, steady-state conditions, constant thermal conductivity, no heat generation, constant and uniform convection heat transfer coefficient over the entire surface, and negligible radiation from the surface. Under these assumptions, the system of energy equation and boundary conditions assumes the form (refer to Fig. 2): 2 d T 2 -m ( T -T (1) 2 )= 0 dx T( 0)= T o (2) TL ( Æ )= T (3) hp Where m = kac The resulting temperature distribution and total heat transfer by the fin are given, respectively, by: Fig. 2 Schematic of the fin.

5 Fin experiment in heat transfer 87 Tx ( )- T = ( To -T ) exp( -mx) (4) Qf = hpkac ( To -T ) (5) The fin efficiency, h, is defined as the ratio of the actual heat transfer through the fin to the ideal heat transfer through the fin if the entire fin surface were at fin base temperature. For the present experiment, the fin efficiency is expressed by: h longfin = 1 ml Finite-difference solution The numerical method solution is employed to determine the temperature distribution in the fins. The numerical scheme that the students are asked to use is the finitedifference method. The finite-difference numerical scheme is described by Chapra and Canale [4]. In this method, the differential equation of heat conduction is approximated by a set of algebraic equations for temperature at a number of nodal points. Therefore, the first step in the analysis is the transformation of the differential equation of heat conduction in the fin into a set of algebraic equations (i.e., the finite-difference representation of the differential equation). This can be done considering an energy balance for a typical internal node of the fin rod. It should be noted that the temperatures at the boundaries are prescribed; that is T(0) = T o and T(L) = T. The rod is divided into N subregions, each Dx = L/N, and the node temperature is denoted by T n, n = 0, 1, 2,..., N, as shown in Fig. 3. The resulting general form of the finite-difference equation for the internal nodes (i.e., n = 1, 2,..., N - 1) is: kac (7) x T T kac ( n- 1 - n)+ ( x T n+ 1 - T n)+ hp D x ( T - T n)= 0 D D The simultaneous algebraic equations for temperatures at the nodal points can be solved by the Gaussian elimination method, Gauss Seidel iteration, or by the matrix (6) Fig. 3 Notation for finite-difference nodes.

6 88 H. I. Abu-Mulaweh inversion method. Computer programs for the solution of the simultaneous algebraic equations using these schemes are found in Özisik [3]. Estimation of the convection heat transfer coefficient The convection heat transfer coefficient, in general, varies along the fin as well as its circumference. For convenience in the analysis, however, it is assumed that the convection heat transfer coefficient is constant and uniform over the entire surface of the fin. The value of the convection heat transfer coefficient is needed in order to determine the temperature distribution in the fin using the analytical and finitedifference solutions as given by equations 4 and 7, respectively. There are two possible methods for the estimation of the convection heat transfer coefficient in this situation. The first method utilizes equation 4 and the measured temperature distribution along the fin. This is accomplished by rearranging equation 4 and taking the natural logarithm of both sides. This yields: È ln T - T Í ÎTo - T È Use the measured temperature distribution and plot-ln T - T Í against x and then T - T Î o use the least squares method to find the slope of the line which is equal to m. Once the value of m is known, the convection heat transfer coefficient value can be calculated from the following relation: m = hp ka c mx =- Also, the value of the convection heat transfer coefficient, h, can be estimated by considering an energy balance for a differential volume element Dx/2 at node n = 0, as shown in Fig. 4: (8) Fig. 4 Notation for energy balance at node n = 0.

7 Fin experiment in heat transfer 89 Q ka c (9) x T T hp D = ( x o - 1)+ ( To -T ) D 2 where Q is the heat entering the element from the base, which is equal to the heat lost by the fin to the adjacent fluid by convection as given by equation 5, and T 0, T 1, and T are from the measured data. Combining equations 5 and 9 yields: kac hpka T T (10) x T T hp D x c ( o - )= ( o - 1)+ ( To -T ) D 2 Equation 10 can be solved for the convection heat transfer coefficient, h, by trial and error. Sample results and discussion Measurements of the axial temperature distribution along the fin were carried out for four different base temperatures (q o = 73.8, 90.1, 109.2, and C). For all of these conditions, the temperature at the tip of the fin was the same as that of the air. The convection heat transfer coefficient value was estimated using the least squares method as shown in Fig. 5. In Fig. 5, the measured data are represented by the circles and the solid line represents the best fit using least squares. The value of Fig. 5 Least squares method for estimation of the convection heat transfer coefficient.

