459 Chapter 18 Engineering Fundamentals: Part 3 Heat Transfer 18.1 Introduction This chapter presents a basic overview of heat transfer fundamentals, particularly as they apply to HVAC. For a detailed, rigorous treat- ment, the reader should refer to a good college-level text on heat trans- fer or to the ASHRAE Handbook. 1 18.2 Heat Transfer Modes Heat is transferred between any two bodies by one or more of three modes: conduction, convection, and radiation. Thermal conduction re- fers to the direct transfer of energy between particles at the atomic level. Thermal convection may include some conduction but refers pri- marily to energy transfer by eddy mixing and diffusion, i.e., by fluids in motion. Thermal radiation describes a complex phenomenon which includes changes in energy form: from internal energy at the source to electromagnetic energy for transmission, then back to internal en- ergy at the receiver. Radiation transfer requires no intervening ma- terial, and in fact works best in a perfect vacuum. In accordance with the second law of thermodynamics, net heat transfer occurs in the direction of decreasing temperature. In this text, the Fahrenheit (ЊF) scale is used, or for absolute temperatures the Rankine (ЊR) scale: ЊR ϭ ЊF ϩ 460Њ. Source: HVAC Systems Design Handbook Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 460 Chapter Eighteen Figure 18.1 Conduction heat transfer through a wall. 18.3 Thermal Conduction For steady-state conduction in one direction through a homogeneous material, the Fourier equation applies: q ϭϪkA dt/dx (18.1) where q ϭ heat transfer rate, Btu/h k ϭ thermal conductivity, Btu/(h ⅐ ft ⅐ ЊF) A ϭ area normal to flow, ft 2 dt/dx ϭ temperature gradient, ЊF/ft The minus sign shows that heat flow takes place from a higher to a lower temperature. In HVAC calculations, homogeneous barriers are never encount- ered—even when the solid barrier is homogeneous, there will be film resistance at its surface, as shown in Fig. 18.1. The heat transfer equa- tion is then modified as follows: q ϭ UA(T Ϫ T ) (18.2) 12 where U is the overall coefficient of heat transfer per degree of tem- perature difference between the two fluids which are separated by the barrier. Usually, but not always, U is given in Btu per hour per square foot per degree Fahrenheit. The temperatures and the area A must be in units consistent with those of U. Various building materials and combinations thereof have been tested to determine the conductivity k (Btu per hour per square foot per inch or foot of thickness per degree Fahrenheit) or conductance C (for a nonhomogeneous material such as a concrete block, in Btu per hour per square foot per degree Fahrenheit). The tests are made in a Engineering Fundamentals: Part 3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Engineering Fundamentals: Part 3 461 ‘‘guarded hot box,’’ designed so that heat transfer through the edges of the material is essentially eliminated. The results of these tests are tabulated and presented, with discussion, in the ASHRAE Handbook. 2 The thermal conductivity k of any material is the reciprocal of its resistance R: 1 k ϭ (18.3) R For barriers with material combinations which are not tabulated, the U factor may be calculated from the sum of the individual resistances. The general form of the equation is 1 ϭ R ϩ R ϩ R ϩ ⅐⅐⅐ϩ R (18.4) 123 n U Because resistance is the reciprocal of conductance or conductivity, a more specific form of the equation is 11xx111 1 n ϭϩ ϩ⅐⅐⅐ϩϩ ϩ⅐⅐⅐ϩϩ (18.5) Uf k k C C f o 1 n 1 ni where f o ϭ outside film conductance f i ϭ inside film conductance x ϭ thickness of homogeneous section with conductivity k See Ref. 2 for a more detailed discussion. The incremental tempera- ture drop through each element of the barrier is proportional to the resistance of the element. For example, in Fig. 18.1 if the wall is 6-in- thick perlite concrete with a k value of 0.93 per inch, and if the outside and inside film conductances are 4.00 and 1.46, respectively, then the overall U factor is 1161 ϭϩϩ U 4.00 0.93 1.46 ϭ 0.25 ϩ 6.45 ϩ 0.68 ϭ 7.38 1 U ϭϭ0.136 7.38 If a temperature difference of 42ЊF is assumed, based on 72ЊF inside and 30ЊF outside, then the temperature gradient can be determined as shown in Table 18.1. This type of calculation is useful in determin- ing the location