Fundamentals of the Finite Element Method for Heat and Mass Transfer (eBook)

Roland W. Lewis, Perumal Nithiarasu, Kankanhalli N. Seetharamu (Autoren)

eBook Download: EPUB

2016 | 2. Auflage
464 Seiten
Wiley (Verlag)
978-1-118-53543-1 (ISBN)

Infos

Fundamentals of the Finite Element Method for Heat and Mass Transfer, Second Edition is a comprehensively updated new edition and is a unique book on the application of the finite element method to heat and mass transfer.

•           Addresses fundamentals, applications and computer implementation

•           Educational computer codes are freely available to download, modify and use

•           Includes a large number of worked examples and exercises

•           Fills the gap between learning and research

Autor

Perumal Nithiarasu, DSc, PhD, is currently the head of Zienkiewicz Centre for Computational Engineering at Swansea University. He has more than twenty years of teaching and research experience in the areas of finite element method, heat and mass transfer, fluid dynamics and biomedical engineering. He is a founding co-chair of the international conference series, Computational Methods for Thermal Problems (ThermaCOMP, www.thermacomp.com). Professor Nithiarasu is a winner of ECCOMAS young investigator award in 2004 and he was awarded the Zienkiewicz Silver Medal of the Institution of Civil Engineers, UK in 2002. Professor Nithiarasu has published more than 300 articles and two textbooks in the areas of heat and fluid flow.?Professor Nithiarasu is the founding editor of the International Journal for Numerical Methods in Biomedical Engineering, published by Wiley. He serves on the editorial boards of several international journals. Roland Lewis, DSc, PhD, FREng, has more than forty years of experience in teaching, research and administration in the area of heat transfer. Previously, Professor Lewis served as the head of Mechanical Engineering department in Swansea University.?His contributions in the areas of solidification and porous media are very well known. Until recently, he was the editor in chief of the International Journal for Numerical Methods in Engineering and Communications in Numerical Methods in Engineering. Although retired, he is actively editing the International Journal of Numerical Methods for Heat & Fluid Flow. He has also been serving as the honorary chair of the international conference series, Computational Methods in Thermal Problems (ThermaCOMP, www.thermacomp.com).?Author of nearly 400 articles, Professor Lewis was honoured with IACM Computational Mechanics award and fellowship. He is also a fellow of the Royal Academy of Engineering, UK. K.N. Seetharamu currently holds a prestigious chair professor position in the Mechanical Engineering department of the PES University, Bangalore. He has more than forty years of teaching and research experience in the areas of heat transfer and finite element method. Previously he was a professor of Thermal Engineering in Institute of Technology Madras.?Professor Seetharamu also has spent more than ten years in University of Sains Malaysia, carrying out research in the areas of heat transfer, energy and electronics packaging.?Author of more than 300 publications, Professor Seetharamu is one of the top heat transfer engineers in India. He is a fellow of the Indian National Academy. Recently, the Indian Society for Heat and Mass Transfer has established a biennial award in his name to honour Professor Seetharmau's achievements.

Textauszug

1
Introduction

1.1 Importance of Heat and Mass Transfer

The subject of heat and mass transfer is of fundamental importance in many branches of engineering. A mechanical engineer may be interested to know the mechanisms of heat transfer involved in the operation of equipment, for example, boilers, condensers, air pre-heaters, economizers etc., in a thermal power plant in order to improve their performance. Nuclear power plants require precise information on heat transfer as safe operation is an important factor in their design. Refrigeration and air-conditioning systems also involve heat-exchanging devices, which need careful design. Electrical engineers are keen to avoid material damage in electric motors, generators and transformers due to hot spots, developed by improper heat transfer design. An electronic engineer is interested in knowing efficient methods of heat dissipation from chips and semi-conductor devices so that they function within safe operating temperatures. A computer hardware engineer is interested to know the cooling requirements of circuit-boards, as the miniaturization of computing devices is advancing at a rapid rate. Chemical engineers are interested in heat and mass transfer processes in various chemical reactions. A metallurgical engineer would be interested in knowing the rate of heat transfer required for a particular heat treatment process, e.g. the rate of cooling in a casting process has a profound influence on the quality of the final product. Aeronautical engineers are interested in knowing the heat transfer rate in rocket nozzles and in heat shields used in re-entry vehicles. An agricultural engineer would be interested in the drying of food grains, food processing and preservation. A civil engineer would need to be aware of the thermal stresses developed in quick setting concrete, the influence of heat and mass transfer on building and building materials as well as the effect of heat on nuclear containment and buildings etc. An environmental engineer is concerned with the effect of heat on dispersion of pollutants in air, transport of pollutants in soils, lakes and seas and their impact on life. A bioengineer is often interested in the heat and mass transfer processes, such as hypothermia and hyperthermia associated with the human body.

The above-mentioned applications are only a sample of heat and mass transfer applications. The solar system and the associated energy transfer from the sun are the principal factors for existence of life on Earth. It is not untrue to say that it is extremely difficult, often impossible, to avoid some form of heat transfer in any process on Earth.