8 90 H. I. Abu-Mulaweh the convection heat transfer coefficient was estimated to be h = 11.6 W/m 2. C. And subsequently the rate of heat dissipation by the fin and its efficiency were determined using equations 5 and 6, respectively. The efficiency of the fin in the present experimental set-up was estimated at h = 16.6%. The variations in the rate of heat dissipation by the fin with the base temperature are presented in Fig. 6. Fig. 6 shows, as expected, that the rate of heat loss by the fin increases linearly as the base temperature increases. It should be noted that once the fin efficiency is known, the rate of heat dissipation by the fin can be obtained from the following relation: Qf = hhafq o (11) The measured and the predicted dimensionless temperature distributions for the four different base temperatures (q o = 73.8, 90.1, 109.2, and C) are presented in Fig. 7. In Fig. 7, the solid lines represent the results from the analytical solution (equation 4), and the points represented by the + and circle symbols are, respectively, the predicted results from the finite-difference solution (equation 7) and the measured values. As can be seen, the measured results agree favorably with both the Fig. 6 Rate of heat dissipation by the fin.

9 Fin experiment in heat transfer 91 Fig. 7 Dimensionless temperature distribution along the fin.

10 92 H. I. Abu-Mulaweh analytical and the numerical solutions. The reason for carrying out the experiment at four different base temperatures is to show that the measured results are repeatable. The good agreement between the measured results and the analytical and numerical solutions and the repeatability of the experimental results indicate that the apparatus is well designed for its intended purpose of demonstrating basic heat transfer principles. Conclusion The experimental fin apparatus described in this paper is a valuable addition to the undergraduate heat transfer laboratory. The experimental set-up is relatively simple and the equipment relatively inexpensive and available in almost all undergraduate heat transfer laboratory. The sample results prove that the apparatus is well designed for its intended purpose of demonstrating basic heat transfer principles. The experimental apparatus is portable. This allows it to be used for laboratory experiments and classroom demonstrations. The integration of this experiment into the undergraduate heat transfer laboratory would enhance and add another dimension to the teaching and learning of the subject of heat transfer. References [1] H. I. Abu-Mulaweh, Portable experimental apparatus for demonstrating thermodynamics principles, International Journal of Mechanical Engineering Education Vol. 32, No. 3, pp , (2004). [2] F. P. Incropera and D. P. DeWitt, Fundamentals of Heat and Mass Transfer (John Wiley, New York, 2002). [3] M. N. Özisik, Heat Transfer (McGraw-Hill, New York, 1985). [4] S. C. Chapra and R. P. Canale, Numerical Methods for Engineers, 2nd edn (McGraw-Hill, New York, 1988).

### Module 1 : Conduction. Lecture 5 : 1D conduction example problems. 2D conduction

Module 1 : Conduction Lecture 5 : 1D conduction example problems. 2D conduction Objectives In this class: An example of optimization for insulation thickness is solved. The 1D conduction is considered

Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another. hermodynamics gives no indication of how long

### Fundamentals of Heat and Mass Transfer

2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. SIXTH EDITION Fundamentals of Heat and Mass Transfer FRANK P. INCROPERA

### Heat Transfer and Energy

What is Heat? Heat Transfer and Energy Heat is Energy in Transit. Recall the First law from Thermodynamics. U = Q - W What did we mean by all the terms? What is U? What is Q? What is W? What is Heat Transfer?

### EFFECT ON HEAT TRANSFER AND THERMAL DEVELOPMENT OF A RADIATIVELY PARTICIPATING FLUID IN A CHANNEL FLOW

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 6340(Print), ISSN 0976 6340 (Print) ISSN 0976 6359

### Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

### Solving Direct and Inverse Heat Conduction Problems

Jan Taler Piotr Duda Solving Direct and Inverse Heat Conduction Problems 4y Springer Part I Heat Conduction Fundamentals 1 1 Fourier Law 3 Literature 6 2 Mass and Energy Balance Equations 7 2.1 Mass Balance

### Heat Transfer Prof. Dr. Aloke Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati

Heat Transfer Prof. Dr. Aloke Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module No. # 02 One Dimensional Steady State Heat Transfer Lecture No. # 05 Extended

### HEAT TRANSFER IM0245 3 LECTURE HOURS PER WEEK THERMODYNAMICS - IM0237 2014_1

COURSE CODE INTENSITY PRE-REQUISITE CO-REQUISITE CREDITS ACTUALIZATION DATE HEAT TRANSFER IM05 LECTURE HOURS PER WEEK 8 HOURS CLASSROOM ON 6 WEEKS, HOURS LABORATORY, HOURS OF INDEPENDENT WORK THERMODYNAMICS

