Basics of Heat Transfer PDF

1 Chapter 1 Introduction to Heat Transfer Syllabus: Various modes of heat transfer, combined modes, conductivity and film coefficient of heat transfer, Thermal diffusivity, overall heat transfer coeff...

1 Chapter 1 Introduction to Heat Transfer Syllabus: Various modes of heat transfer, combined modes, conductivity and film coefficient of heat transfer, Thermal diffusivity, overall heat transfer coefficient, thermal resistance and conductance. Conduction: 1–1 HEAT TRANSFER MECHANISMS Heat is a form of energy that can be transferred from one system to another as a result of temperature difference. A thermodynamic analysis is concerned with the amount of heat transfer as a system undergoes a process from one equilibrium state to another. The science that deals with the determination of the rates of such energy transfers is the heat transfer. The transfer of energy as heat is always from the higher-temperature medium to the lower- temperature one, and heat transfer stops when the two mediums reach the same temperature. Heat can be transferred in three different modes: conduction, convection and radiation. All modes of heat transfer require the existence of a temperature difference, and all modes are from the high-temperature medium to a lower-temperature one. 1.2 CONDUCTION Conduction is the transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles. Conduction can take place in solids, liquids, or gases. In gases and liquids, conduction is due to the collisions and diffusion of the molecules during their random motion. In solids, it is due to the combination of vibrations of the molecules in a lattice and the energy transport by free electrons. A cold canned drink in a warm room, for example, eventually warms up to the room temperature as a result of heat transfer from the room to the drink through the aluminum can by conduction. The rate of heat conduction through a medium depends on the geometry of the medium, its thickness, and the material of the medium, as well as the temperature difference across the medium. We know that wrapping a hot water tank with glass wool (an insulating material) reduces the rate of heat loss from the tank. The thicker the insulation, the smaller the heat loss. We also know that a hot water tank will lose heat at a higher rate when the temperature of the room housing the tank is lowered. Further, the larger the tank, the larger the surface area and thus the rate of heat loss. Consider steady heat conduction through a large plane wall of thickness x = L and area A, as shown in Fig. 1.1. The temperature difference across the wall is  T = T1 − T2. Experiments have shown that the rate of heat transfer Q · through the wall is doubled when the temperature difference  T across the wall or the area A normal to the - Dr. K. V. Karanth, MIT Manipal -  2 direction of heat transfer is doubled, but is halved when the wall thickness L is doubled. Thus we conclude that the rate of heat conduction through a plane layer is proportional to the temperature difference across the layer and the heat transfer area, but is inversely proportional to the thickness of the layer. That is, Area  temperature difference Rate of heat conduction  thickness T −T T Q cond = − kA 1 2 = − kA x x Where the constant of proportionality k is the thermal conductivity of the material, which is a measure of the ability of a material to conduct heat (Fig. 1.2). In the limiting case of x →0, the equation above reduces to the differential form dT Q cond = − kA ------(1.1) dx Fig. 1.1 Fig. 1.2 Fig. 1.3 Which is called Fourier’s law of heat conduction after J. Fourier, who expressed it first in his heat transfer text in 1822? Here dT/dx is the temperature gradient, which is the slope of the temperature curve on a T-x diagram (the rate of change of T with x), at location x. The relation above indicates that the rate of heat conduction in a direction is proportional to the temperature gradient in that direction. Heat is conducted in the direction of decreasing temperature, and the temperature gradient becomes negative when temperature decreases with increasing x. The negative sign in Eq. 1.1 ensures that heat transfer in the positive x direction is a positive quantity. The heat transfer area A is always normal to the direction of heat transfer. For heat loss through a 5-m-long, 3-m-high, and 0.25-m-thick wall, for example, the heat transfer area is A= 15 m2. Note that the thickness of the wall has no effect on A (Fig. 1.3). - Dr. K. V. Karanth, MIT Manipal -  3 1.4 Thermal Conductivity We have seen that different materials store heat differently, and we have defined the property specific heat Cp as a measure of a material’s ability to store thermal energy. For example, Cp = 4.18 kJ/kg · °C for water and Cp = 0.45 kJ/kg · °C for iron at room temperature, which indicates that water can store almost 10 times the energy that iron can per unit mass. Likewise, the thermal conductivity k is a measure of a material’s ability to conduct heat. For example, k = 0.608 W/m · °C for water and k = 80.2 W/m · °C for iron at room temperature, which indicates that iron conducts heat more than 100 times faster than water can. Thus we say that water is a poor heat conductor relative to iron, although water is an excellent medium to store thermal energy. Equation 1.1 for the rate of conduction heat transfer under steady conditions can also be viewed as the defining equation for thermal conductivity. Thus the thermal conductivity of a material can be defined as the rate ofheat transfer