Thermal Conductivity

11 Key excerpts on "Thermal Conductivity"

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  eBook - ePub

  Green Nanomaterials in Energy Conversion and Storage Applications

  • Ishani Chakrabartty, Khalid Rehman Hakeem, Ishani Chakrabartty, Khalid Rehman Hakeem(Authors)
  • 2024(Publication Date)
  • Apple Academic Press

    (Publisher)

  38 Therefore, the first and foremost confrontation in the current need for developments is to produce more unique green nanomaterials and devices with numerous utilizations, in the fields of medicine and electronics, etc. The influential green concept in nano-scale materials has admired immense consideration that delivers uniqueness against the traditional approach. Apart from the different processes or methodology of nanomaterials synthesis and applications, the green nanomaterials are defined as materials derived from the different bioresources, hence the term “Green.” Currently, green nanotechnology research specifically involves nanomaterial preparation from green resources, appropriate characterization for potential use in biomedical sector, micro-electronics, agribiotechnology, space science, energy, computer technology, and the environment. The modifications in the properties of nanomaterials are growing area for researchers to adopt them for utilizing in various fields.

  8.2 Thermal Conductivity of Materials: Background

  Heat and temperature are very routine and frequently used terminologies in day-to-day life, which are directly associated with thermal energy. The microscopic vibrations of particles are called thermal energy. Heat is directly related to Thermal Conductivity. The measurement of a material’s ability to conduct or transfer heat is called Thermal Conductivity which determines its working temperature and the development of effective heating/cooling properties. Another definition of Thermal Conductivity is the rate of heat transferred by conduction through a unit cross-section area of a material when a temperature gradient exists perpendicular to the area.42 It is generally denoted by the symbol “k” or sometimes λ. Every individual material has its particular conducting capacity and heat transfer. The Thermal Conductivity of a material is explained by the following formula:

  K = Qd / AΔT

  • K = the Thermal Conductivity in Watt m−1 K−1
  • Q = heat transferred quantity through the material in Joules/second or Watts
  • d = the distance between the two isothermal planes
  • A = surface area in square meters
  • ΔT = the difference in temperature (Thot −Tcold )

  The Thermal Conductivity of materials can be measured by two popular methods like Steady State Method (with constant temperature; Searle’s bar method and Lee’s dice method) and Transient State Method (with varied temperature; Plane source method, transient line source method, and laser flash method). The Thermal Conductivity of a material or element is a crucial property and can be calculated by scaling the rate of heat passed through a material. Most of the electronic applications that depend on heat (flow) extractions may require advanced material with specific Thermal Conductivity. The metals possess free electrons which carry heat/change to determine their Thermal Conductivity. Cooling of microelectronics and high-voltage devices is an important technical challenge. High Thermal Conductivity material can be utilized to increase cooling rates with various applications in integrated circuits, optoelectronics, and power plant industries.34

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  Nanomaterials, Nanotechnologies and Design

  An Introduction for Engineers and Architects

  • Daniel L. Schodek, Paulo Ferreira, Michael F. Ashby(Authors)
  • 2009(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  In products, attention is invariably directed toward the way heat or extreme temperature differentials affect the design of the product and to assure that the product effectively continues to provide its intended role. In some cases, the surrounding environment might have extremes—especially high or low temperatures. Maintaining the functioning of a product in an extreme environment is not always an easy task, especially since many of the mechanical properties of materials, including strength and stiffness, are temperature dependent. In other cases, the role of a product might necessitate the inclusion of components that generate heat, which in turn must be managed. Often there must be components that mitigate heat transfer, provide cooling functions, or otherwise provide this heat management. In these design situations, the intrinsic thermal properties of materials are of fundamental importance. Heat affects not only mechanical properties but electrical and optical properties as well (see the following discussion).

  Basic Heat Transfer

  In designing both types of thermal environments we’ve outlined, the fundamental means of heat transfer—conduction, convection, radiation—are of intrinsic importance (see Figure 9.9 ) as are the intrinsic thermal properties of materials. Chapter 4 addressed thermal properties in detail. Here we only briefly summarize salient issues to put the following discussions into context.

  Figure 9.9 Basic heat-transfer mechanisms.

  Heat is a form of energy associated with molecules in motion. Conductive heat transfer takes place in solids because of temperature differences between various parts of the solid. Thermal energy is transferred from hotter to lower regions via vibrations of adjacent molecules or the movement of free electrons through the material. Metals, with many free electrons, are good conductors of heat. Convective heat transfer takes place in a fluid (gas or liquid) through molecular motion and the circulation of currents. It can be divided into natural convection and forced convection. Natural convection is driven by the temperature gradients that cause density gradients in gases or fluids, and as a result of these phenomena, buoyancy forces occur and cause fluid movements. Forced convection is caused by the some external force (e.g., a fan or pump). Radiation is a flow of thermal energy from one source to another in the form of electromagnetic waves and does not depend on a specific medium of transfer.