### Figure 1 - Unsteady-State Heat Conduction in a One-dimensional Slab

The Numerical Method of Lines for Partial Differential Equations by Michael B. Cutlip, University of Connecticut and Mordechai Shacham, Ben-Gurion University of the Negev The method of lines is a general

### Experimental Study of Free Convection Heat Transfer From Array Of Vertical Tubes At Different Inclinations

Experimental Study of Free Convection Heat Transfer From Array Of Vertical Tubes At Different Inclinations A.Satyanarayana.Reddy 1, Suresh Akella 2, AMK. Prasad 3 1 Associate professor, Mechanical Engineering

### The First Law of Thermodynamics: Closed Systems. Heat Transfer

The First Law of Thermodynamics: Closed Systems The first law of thermodynamics can be simply stated as follows: during an interaction between a system and its surroundings, the amount of energy gained

### Thermal Management in Surface-Mounted Resistor Applications

VISHAY BEYSCHLAG Resistive Products 1. INTRODUCTION Thermal management is becoming more important as the density of electronic components in modern printed circuit boards (PCBs), as well as the applied

### Chapter 11. Objectives

Chapter 11 Heat Exchangers Islamic Azad University Karaj Branch Objectives When you finish studying this chapter, you should be able to: Recognize numerous types of heat exchangers, and classify them,

### Natural Convection. Buoyancy force

Natural Convection In natural convection, the fluid motion occurs by natural means such as buoyancy. Since the fluid velocity associated with natural convection is relatively low, the heat transfer coefficient

### 1-D Steady Conduction: Plane Wall

1-D Steady Conduction: Plane Wall Governing Equation: d 2 T dx 2 0 Dirichlet Boundary Conditions: T(0) T s,1 ; T(L) T s,2 Solution: Heat Flux: Heat Flow: T(x) T s,1 + ( T s,2 T s,1 ) x L q ʹ x ʹ k dt dx

### 1. (Problem 8.23 in the Book)

1. (Problem 8.23 in the Book) SOLUTION Schematic An experimental nuclear core simulation apparatus consists of a long thin-walled metallic tube of diameter D and length L, which is electrically heated

### Comsol Laboration: Heat Conduction in a Chip

Comsol Laboration: Heat Conduction in a Chip JO, CSC January 11, 2012 1 Physical configuration A chip on a circuit board is heated inside and cooled by convection by the surrounding fluid. We consider

### Entrance Conditions. Chapter 8. Islamic Azad University

Chapter 8 Convection: Internal Flow Islamic Azad University Karaj Branch Entrance Conditions Must distinguish between entrance and fully developed regions. Hydrodynamic Effects: Assume laminar flow with

### FIND: Characteristic length and Biot number. Validity of lumped capacitance approximation.

Mech 302 Heat Transfer HW5 Solution 1. (Problem 5.5 in the Book except for part (e)) For each of the following cases, determine an appropriate characteristic length Lc and the corresponding Biot number

### The examination rubric is: Answer THREE questions, from FIVE offered. All questions carry equal weight.

MODULE DESCRIPTOR MECHGM06 Heat Transfer and Heat Systems Code: MECHGM06 Alt. Codes(s) MECHGR06, MECHM007 Title: Heat Transfer and Heat Systems Level: M UCL Credits/ECTS: 15/6 Start: September End: March

### THERMAL ANALYSIS. Overview

W H I T E P A P E R THERMAL ANALYSIS Overview In this white paper we define and then outline the concept of thermal analysis as it relates to product design. We discuss the principles of conduction, convection,

### Computation of Tissue Temperature in Human Periphery during Different Biological and Surrounding Conditions

Computation of Tissue Temperature in Human Periphery during Different Biological and Surrounding Conditions M. P. Gupta National Institute of Technical Teachers Training and Research Bhopal Abstract--

### Instructional Laboratory Apparatuses Designed and Built by Capstone Senior Design Students

Global J. of Engng. Educ., Vol.11, No.1 Published in Australia 2007 UICEE Instructional Laboratory Apparatuses Designed and Built by Capstone Senior Design Students Hosni I. Abu-Mulaweh Department of Engineering,

### CFD SIMULATION OF SDHW STORAGE TANK WITH AND WITHOUT HEATER

International Journal of Advancements in Research & Technology, Volume 1, Issue2, July-2012 1 CFD SIMULATION OF SDHW STORAGE TANK WITH AND WITHOUT HEATER ABSTRACT (1) Mr. Mainak Bhaumik M.E. (Thermal Engg.)