through a unit thickness of the material per unit area per unit temperature difference. The thermal conductivity of a material is a measure of the ability of the material to conduct heat. Ahigh value for thermal conductivity indicates that the material is a good heat conductor, and a low value indicates that the material is a poor heat conductor or insulator. The thermal conductivities of some common materials at room temperature are given in Table 1–1. The thermal conductivity of pure copper at room temperature is k 401 W/m · °C, which indicates that a 1-m-thick copper wall will conduct heat at a rate of 401 W per m2 area per °C temperature difference across the wall. Note that materials such as copper and silver that are good electric conductors are also good heat conductors, and have high values of thermal conductivity. Fig. 1.4 and 1.5 shows the thermal conductivity of various materials. Table 1 Material K Diamond 2300 Silver 429 Copper 401 Gold 317 Aluminum 237 Iron 80.2 Mercury (l) 8.54 Glass 0.78 Brick 0.72 Water (l) 0.613 Wood (oak) 0.17 Helium (g) 0.152 Soft rubber 0.13 Glass fiber 0.043 Air (g) 0.026 - Dr. K. V. Karanth, MIT Manipal -  4 Temperature is a measure of the kinetic energies of the particles such as the molecules or atoms of a substance. In a liquid or gas, the kinetic energy of the molecules is due to their random translational motion as well as their vibrational and rotational motions. When two molecules possessing different kinetic energies collide, part of the kinetic energy of the more energetic (higher-temperature) molecule is transferred to the less energetic (lower temperature) molecule, much the same as when two elastic balls of the same mass at different velocities collide, part of the kinetic energy of the faster ball is transferred to the slower one. The higher the temperature, the faster the molecules move and the higher the number of such collisions, and the better the heat transfer. FIG. 1.4 The range of thermal conductivity of various materials at room temperature. - Dr. K. V. Karanth, MIT Manipal -  5 Fig. 1.5 The variation of the thermal conductivity of various solids, liquids, and gases with temperature 1.5 Thermal Diffusivity The term Cp, which is frequently encountered in heat transfer analysis, is called the heat capacity of a material. Both the specific heat Cp and the heat capacity  c p represent the heat storage capability of a material. But cp expresses it per unit mass whereas  C p expresses it per unit volume, as can be noticed from their units J/kg°C and J/m3°C, respectively. Another - Dr. K. V. Karanth, MIT Manipal -  6 material property that appears in the transient heat conduction analysis is the thermal diffusivity, which represents how fast heat diffuses through a material and is defined as heat concucted k = = heat stored cp Note that the thermal conductivity k represents how well a material conducts heat, and the heat capacity  c p represents how much energy a material stores per unit volume. Therefore, the thermal diffusivity of a material can be viewed as the ratio of the heat conducted through the material to the heat stored per unit volume. A material that has a high thermal conductivity or a low heat capacity will obviously have a large thermal diffusivity. The larger the thermal diffusivity, the faster the propagation of heat into the medium. A small value of thermal diffusivity means that heat is mostly absorbed by the material and a small amount of heat will be conducted further. 1.6 CONVECTION Convection is the mode of energy transfer between a solid surface and the adjacent liquid or gas that is in motion, and it involves the combined effects of conduction and fluid motion. The faster the fluid motion, the greater the convection heat transfer. In the absence of any bulk fluid motion, heat transfer between a solid surface and the adjacent fluid is by pure conduction. The presence of bulk motion of the fluid enhances the heat transfer between the solid surface and the fluid, but it also complicates the determination of heat transfer rate Consider the cooling of a hot block by blowing cool air over its top surface (Fig. 1–31). Energy is first transferred to the air layer adjacent to the block by conduction. This energy is then carried away from the surface by convection, that is, by the combined effects of conduction within the air that is due to random motion of air molecules and the bulk or macroscopic motion of the air that removes the heated air near the surface and replaces it by the cooler air. Fig. 1.6b The cooling of a boiled egg by forced and natural convection. Fig 1.6a Heat transfer from a hot surface to air by convection. - Dr. K. V. Karanth, MIT Manipal -  7 Convection is called forced convection if the fluid is forced to flow over the surface by external means such as a fan, pump, or the wind. In contrast, convection is called natural (or free) convection if the fluid motion is caused by buoyancy forces that are induced by density differences due to the variation of temperature in the fluid (Fig. 1–6a). For example, in the absence of a fan, heat transfer from the surface of the hot block in Fig. 1.6b will be by natural convection since any motion in the air in this case will be due to the rise of the warmer (and thus lighter) air near the surface and the fall of the cooler (and thus heavier) air to fill its place. Heat transfer between the block and the surrounding air will be by conduction if the temperature difference between the air and the block is not large enough to overcome the resistance of air