where moisture condensation or freezing will take Engineering Fundamentals: Part 3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 462 Chapter Eighteen TABLE 18.1 Temperature Gradient Information place, such as on inside window surfaces. To avoid problems, extra insulation, double glazing, or surface heating may then be used. In HVAC practice, steady-state conduction seldom, if ever, takes place, because the outside air temperature and inside load conditions are constantly changing. The transient heat flow effects which result are functions of several variables, including the mass (storage effect) of the barrier. The sensible heat gain and cooling load factors dis- cussed in Chap. 3 are approximations which allow the designer to compensate for these transients. 18.4 Thermal Convection Thermal convection refers to heat transfer by eddy mixing and diffu- sion, as in a flowing airstream. In the typical airstream heating or cooling process, heat transfer takes place as a result of mixing with, and diffusion through, the air in the conditioned space. The final transfer is by conduction between air particles. Convection may be natural or free convection, due to differences in density, or it may be forced by mechanical means such as fans or pumps. An HVAC process illustrating almost pure convective heat transfer is the mixing of two airstreams such as return air and outside air. If complete mixing takes place, the mixed airstream has a temperature (and humidity) resulting from a weighed average of the properties and masses of the two original air-streams. This is a result of convective eddy mixing and diffusion plus conductive heat transfer between par- ticles. A major HVAC application involving a combination of convection and conduction is heat exchange between two fluids such as refriger- ant, water, steam, brine, and air, in many combinations. In general, the two fluids are separated by a barrier, usually the wall of a tube or pipe. Typical examples are the shell-and-tube heat exchanger (see Fig. Engineering Fundamentals: Part 3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Engineering Fundamentals: Part 3 463 Figure 18.2 Heat transfer through a tube wall. Figure 18.3 Velocity pattern for fluid flow in a conduit. 9.10) and the finned coil (see Fig. 9.20). In both cases, the barrier is a tube wall, as in Fig. 18.2. Heat transfer takes place within each fluid stream by convection, then by conduction through the wall and the contiguous films. The velocity of a fluid stream flowing uniformly in a conduit (tube or duct) is greatest at the center of the conduit and least near the edges (Fig. 18.3). This is due to friction of the fluid particles against the wall and against each other. The films of nearly motionless fluids on each side of the wall resist heat transfer, as noted above. Because the tubes in heat exchangers are usually copper, with its high conductivity factor, the films provide the major part of the resistance. Additional resistance is provided by the buildup of dirt, oil, or solids deposition on the tube surface. This is known as the fouling factor, and it is usually significant. The film resistance is a function of the fluid velocity, being highest with laminar flow and lowest with turbulent flow. To estimate the degree of turbulence in a system, the Reynolds number Re is calcu- lated: DV ␳ Re ϭ (18.6) ␮ where D ϭ conduit diameter, ft V ϭ average fluid velocity, ft/s ␮ ϭ fluid viscosity, lb/(ft ⅐ s) ␳ ϭ density, lb/ft 3 The transition value of the Reynolds number is in the range of 2100 Engineering Fundamentals: Part 3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 464 Chapter Eighteen to 3100. Below 2100 flow is assumed to be laminar. Above 3100 tur- bulence is assumed. Between 2100 and 3100 it may be either, depend- ing on various factors such as the roughness of the conduit. From the equation it is evident that laminar flow is equated with low velocities and high viscosities—i.e., other conditions being equal, oil will have a lower Reynolds number than water. The overall heat transfer rate in- creases abruptly as flow changes from laminar to turbulent. For a finned-coil fluid-to-air heat exchanger, the general equation for heat transfer is Q ϭ kA ϫ ROWS ϫ MED (18.7) where Q ϭ total heat transfer, Btu/h k ϭ heat transfer coefficient