### HEAT TRANSFER AUGMENTATION THROUGH DIFFERENT PASSIVE INTENSIFIER METHODS

HEAT TRANSFER AUGMENTATION THROUGH DIFFERENT PASSIVE INTENSIFIER METHODS P.R.Hatwar 1, Bhojraj N. Kale 2 1, 2 Department of Mechanical Engineering Dr. Babasaheb Ambedkar College of Engineering & Research,

### ME 315 - Heat Transfer Laboratory. Experiment No. 7 ANALYSIS OF ENHANCED CONCENTRIC TUBE AND SHELL AND TUBE HEAT EXCHANGERS

ME 315 - Heat Transfer Laboratory Nomenclature Experiment No. 7 ANALYSIS OF ENHANCED CONCENTRIC TUBE AND SHELL AND TUBE HEAT EXCHANGERS A heat exchange area, m 2 C max maximum specific heat rate, J/(s

### WEEKLY SCHEDULE. GROUPS (mark X) SPECIAL ROOM FOR SESSION (Computer class room, audio-visual class room)

SESSION WEEK COURSE: THERMAL ENGINEERING DEGREE: Aerospace Engineering YEAR: 2nd TERM: 2nd The course has 29 sessions distributed in 14 weeks. The laboratory sessions are included in these sessions. The

### The Basics of FEA Procedure

CHAPTER 2 The Basics of FEA Procedure 2.1 Introduction This chapter discusses the spring element, especially for the purpose of introducing various concepts involved in use of the FEA technique. A spring

### Two-Dimensional Conduction: Shape Factors and Dimensionless Conduction Heat Rates

Two-Dimensional Conduction: Shape Factors and Dimensionless Conduction Heat Rates Chapter 4 Sections 4.1 and 4.3 make use of commercial FEA program to look at this. D Conduction- General Considerations

### HEAT TRANSFER ENHANCEMENT AND FRICTION FACTOR ANALYSIS IN TUBE USING CONICAL SPRING INSERT

HEAT TRANSFER ENHANCEMENT AND FRICTION FACTOR ANALYSIS IN TUBE USING CONICAL SPRING INSERT Rahul M. Gupta 1, Bhushan C. Bissa 2 1 Research Scholar, Department of Mechanical Engineering, Shri Ramdeobaba

### For one dimensional heat transfer by conduction in the x-direction only, the heat transfer rate is given by

Chapter.3-1 Modes of Heat Transfer Conduction For one dimensional heat transfer by conduction in the -direction only, the heat transfer rate is given by Q ka d (.3-4) In this epression, k is a property

### Motor-CAD Software for Thermal Analysis of Electrical Motors - Links to Electromagnetic and Drive Simulation Models

Motor-CAD Software for Thermal Analysis of Electrical Motors - Links to Electromagnetic and Drive Simulation Models Dave Staton, Douglas Hawkins and Mircea Popescu Motor Design Ltd., Ellesmere, Shropshire,

### Introduction to the Finite Element Method (FEM)

Introduction to the Finite Element Method (FEM) ecture First and Second Order One Dimensional Shape Functions Dr. J. Dean Discretisation Consider the temperature distribution along the one-dimensional

### Calculating Heat Loss by Mark Crombie, Chromalox

Calculating Heat Loss by Mark Crombie, Chromalox Posted: January 30, 2006 This article deals with the basic principles of heat transfer and the calculations used for pipes and vessels. By understanding

### ME 144: Heat Transfer Convection Relations for External Flows. J. M. Meyers

ME 144: Heat Transfer Convection Relations for External Flows Empirical Correlations Generally, convection correlations for external flows are determined experimentally using controlled lab conditions

### Q ( q(m, t 0 ) n) S t.

THE HEAT EQUATION The main equations that we will be dealing with are the heat equation, the wave equation, and the potential equation. We use simple physical principles to show how these equations are

### NUMERICAL AND EXPERIMENTAL ANALYSIS OF ICE MELTING IN WATER

0HFiQLFD&RPSXWDFLRQDO9RO;;,SS± 5,GHOVRKQ9(RQ]RJQLDQG\$&DUGRQD(GV DQWD)H±3DUDQi\$UJHQWLQD2FWREHU NUMERICAL AND EXPERIMENTAL ANALYSIS OF ICE MELTING IN WATER Cristian A. Peña, Marcela A. Cruchaga and Diego

### An Analysis of Heat Conduction with Phase Change during the Solidification of Copper

An Analysis of Heat Conduction with Phase Change during the Solidification of Copper J. Michalski and E. Gutierrez-Miravete *2 1 Hamilton Sundstrand, 2 Rensselaer at Hartford *Corresponding author: 275

### Fluid structure interaction of a vibrating circular plate in a bounded fluid volume: simulation and experiment

Fluid Structure Interaction VI 3 Fluid structure interaction of a vibrating circular plate in a bounded fluid volume: simulation and experiment J. Hengstler & J. Dual Department of Mechanical and Process