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  Infrared Thermal Imaging

  Fundamentals, Research and Applications

  • Michael Vollmer, Klaus-Peter Möllmann(Authors)
  • 2017(Publication Date)
  • Wiley-VCH

    (Publisher)

  heat flow. In physics, one usually distinguishes three kinds of heat flow: conduction, convection, and radiation. As a matter of fact, the underlying physical processes for conduction and convection are very similar, so the distinction is rather artificial.

  4.2.1 Conduction

  Conduction refers to the heat flow in a solid or fluid (liquid or gas) that is at rest (Figure 4.2 ). Conduction of heat within an object, for example, a wall of infinitesimally small thickness ds, is usually assumed to be proportional to the temperature difference dT on the two sides of the object as well as the surface area A of the object, and inversely proportional to the thickness ds of the sample, that is,

  (4.1a )

  For the specific example of a macroscopic one-dimensional (1D) wall of thickness s = s1 − s2 , steady-state conduction leads to a temperature that varies linearly with distance. In this case,

  (4.1b )

  In what follows, we mostly refer to the simplified heat conduction equation . The heat transfer coefficient is defined as αcond = λ/s, where λ is the Thermal Conductivity of the wall material given in W (m K)–1 and s is the wall thickness given in meters. (Note that λ uses the same Greek symbol that is usually reserved for wavelength. Rather than introducing additional subindices that would unnecessarily complicate the notation, in particular when later a distinction between thermal conductivities for different materials – indicated by subindices – will be made, we will stick with the same symbol since the context of the corresponding equations will usually make it clear which quantity – wavelength or Thermal Conductivity – is meant.) The heat transfer coefficient αcond describes heat transfer in watts per unit area and Kelvin, that is, W (m2 K)–1 . Hence, the heat flux through the wall in watts gives the energy flow per second through the wall of surface area A if the temperature difference between the inner and outer surfaces is given. Table 4.1 gives typical values of thermal conductivities of materials as well as their corresponding heat transfer coefficients for s

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  eBook - ePub

  Heat Transfer

  A Problem Solving Approach

  • Kubie Jorge, Tariq Muneer, Grassie Thomas(Authors)
  • 2012(Publication Date)
  • Routledge

    (Publisher)

  ∞ , but for external flows past solid bodies it can be closely approximated by the free stream temperature. Additionally, the heat transfer coefficient may not be easily determined and may not necessarily be constant. However, even with these limitations, this is a very versatile boundary condition.

  3.4 Thermophysical properties

  Several important properties required for the analysis of conduction heat transfer have been already introduced: Thermal Conductivity k , density ρ , and specific heat c . These properties, together with additional properties discussed below, are collectively known as thermophysical properties . Two categories of thermophysical properties are generally considered: (i) transport properties and (ii) thermodynamic properties .

  Transport properties govern the rates of transfer of energy, momentum, and mass. For example, Thermal Conductivity k controls the diffusion rate of heat transfer and kinematic viscosity ν controls the diffusion rate of momentum transfer.

  Thermodynamic properties describe the equilibrium state of a system. For example, density ρ and specific heat c are two such properties.

  These and other thermophysical properties are extensively discussed in many available textbooks (Brodkey and Hershey, 1988). The recommended values of the thermophysical properties are also generally available (Rohsenow and Hartnett, 1973; Perry, 1998). Property tables for a selection of materials are provided in appendices to this book.

  3.5 The plane wall

  3.5.1 Introduction

  We consider one-dimensional steady-state conduction in a plane wall, as shown in Fig. 3.5.1 . The general heat diffusion Eq. (3.2.7) reduces to

  and this must be solved, subject to suitable boundary conditions. Equation (3.5.1)