to movement and thus to initiate natural convection currents. Heat transfer processes that involve change of phase of a fluid are also considered to be convection because of the fluid motion induced during the process, such as the rise of the vapor bubbles during boiling or the fall of the liquid droplets during condensation. Despite the complexity of convection, the rate of convection heat transfer is observed to be proportional to the temperature difference, and is conveniently expressed by Newton’s law of cooling as Qconv = hAs (Ts − T ) ------(1.6) where h is the convection heat transfer coefficient in W/m2 °C ·, As is the surface area through which convection heat transfer takes place, Ts is the surface temperature, and T is the temperature of the fluid sufficiently far from the surface. Note that at the surface, the fluid temperature equals the surface temperature of the solid. The convection heat transfer coefficient h is not a property of the fluid. It is an experimentally determined parameter whose value depends on all the variables influencing convection such as the surface geometry, the nature of fluid motion, the properties of the fluid, and the bulk fluid velocity. Typical values of h are given in Table 1.6. Some people do not consider convection to be a fundamental mechanism of heat transfer since it is essentially heat conduction in the presence of fluid motion. But we still need to give this combined phenomenon a name, unless we are willing to keep referring to it as “conduction with fluid motion.” Thus, it is practical to recognize convection as a separate heat transfer mechanism despite the valid arguments to the contrary. TABLE 1–6 Typical values of convection heat transfer coefficient Type of convection h, W/m2 °C Free convection of gases 2–25 Free convection of liquids 10–1000 Forced convection of gases 25–250 Forced convection of liquids 50–20,000 Boiling and condensation 2500–100,000 - Dr. K. V. Karanth, MIT Manipal -  8 1.7 RADIATION Radiation is the energy emitted by matter in the form of electromagnetic waves (or photons) as a result of the changes in the electronic configurations of the atoms or molecules. Unlike conduction and convection, the transfer of energy by radiation does not require the presence of an intervening medium. In fact, energy transfer by radiation is fastest (at the speed of light) and it suffers no attenuation in a vacuum. This is how the energy of the sun reaches the earth. In heat transfer studies we are interested in thermal radiation, which is the form of radiation emitted by bodies because of their temperature. It differs from other forms of electromagnetic radiation such as x-rays, gamma rays, microwaves, radio waves, and television waves that are not related to temperature. All bodies at a temperature above absolute zero emit thermal radiation. Radiation is a volumetric phenomenon, and all solids, liquids, and gases emit, absorb, or transmit radiation to varying degrees. However, radiation is usually considered to be a surface phenomenon for solids that are opaque to thermal radiation such as metals, wood, and rocks since the radiation emitted by the interior regions of such material can never reach the surface, and the radiation incident on such bodies is usually absorbed within a few microns from the surface. The maximum rate of radiation that can be emitted from a surface at an absolute temperature Ts (in K or R) is given by the Stefan–Boltzmann law as Qemit max =  AsTs4 ------1.7 Where,  = 5.67  10 −8W / m 2 K 4 is the Stefan–Boltzmann constant. The idealized surface that emits radiation at this maximum rate is called a blackbody, and the radiation emitted by a blackbody is called black body radiation. The radiation emitted by all real surfaces is less than the radiation emitted by a blackbody at the same temperature, and is expressed as Qemit =  AsTs4 Where,  is the emissivity of the surface. The property emissivity, whose value is in the range 0    1 is a measure of how closely a surface approximates a blackbody for which  =1. The emissivities of some surfaces are given in Table 1.7. Another important radiation property of a surface is its absorptivity  which is the fraction of the radiation energy incident on a surface that is absorbed by the surface. Like emissivity, its value is in the range 0    1. A blackbody absorbs the entire radiation incident on it. That is, a blackbody is a perfect absorber ( = 1) as it is a perfect emitter. In general, both  and  of a surface depend on the temperature and the wavelength of the radiation. Kirchhoff’s law of radiation states that the emissivity and the absorptivity of a surface at a given temperature and wavelength are equal. In many practical applications, the surface temperature and the temperature of the source of - Dr. K. V. Karanth, MIT Manipal -  9 incident radiation are of the same order of magnitude, and the average absorptivity of a surface is taken to be equal to its average emissivity. Table 1.7 Emissivities of some materials at 300 K Material Emissivity Aluminum foil 0.07 Anodized aluminum 0.82 Polished copper 0.03 Polished gold 0.03 Polished silver 0.02 polished stainless steel 0.17 Black paint 0.98 White paint 0.90 White paper 0.92–0.97 Red brick 0.93–0.96 Wood 0.82–0.92 Water 0.96 Vegetation 0.92–0.96 Reference: Y. A. Cengel, A. J. Ghair, Heat & Mass Transfer: A Practical Approach, McGraw-Hill Education (India) Pvt Limited, 2007. ISBN, 007063453X..4th edition. R.K. Rajput, Heat and Mass Transfer, S. Chand, New Delhi, 2007. 7. - Dr. K. V. Karanth, MIT Manipal -