### Engineering design experience of an undergraduate thermodynamics course

World Transactions on Engineering and Technology Education Vol.10, No.1, 2012 2012 WIETE Engineering design experience of an undergraduate thermodynamics course Hosni I. Abu-Mulaweh & Abdulaziz A. Al-Arfaj

### Thermal Management of Electronic Devices used in Automotive Safety A DoE approach

Thermal Management of Electronic Devices used in Automotive Safety A DoE approach Vinod Kumar, Vinay Somashekhar and Srivathsa Jagalur Autoliv India Private Limited, Bangalore, India Abstract: Electronic

### Determination of Thermal Conductivity of Coarse and Fine Sand Soils

Proceedings World Geothermal Congress Bali, Indonesia, - April Determination of Thermal Conductivity of Coarse and Fine Sand Soils Indra Noer Hamdhan 1 and Barry G. Clarke 2 1 Bandung National of Institute

### Coupling Forced Convection in Air Gaps with Heat and Moisture Transfer inside Constructions

Coupling Forced Convection in Air Gaps with Heat and Moisture Transfer inside Constructions M. Bianchi Janetti 1, F. Ochs 1 and R. Pfluger 1 1 University of Innsbruck, Unit for Energy Efficient Buildings,

### Experimental Observation and Numerical Prediction of Induction Heating in a Graphite Test Article

Excerpt from the Proceedings of the COMSOL Conference 2009 Boston Experimental Observation and Numerical Prediction of Induction Heating in a Graphite Test Article Todd A. Jankowski* 1, Debra P. Johnson

### 4 Thermomechanical Analysis (TMA)

172 4 Thermomechanical Analysis 4 Thermomechanical Analysis (TMA) 4.1 Principles of TMA 4.1.1 Introduction A dilatometer is used to determine the linear thermal expansion of a solid as a function of temperature.

### RESPONSE TIME INDEX OF SPRINKLERS

, Number l, p.1-6, 29 RESPONSE TIME INDEX OF SPRINKLERS C.K. Sze Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong, China ABSTRACT The Plunge test would be carried

### Finite Element Analysis of Aluminum Billet Heating by Rotation in DC Magnetic Fields

Finite Element Analysis of Aluminum Billet Heating by Rotation in DC Magnetic Fields Virgiliu Fire eanu, Tiberiu Tudorache POLITEHNICA University of Bucharest, EPM_NM Laboratory, 313 Spl. Independentei,

### General Framework for an Iterative Solution of Ax b. Jacobi s Method

2.6 Iterative Solutions of Linear Systems 143 2.6 Iterative Solutions of Linear Systems Consistent linear systems in real life are solved in one of two ways: by direct calculation (using a matrix factorization,

### The temperature of a body, in general, varies with time as well

cen2935_ch4.qxd 11/3/5 3: PM Page 217 TRANSIENT HEAT CONDUCTION CHAPTER 4 The temperature of a body, in general, varies with time as well as position. In rectangular coordinates, this variation is expressed

### HEAT TRANSFER ANALYSIS IN A 3D SQUARE CHANNEL LAMINAR FLOW WITH USING BAFFLES 1 Vikram Bishnoi

HEAT TRANSFER ANALYSIS IN A 3D SQUARE CHANNEL LAMINAR FLOW WITH USING BAFFLES 1 Vikram Bishnoi 2 Rajesh Dudi 1 Scholar and 2 Assistant Professor,Department of Mechanical Engineering, OITM, Hisar (Haryana)

### INTERNATIONAL ASSOCIATION OF CLASSIFICATION SOCIETIES. Interpretations of the FTP

INTERNATIONAL ASSOCIATION OF CLASSIFICATION SOCIETIES Interpretations of the FTP CONTENTS FTP1 Adhesives used in A or B class divisions (FTP Code 3.1, Res A.754 para. 3.2.3) June 2000 FTP2 Pipe and duct

### Energy Efficient Process Heating: Insulation and Thermal Mass

Energy Efficient Process Heating: Insulation and Thermal Mass Kevin Carpenter and Kelly Kissock Department of Mechanical and Aerospace Engineering University of Dayton 300 College Park Dayton, OH 45469-0210

### Heat Transfer Analysis of Cylindrical Perforated Fins in Staggered Arrangement

International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-2, Issue-5, April 203 Heat Transfer Analysis of Cylindrical Fins in Staggered Arrangement Amol