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  Understanding Physics

  • Michael M. Mansfield, Colm O'Sullivan(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  The rate of heat energy flow through the area ΔA, indicated in the figure, will be proportional to ΔA and to the temperature gradient, that is. Thus, the power transferred per unit area is given by (11.7) Figure 11.6 Heat conduction in a solid. The coloured dashed lines represent surfaces of constant temperature and the flow of heat energy is perpendicular to these surfaces. The rate of flow of energy is proportional to the temperature gradient. where the constant λ is characteristic of the material and is called the Thermal Conductivity of the material. From this definition, the SI unit of Thermal Conductivity is seen to be W m −1 K −1. Returning now to the experiment illustrated in Figure 11.5, if the cross‐sectional area of the bar in the figure is A, then and the rate of heat energy flow through the bar (assuming that no heat flows out through the sides of the bar) is given by The heat flow rate could be measured, for example, by measuring the rise in temperature of water which is made to flow across the end of the bar to keep the temperature of the cold end fixed. After the experiment is first set up it will take a short period of time for the system to reach an equilibrium state but, once such steady state conditions have been reached, is constant and is given by so that Values of Thermal Conductivity of a range of substances can be determined using experimental arrangements which are variations of that shown in Figure 11.5. These experiments differ from one another only in the techniques used to measure. The thermal conductivities of some common substances are listed in Table 11.1. For problems based on the material presented in this section visit up.ucc.ie/11/ and follow the link to the problems. 11.6 Convection The density of most fluids decreases as the fluid is heated, a well‐known consequence being that hot air rises

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  Theory of Heat

  • (Author)
  • 2012(Publication Date)
  • Dover Publications

    (Publisher)

  Now, in the experimental bar the temperature of every part was known, and therefore the loss of heat from any given portion of the bar could be found by making use of the table. To determine the flow of heat across any particular section, it was necessary to sum up the loss of heat from all parts of the bar beyond this section, and when this was done, by comparing the flow of heat across the section with the rate of diminution of temperature per linear foot in the curve of temperature, the conductivity of the bar for the temperature of the section was ascertained. Principal Forbes found that the Thermal Conductivity of iron decreases as the temperature increases.

  The conductivity thus determined is expressed in terms of the quantity of heat required to raise unit of volume of the substance one degree. If we wish to express it in the ordinary way in terms of the thermal unit as defined with reference to water at its maximum density, we must multiply our result by the specific heat of the substance, and by its density ; for the quantity of heat required to raise unit of mass of the substance one degree is its specific heat, and the number of units of mass in unit of volume is the density of the substance.

  As long as we are occupied with questions relating to the diffusion of heat and the waves of temperature in a single substance, the quantity on which the phenomena depend is the thermometric conductivity expressed in terms of the substance itself; but whenever we have to do with the effects of the flow of heat upon other bodies, as in the case of boiler plates, steam-condensers, &c., we must use a definite thermal unit, and express the calorimetric conductivity in terms of it. It has been shown by Professor Tyndall that the wave of temperature travels faster in bismuth than in iron, though the conductivity of bismuth is much less than that of iron. The reason is that the thermal capacity of the iron is much greater than that of an equal volume of bismuth.

  Forbes was the first to remark that the order in which the metals follow one another m respect of Thermal Conductivity is nearly the same as their order as regards electric conductivity. This remark is an important one as regards certain metals, but it must not be pushed too far; for there are substances which are almost perfect insulators of electricity, whereas it is impossible to find a substance which will not transmit heat.

  The electric conductivity of metals diminishes as the temperature rises. The Thermal Conductivity of iron also diminishes, but in a smaller ratio, as the temperature rises.

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  Thermal Management Materials for Electronic Packaging

  Preparation, Characterization, and Devices

  • Xingyou Tian(Author)
  • 2023(Publication Date)
  • Wiley-VCH

    (Publisher)

  B is the Boltzmann constant. The law shows that the Thermal Conductivity of metal is proportional to the electrical conductivity.

  The law of electron heat conduction in metal changing with temperature is shown in Figure 1.4 . At very low temperatures, the electron Thermal Conductivity increases linearly with temperature; at medium temperatures, the electron Thermal Conductivity is almost constant and does not change with temperature; and at very high temperatures, the electron Thermal Conductivity decreases slightly with the increase in temperature.

  Figure. 1.4

  Relationship between metal Thermal Conductivity and temperature.

  1.3.2.2 Inorganic Nonmetals

  Crystal   In dielectric crystals, heat energy is transferred by lattice vibration. Therefore, the propagation of lattice waves is regarded as the movement of phonons. The scattering encountered by lattice waves in the crystal is regarded as the collision between phonons, phonons and grain boundaries, and lattice defects. The thermal resistance in an ideal crystal is attributed to the collision between phonons.

  According to Debye's assumption, by analogy with gases, it is considered that the mathematical expression of Thermal Conductivity in dielectric crystals should be the similar to that in gases. Therefore, the expression of phonon Thermal Conductivity can be expressed by

  (1.27)

  where 

  C

  vpn

  , , and are the volume heat capacity, average velocity, and average free path of phonons, respectively.