The study of heat and mass transfer provides economical and efficient solutions for many critical problems encountered in diverse engineering items of equipment. For example, we can consider the development of heat pipes which can transport heat at a much greater rate than that of copper or silver rods of the same dimensions and even at almost isothermal conditions. The development of present-day gas turbine blades, where the gas temperature exceeds the melting point of the blade material, is possible by providing efficient cooling systems. This is another example of the success of heat transfer design methods. The design of computer chips, which encounter heat flux of the order occurring in re-entry vehicles, especially when the surface temperature of the chips is limited to less than 100 °C, is again a success story of heat transfer design.

Although there are many successful heat transfer designs, further developments on heat and mass transfer studies are necessary in order to increase the life span and efficiency of the many devices discussed previously, which can lead to many more new inventions. Also, if we are to protect our environment, it is essential to understand the many heat and mass transfer processes involved and if necessary to take appropriate action.

1.2 Heat Transfer Modes

Heat transfer is that section of engineering science that studies the energy transport between material bodies due to temperature difference (Bejan 1993; Holman 1989; Incropera and Dewitt 1990; Sukhatme 1992). The three modes of heat transfer are:

1. conduction
2. convection and
3. radiation.

The conduction mode of heat transport occurs either because of an exchange of energy from one molecule to another without actual motion of the molecules, or is due to the motion of free electrons if they are present. Therefore, this form of heat transport depends heavily on the properties of the medium and takes place in solids, liquids and gases if a difference in temperature exists.

Molecules present in liquids and gases have freedom of motion and by moving from a hot to a cold region, they carry energy with them. The transfer of heat from one region to another due to such macroscopic motion in a liquid or gas, added to the energy transfer by conduction within the fluid, is called heat transfer by convection. Convection may be either free, forced or mixed. When fluid motion occurs due to a density variation caused by temperature differences, the situation is said to be a free or natural convection. When the fluid motion is caused by an external force, such as pumping or blowing, the state is defined as being forced convection. A mixed convection state is one in which both natural and forced convection are present. Convection heat transfer also occurs in boiling and condensation processes.

All bodies emit thermal radiation at all temperatures. This is the only mode which does not require a material medium for heat transfer to occur. The nature of thermal radiation is such that a propagation of energy, carried by electromagnetic waves, is emitted from the surface of the body. When these electromagnetic waves strike other body surfaces, a part is reflected, a part transmitted and the remaining part is absorbed.

All modes of heat transfer are generally present in varying degrees in a real physical problem. The important aspects in solving heat transfer problems are to identify the significant modes and to decide whether the heat transferred by other modes can be neglected.

1.3 The Laws of Heat Transfer

It is important to quantify the amount of energy being transferred per unit time and for that we require the use of rate equations. For heat conduction, the rate equation is known as Fourier’s law (Fourier 1955) which is expressed for one dimension, as

(1.1)

where qx is the heat flux in the x direction (W/m2); k is the thermal conductivity (W/mK, a property of the material, see Table 1.1) and dT/dx the temperature gradient (K/m).

Table 1.1 Typical values of thermal conductivity of some materials in W/mK at 20 °C.

Material

Thermal conductivity, k

Metals:

Pure silver

410

Pure copper

385

Pure aluminium

200

Pure iron

73

Alloys:

Stainless steel (18% Cr, 8% Ni)

16

Aluminium alloy (4.5% Cr)

168

Non metals:

Plastics

0.6

Wood

0.2

Liquid:

Water

0.6

Gasses:

Dry air

0.025 (at atmospheric pressure)

For convective heat transfer, the rate equation is given by Newton’s law of cooling (Whewell 1866) as

(1.2)

where q is the convective heat flux; (W/m2); (Tw − Ta) the temperature difference between the wall and the fluid and h is the convection heat transfer coefficient (W/m2K) (or film coefficient, see Table 1.2).

The convection heat transfer coefficient frequently appears as a boundary condition in the solution of heat conduction through solids, where h is often known (Table 1.2).

Table 1.2 Typical values of heat transfer coefficient in W/m2K

Gases (stagnant)

15

Gases (flowing)

15–250

Liquids (stagnant)

100

Liquids (flowing)

100–2000

Boiling liquids

2000–35 000

Condensing vapors

2000–25 000

The maximum flux that can be emitted by radiation from a black surface is given by the Stefan-Boltzmann Law (Boltzmann 1884; Stefan 1879), that is,

(1.3)

where q is the radiative heat flux...

Produkt-Details

• Erscheint lt. Verlag: 27.1.2016
• Reihe/Serie: Wiley Series in Computational Mechanics
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Energie • Energietechnik • Energy • Maschinenbau • Materials Science • Materialwissenschaften • mechanical engineering • Power Technology & Power Engineering • thermodynamics • Thermodynamik
• ISBN-10: 1-118-53543-X / 111853543X
• ISBN-13: 978-1-118-53543-1 / 9781118535431