### Testing and Performance of the Convex Lens Concentrating Solar Power Panel Prototype

Testing and Performance of the Convex Lens Concentrating Solar Power Panel Prototype Ankit S. Gujrathi 1, Prof. Dilip Gehlot 2 1 M.tech (2 nd Year), 2 Assistant Professor, Department of Mechanical Engg.,

### Dynamic Temperature Measurements OBJECTIVES

Dynamic Temperature Measurements OBJECTIVES (1) Investigate the dynamic response of a thermometer and a thermocouple. (2) Apply data acquisition and control to a dynamic experiment. (3) Gain experience

### L r = L m /L p. L r = L p /L m

NOTE: In the set of lectures 19/20 I defined the length ratio as L r = L m /L p The textbook by Finnermore & Franzini defines it as L r = L p /L m To avoid confusion let's keep the textbook definition,

### INCORPORATING CFD INTO THE UNDERGRADUATE MECHANICAL ENGINEERING PROGRAMME AT THE UNIVERSITY OF MANITOBA

INCORPORATING CFD INTO THE UNDERGRADUATE MECHANICAL ENGINEERING PROGRAMME AT THE UNIVERSITY OF MANITOBA Scott J. Ormiston SJ Ormiston@UManitoba.ca Associate Professor, Dept. of Mechanical and Industrial

### Experimental Study On Heat Transfer Enhancement In A Circular Tube Fitted With U -Cut And V -Cut Twisted Tape Insert

Experimental Study On Heat Transfer Enhancement In A Circular Tube Fitted With U -Cut And V -Cut Twisted Tape Insert Premkumar M Abstract Experimental investigation of heat transfer and Reynolds number

### Adaptation of General Purpose CFD Code for Fusion MHD Applications*

Adaptation of General Purpose CFD Code for Fusion MHD Applications* Andrei Khodak Princeton Plasma Physics Laboratory P.O. Box 451 Princeton, NJ, 08540 USA akhodak@pppl.gov Abstract Analysis of many fusion

### Specific Heats of Metals

Johnson 1 Cameron Johnson Jun Li Physics 222 March 6, 2013 Specific Heats of Metals Abstract The purpose of this lab is to determine the specific heat of various types of metals by adding a known amount

### TWO-DIMENSIONAL FINITE ELEMENT ANALYSIS OF FORCED CONVECTION FLOW AND HEAT TRANSFER IN A LAMINAR CHANNEL FLOW

TWO-DIMENSIONAL FINITE ELEMENT ANALYSIS OF FORCED CONVECTION FLOW AND HEAT TRANSFER IN A LAMINAR CHANNEL FLOW Rajesh Khatri 1, 1 M.Tech Scholar, Department of Mechanical Engineering, S.A.T.I., vidisha

### Effective parameters on second law analysis for semicircular ducts in laminar flow and constant wall heat flux B

International Communications in Heat and Mass Transfer 32 (2005) 266 274 www.elsevier.com/locate/ichmt Effective parameters on second law analysis for semicircular ducts in laminar flow and constant wall

### HEAT TRANSFER ENHANCEMENT ON DOUBLE PIPE HEAT EXCHANGER BY WIRE COILED AND TAPER WIRE COILED TURBULATOR INSERTS

HEAT TRANSFER ENHANCEMENT ON DOUBLE PIPE HEAT EXCHANGER BY WIRE COILED AND TAPER WIRE COILED TURBULATOR INSERTS J.Kalil basha 1,G.Karthikeyan 2, S.Karuppusamy 3 1,2 Assistant Professor, Dhanalakshmi Srinivasan

### Physics Final Exam Chapter 13 Review

Physics 1401 - Final Exam Chapter 13 Review 11. The coefficient of linear expansion of steel is 12 10 6 /C. A railroad track is made of individual rails of steel 1.0 km in length. By what length would

### EXPERIMENTAL ANALYSIS OF HEAT TRANSFER ENHANCEMENT IN A CIRCULAR TUBE WITH DIFFERENT TWIST RATIO OF TWISTED TAPE INSERTS

INTERNATIONAL JOURNAL OF HEAT AND TECHNOLOGY Vol.33 (2015), No.3, pp.158-162 http://dx.doi.org/10.18280/ijht.330324 EXPERIMENTAL ANALYSIS OF HEAT TRANSFER ENHANCEMENT IN A CIRCULAR TUBE WITH DIFFERENT

### FUNDAMENTAL FINITE ELEMENT ANALYSIS AND APPLICATIONS

FUNDAMENTAL FINITE ELEMENT ANALYSIS AND APPLICATIONS With Mathematica and MATLAB Computations M. ASGHAR BHATTI WILEY JOHN WILEY & SONS, INC. CONTENTS OF THE BOOK WEB SITE PREFACE xi xiii 1 FINITE ELEMENT

### Comparing naturally cooled horizontal baseplate heat sinks with vertical baseplate heat sinks

Comparing naturally cooled horizontal baseplate heat sinks with vertical baseplate heat sinks Keywords: heat sink heatsink fin array natural convection natural cooling free convection horizontal baseplate

### Conductive and Radiative Heat Transfer in Insulators

Conductive and Radiative Heat Transfer in Insulators Akhan Tleoubaev, Ph.D. LaserComp, Inc., December 1998 Heat transfer for most thermal insulation materials occurs via both conduction and radiation.