per row per square foot A ϭ face area of coil normal to airflow direction ROWS ϭ number of rows of tubes in direction of airflow MED ϭ mean temperature difference For a discussion and derivation of MED, see Sec. 9.7.2. The value of k is greatly increased if steam or refrigerant is used in the coil; the effect of two-phase boiling or condensing is to increase the value of k over that obtained with single-phase flow. For a shell-and-tube fluid-to-fluid heat exchanger, the equation for heat transfer is Q ϭ kA(MED) (18.8) where k ϭ heat transfer coefficient per square foot per degree Fah- renheit and A ϭ total outside surface area of tubing in square feet. Again, two-phase flow increases the value of k. In Eqs. (18.7) and (18.8), the value of k must include the film and fouling factors. The heat exchanger manufacturer can provide values of k for a range of flow rates and fouling factors. 18.5 Thermal Radiation Radiation heat transfer between two bodies takes place directly, by using electromagnetic energy across the intervening space. It is most efficient through a vacuum, because any intervening medium, even if transparent in the visible spectrum, will absorb some of the radiant energy. Several mechanisms are at work in radiant energy transfer, such as surface emittance and absorptance, absolute temperature differences, and geometry. Engineering Fundamentals: Part 3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Engineering Fundamentals: Part 3 465 18.5.1 Emittance, absorptance, reflectance, and transmittance These terms describe properties of material surfaces as they relate to radiant heat transfer. A perfect blackbody absorbs all energy received and is said to have an absorptance of 1.0. This blackbody will also have an emittance of 1.0. (Blackbody is not a color description.) A perfect reflecting surface has a reflectance of 1.0 and absorbs none of the energy received. Not all the radiant energy received by a surface is reradiated, because some energy may be stored in the material, transmitted through it by conduction, or lost by convection. Transmittance describes the ability of a body to allow some of (or all) the radiant energy impinging on it to pass through without being absorbed or reflected; this property is often called transparency or translucence, when it is related to the visible spectrum. An opaque body has zero transmittance. Values of these properties for various materials and surface finishes are published in heat transfer textbooks and manufacturers’ litera- ture, in addition to the ASHRAE Handbook. 1,2,4 Painted surfaces in general have high emittances, regardless of color, ranging from 0.85 to 0.95, although metallic paints range from 0.40 to 0.60. Many sur- faces that appear highly reflective have fairly high emittances. Win- dow glass, which is highly transparent, can have a high absorptance and emittance. For all surfaces, the emittance varies with the angle at which energy impinges on the surface, being greatest when that angle is 90Њ. 18.5.2 Radiant energy transfer Radiant energy is transferred between two surfaces which can ‘‘see’’ each other and are at different temperatures. One theory holds that radiant energy transfer takes place continually in both directions but that the two heat flows are equal at equal surface temperatures. One general equation for the net radiant heat transfer between two sur- faces is 44 Q ϭ ␴ FFA(T Ϫ T ) (18.9) eA11 2 where Q ϭ net heat transfer, Btu/h ␴ ϭ Stefan-Boltzmann constant ϭ 0.173 ϫ 10 Ϫ8 [Btu/(h ⅐ ft 2 ⅐ ЊF)] F e ϭ factor to correct for surface emittances not being equal to 1.0 F A ϭ factor to correct for geometric relationship of surfaces (F A ϭ 1.0 if surfaces face each other directly) Engineering Fundamentals: Part 3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 466 Chapter Eighteen Figure 18.4 Solar spectral irradiation at sea level for air mass 1.0. ( SOURCE : Copyright 1999, American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc., www.ashrae.org. Reprinted by permission from ASHRAE Handbook, 1999 HVAC Ap- plications, Chap. 32, Fig. 3.) A 1 ϭ face area of smaller surface, ft 2 T 1 , T 2 ϭ absolute (Rankine) temperatures of two surfaces The absolute temperature difference is a major factor in radiant trans- fer. Most of the radiant energy transfer takes place within the spectrum defined by wavelengths from 0.3 to 1.4 ␮ m. Visible light ranges from 0.4- to 0.7- ␮ m wavelength. The solar irradiation spectrum is shown in Fig. 18.4. The areas of primary concern in HVAC use are solar energy effects, discussed in Sec. 10.18, and the mean radiant temperature (MRT). The MRT is a weighed average of all the surface temperatures surrounding and within a space, including people. A high value of MRT can cause discomfort even at a low air temperature. Very hot manufacturing processes and crowds of people are extreme examples. 