  According to the Klemens model, the lattice Thermal Conductivity of blocky solid is given by

  (1.28)

  where i is the index of phonons, v is the group velocity of phonons, τ is the relaxation time, and q is the wave vector.

  The curve of Thermal Conductivity of dielectric crystal changing with temperature is shown in Figure 1.5 [7] . At very low temperatures, the phonon‐specific heat capacity is proportional to T3 . It means that heat conduction of crystal increases proportionally with the third power of temperature [8] . At higher temperatures, on the one hand, the phonon heat capacity does not change with temperature and is close to a constant 3R. On the other hand, the mean free path of phonons decreases gradually with the increase in temperature, and the mean free path of phonons is inversely proportional to the temperature (

  l ∝ 1/T

  ). Therefore, the Thermal Conductivity of the dielectric crystal at a higher temperature decreases [9]

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  eBook - ePub

  Bioinspired Engineering of Thermal Materials

  • Tao Deng(Author)
  • 2018(Publication Date)
  • Wiley-VCH

    (Publisher)

  Heat transfer forms a vital kinetic force in the maintenance of the basic energy operation of the whole natural system for the activities of all the creatures on earth. As an engineering discipline, the inherent laws of heat transfer do not merely explain the way of energy transportation but also deal with the thermodynamics of both objects and the equilibrium principle under specified conditions. Fundamental learning of the equilibrium principle is provided by the first and second laws of thermodynamics, and follows the classic mechanics of conduction, convection, and radiation. In the following sections, the conduction, convection, and radiation of macroscale heat transfer problems will be shown and the working principles formulated by energy equations. In thermal physics and engineering problems, we use critical quantitative criteria to characterize the thermal properties of material. These thermal properties are modified as representations of thermal energy transportation and energy conservation models, and can be used to analytically or numerically solve problems in thermal engineering and nature. Therefore, in the following sections, the basic principles of thermal transfer will be introduced first through a discussion of the thermal energy transportation and energy conservation models.

  1.1.1 Normalization

  To describe the process of heat transfer based on quantitative criteria, the primary quantities involved in a thermal process are listed in Table 1.1 and the quantitative criteria of thermal process are derived by these basic units. For analyzing much more complicated situations, the units of some derived quantities in Table 1.2 are defined as scientific descriptions of thermal properties of materials. Especially in numerical calculations and study of material heat transfer models, these derived units such as specific heat capacity C

  p

  , Thermal Conductivity κ, heat flux q and thermal diffusivity α in thermodynamics cases will facilitate the systematic learning and understanding of the details of heat transfer.

  Table 1.1

  Basic parameter units

  Primary quantity	Parameter
  Length	L (m)
  Time	t (s)
  Mass	m (kg)
  Temperature	T (°C or K)
  Current	Je (A)

  Table 1.2

  Parameter units driven by the primary quantities in Table 1.1

  Driven quantity	Parameter
  Specific heat capacity	C p (J/kg K)
  Energy	E (J or N m)
  Force	F (N m/s2 )
  Electric charge	C (coulomb or A s)
  Thermal Conductivity	k (W/m k)
  Pressure	p (Pa or N/m2

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  eBook - ePub

  Mechanical Engineering Exam Prep

  Problems and Solutions

  • Layla S. Mayboudi, S. Musa, PhD(Authors)
  • 2021(Publication Date)
  • Mercury Learning and Information

    (Publisher)

  As gas is heated, the molecules’ kinetic energy . . . ; temperature . . . ; frequency of intermolecular collisions . . . ; and the number of gas molecules . . . (a) increases / increases / increases / remains the same (b) increases / decreases / increases / remains the same (c) increases / increases / decrease / remains the same (d) decreases / increases / increases / decreases
• Thermal Conductivity shows how: (a) well a substance lets heat be transmitted (b) poorly a substance allows energy to accumulate (c) disruptive a barrier is to energy (d) restrictive current is
• A substance that does not allow heat to be easily transmitted is a(an): (a) thermal insulator (b) electrical insulator (c) insulator (d) energy insulator
• A substance that allows heat to easily flow through it is a(an): (a) insulator (b) combustor (c) conductor (d) acoustic absorber
• Radiation transfer can only take place between objects in a vacuum. (T/F)
• In convection heat transfer, the medium of energy transfer is: (a) a fluid (b) a solid (c) the vacuum (d) a gas
• In conduction heat transfer, the medium of energy transfer is: (a) a fluid (b) a solid (c) the vacuum (d) a gas
• In convection heat transfer, warmer fluid . . . and cooler fluid . . .