### Introduction to the Finite Element Method (FEM)

Introduction to the Finite Element Method (FEM) Lecture 1 The Direct Stiffness Method and the Global StiffnessMatrix Dr. J. Dean 1 Introduction The finite element method (FEM) is a numerical technique

### Thermocline Management of Stratified Tanks for Heat Storage

Thermocline Management of Stratified Tanks for Heat Storage M.R.W. Walmsley, M. J. Atkins, J. Riley Energy Research Group, Department of Engineering, University of Waikato Hamilton, NZ Stratified tanks

### Permanent Magnet DC Motor Brush Transient Thermal Analysis

Paper ID 1109 Permanent Magnet DC Motor Brush Transient Thermal Analysis Jacek Junak 1, Grzegorz Ombach 1, Dave Staton 2 1 VDO Automotive AG, Werner-von-Siemens 3, D-97076, Wuerzburg, Germany 2 Motor Design

### Chapter 8 Steady Incompressible Flow in Pressure Conduits

Chapter 8 Steady Incompressible Flow in Pressure Conduits Outline 8.1 Laminar Flow and turbulent flow Reynolds Experiment 8.2 Reynolds number 8.3 Hydraulic Radius 8.4 Friction Head Loss in Conduits of

### THERMAL ANALYSIS OF HEAT EXCHANGER WITH THE HELP OF TAGUCHI METHOD

International Journal of Advanced Research in Engineering and Technology (IJARET) Volume 7, Issue 1, Jan-Feb 2016, pp. 01-06, Article ID: IJARET_07_01_001 Available online at http://www.iaeme.com/ijaret/issues.asp?jtype=ijaret&vtype=7&itype=1

### Transient Mass Transfer

Lecture T1 Transient Mass Transfer Up to now, we have considered either processes applied to closed systems or processes involving steady-state flows. In this lecture we turn our attention to transient

### Optimum fin spacing for fan-cooled heat sinks

Optimum fin spacing for fan-cooled heat sinks Keywords: optimum fin spacing fan-cooled heat sink heatsink optimal fin pitch parallel plate fin array optimization forced air cooling fan curve pressure drop

### Thermal Diffusivity, Specific Heat, and Thermal Conductivity of Aluminum Oxide and Pyroceram 9606

Report on the Thermal Diffusivity, Specific Heat, and Thermal Conductivity of Aluminum Oxide and Pyroceram 9606 This report presents the results of phenol diffusivity, specific heat and calculated thermal

### Laminar Flow and Heat Transfer of Herschel-Bulkley Fluids in a Rectangular Duct; Finite-Element Analysis

Tamkang Journal of Science and Engineering, Vol. 12, No. 1, pp. 99 107 (2009) 99 Laminar Flow and Heat Transfer of Herschel-Bulkley Fluids in a Rectangular Duct; Finite-Element Analysis M. E. Sayed-Ahmed

### Iterative calculation of the heat transfer coefficient

Iterative calculation of the heat transfer coefficient D.Roncati Progettazione Ottica Roncati, via Panfilio, 17 44121 Ferrara Aim The plate temperature of a cooling heat sink is an important parameter

### Theoretical and Experimental Investigation of Heat Transfer Characteristics through a Rectangular Microchannel Heat Sink

Theoretical and Experimental Investigation of Heat Transfer Characteristics through a Rectangular Microchannel Heat Sink Dr. B. S. Gawali 1, V. B. Swami 2, S. D. Thakre 3 Professor Dr., Department of Mechanical

### Convection Heat Transfer From Tube Banks in Crossflow: Analytical Approach

AIAA 2005-0958 Convection Heat Transfer From Tube Banks in Crossflow: Analytical Approach M. M. Yovanovich, Fellow AIAA W. A. Khan J. R. Culham Microelectronics Heat Transfer Laboratory Department of Mechanical