18.6 Latent Heat and Moisture Heat transfer due to condensation or evaporation may be considered a special form of convection. There is an important distinction. Heat transfer by conduction, convection, and radiation requires a temper- ature difference and is called sensible heat transfer. The processes of condensation and evaporation involve a change of state of a fluid at constant temperature, with heat added for evaporation or removed for condensation. This heat energy is called latent heat. In HVAC, the fluids used are water and refrigerants. Water is sometimes used as a refrigerant. Moisture (water vapor) migration occurs through building construc- tion materials in a manner similar to sensible heat transfer. The rate Engineering Fundamentals: Part 3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Engineering Fundamentals: Part 3 467 of moisture migration is a function of the permeability of the barrier and the difference in vapor pressure across the barrier. The vapor pressure is related to the temperature and relative humidity (RH) of the air. Vapor pressures for saturated air (100 percent RH) are shown in Table 1 of Ref. 3, from which Table 19.1 of this book is abstracted. For example, the vapor pressure at 70ЊF, saturated, is 0.73966 inHg (inches of mercury). At 50 percent saturation it would be half of that amount. Note that vapor pressure is a function of temperature only, and at a given temperature and relative humidity, the vapor pressure is the same at any altitude or total atmospheric pressure. Moisture sources of importance in HVAC are migration through building construction, moisture brought in by ventilation air, and moisture generated by people and processes within the building. In general, vapor pressures will be higher at higher temperatures. To avoid problems, the moisture barrier should be on the warm side of the thermal barrier. When the air temperature on one side is below freezing, as in winter heating or a cold storage freezer, moisture mi- gration into the barrier can result in condensation and freezing within the barrier, leading to damage or destruction of the barrier. Even small breaks, such as staple holes, in a moisture barrier can render it in- effective. In a similar way, insulation on chilled water piping may be rendered ineffective if its covering does not form a good vapor barrier. 18.7 Summary As noted in earlier chapters, the entire heating and air conditioning process is a series of fluid mechanics, thermodynamics, and heat transfer processes where energy is moved from one place to another. All three heat transfer mechanisms, conduction, convection, and ra- diation, are involved in nearly every system. All heat transfer is a function of a temperature difference between two points or entities. Conduction and convection are first-order functions of temperature (T 1 Ϫ T 2 ) while radiation is a fourth-order function Ϫ Heat 44 (TT). 12 transfer by evaporation and condensation of moisture creates addi- tional design issues which must be addressed by the HVAC system designer. References 1. ASHRAE Handbook, 2001 Fundamentals, Chap. 3, ‘‘Heat Transfer.’’ 2. Ibid., Chap. 25, ‘‘Thermal and Water Vapor Transmission Data.’’ 3. Ibid., Chap. 6, ‘‘Psychrometrics.’’ 4. Ibid., Chap. 30, ‘‘Fenestration.’’ Engineering Fundamentals: Part 3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Engineering Fundamentals: Part 3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. . Chapter 18 Engineering Fundamentals: Part 3 Heat Transfer 18. 1 Introduction This chapter presents a basic overview of heat transfer fundamentals, particularly. absolute temperatures the Rankine (ЊR) scale: ЊR ϭ ЊF ϩ 460Њ. Source: HVAC Systems Design Handbook Downloaded from Digital Engineering Library @ McGraw-Hill