### The Effect of Forced Air Cooling on Heat Sink Thermal Ratings

zpero 1 The Effect of Forced Air Cooling on Heat Sink Thermal Ratings By Paul Bachman, Fellow Engineer & Ronnie Haiduk, Applications Engineer, Crydom, Inc. ABSTRACT A heat sink s ability to dissipate thermal

### FREESTUDY HEAT TRANSFER TUTORIAL 3 ADVANCED STUDIES

FREESTUDY HEAT TRANSFER TUTORIAL ADVANCED STUDIES This is the third tutorial in the series on heat transfer and covers some of the advanced theory of convection. The tutorials are designed to bring the

### Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati

Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module No. # 04 Convective Heat Transfer Lecture No. # 03 Heat Transfer Correlation

### PHYS 1020 Final Exam. Seating (from exam listing on Aurora) Brown Gym. Gold Gym

PHYS 1020 Final Exam Monday, December 17, 6-9 pm The whole course 30 multiple choice questions Formula sheet provided Seating (from exam listing on Aurora) Brown Gym A - SIM Gold Gym SIN - Z 27 Week of

### 978-1-4673-1965-2/12/\$31.00 2012 IEEE 1488

Generic Thermal Analysis for Phone and Tablet Systems Siva P. Gurrum, Darvin R. Edwards, Thomas Marchand-Golder, Jotaro Akiyama, Satoshi Yokoya, Jean-Francois Drouard, Franck Dahan Texas Instruments, Inc.,

### Mass Transfer in Laminar & Turbulent Flow. Mass Transfer Coefficients

Mass Transfer in Laminar & Turbulent Flow Mass Transfer Coefficients 25 MassTransfer.key - January 3, 204 Convective Heat & Mass Transfer T T w T in bulk and T w near wall, with a complicated T profile

### Technology of EHIS (stamping) applied to the automotive parts production

Laboratory of Applied Mathematics and Mechanics Technology of EHIS (stamping) applied to the automotive parts production Churilova Maria, Saint-Petersburg State Polytechnical University Department of Applied

### Fourier Series. A Fourier series is an infinite series of the form. a + b n cos(nωx) +

Fourier Series A Fourier series is an infinite series of the form a b n cos(nωx) c n sin(nωx). Virtually any periodic function that arises in applications can be represented as the sum of a Fourier series.

### MATHEMATICAL MODEL FOR VIBRATIONS OF NON-UNIFORM FLEXURAL BEAMS

Engineering MECHANICS, Vol. 15, 2008, No. 1, p. 3 11 3 MATHEMATICAL MODEL FOR VIBRATIONS OF NON-UNIFORM FLEXURAL BEAMS Mohamed Hussien Taha, Samir Abohadima* A simplified mathematical model for free vibrations

### Macroscopic Balances for Nonisothermal Systems

Transport Phenomena Macroscopic Balances for Nonisothermal Systems 1 Macroscopic Balances for Nonisothermal Systems 1. The macroscopic energy balance 2. The macroscopic mechanical energy balance 3. Use

### Application of First Order Differential Equations in Mechanical Engineering Analysis

ME 130 Applied Engineering Analysis Chapter 3 Application of First Order Differential Equations in Mechanical Engineering Analysis Tai-Ran Hsu, Professor Department of Mechanical and Aerospace Engineering

### Thermal Considerations for Surface Mount Layouts

Thermal onsiderations for Surface Mount Layouts harles Mauney, Texas Instruments ABSTRAT The focus of this paper is to present the techniques that are effective in removing the heat from the surface mounted

### Sizing of triple concentric pipe heat exchanger

Sizing of triple concentric pipe heat exchanger 1 Tejas M. Ghiwala, 2 Dr. V.K. Matawala 1 Post Graduate Student, 2 Head of Department 1 Thermal Engineering, SVMIT, Bharuch-392001, Gujarat, INDIA, 2 Department

### Finite Element Thermal Analysis of Conformal Cooling Channels in Injection Moulding

5 th Australasian Congress on Applied Mechanics, ACAM 2007 10-12 December 2007, Brisbane, Australia Finite Element Thermal Analysis of Conformal Cooling Channels in Injection Moulding A.B.M. Saifullah

### 1150 hp motor design, electromagnetic and thermal analysis

115 hp motor design, electromagnetic and thermal analysis Qasim Al Akayshee 1, and David A Staton 2 1 Mawdsley s Ltd., The Perry Centre, Davey Close, Waterwells, Gloucester GL2 4AD phone: +44 1452 888311

### An Automotive Radiator Employing Wickless Heat Pipes

An Automotive Radiator Employing Wickless Heat Pipes Yiding Cao and Khokiat Kengskool 2 Abstract: Heat pipe is a heat transfer device that may have a thermal conductance hundreds of times higher than that